History.cc

// History.cc is a part of the PYTHIA event generator.
// Copyright (C) 2024 Torbjorn Sjostrand.
// PYTHIA is licenced under the GNU GPL v2 or later, see COPYING for details.
// Please respect the MCnet Guidelines, see GUIDELINES for details.

// This file is written by Stefan Prestel.
// Function definitions (not found in the header) for the
// Clustering and History classes.

#include "Pythia8/History.h"
#include "Pythia8/SharedPointers.h"

namespace Pythia8 {

//==========================================================================

// The Clustering class.

//--------------------------------------------------------------------------

// Declaration of Clustering class
// This class holds information about one radiator, recoiler,
// emitted system.
// This class is a container class for History class use.

// print for debug
void Clustering::list() const {
  cout << " emt " << emitted
       << " rad " << emittor
       << " rec " << recoiler
       << " partner " << partner
       << " pTscale " << pTscale << endl;
}

//==========================================================================

// The History class.

// A History object represents an event in a given step in the CKKW-L
// clustering procedure. It defines a tree-like recursive structure,
// where the root node represents the state with n jets as given by
// the matrix element generator, and is characterized by the member
// variable mother being null. The leaves on the tree corresponds to a
// fully clustered paths where the original n-jets has been clustered
// down to the Born-level state. Also states which cannot be clustered
// down to the Born-level are possible - these will be called
// incomplete. The leaves are characterized by the vector of children
// being empty.

//--------------------------------------------------------------------------

// Number of trial emission to use for calculating the average number of
// emissions
const int History::NTRIAL = 1;

//--------------------------------------------------------------------------

// Declaration of History class
// The only constructor. Default arguments are used when creating
// the initial history node. The \a depth is the maximum number of
// clusterings requested. \a scalein is the scale at which the \a
// statein was clustered (should be set to the merging scale for the
// initial history node. \a beamAIn and beamBIn are needed to
// calcutate PDF ratios, \a particleDataIn to have access to the
// correct masses of particles. If \a isOrdered is true, the previous
// clusterings has been ordered. \a is the PDF ratio for this
// clustering (=1 for FSR clusterings). \a probin is the accumulated
// probabilities for the previous clusterings, and \ mothin is the
// previous history node (null for the initial node).

History::History( int depthIn,
         double scalein,
         Event statein,
         Clustering c,
         MergingHooksPtr mergingHooksPtrIn,
         BeamParticle beamAIn,
         BeamParticle beamBIn,
         ParticleData* particleDataPtrIn,
         Info* infoPtrIn,
         PartonLevel* showersIn,
         CoupSM* coupSMPtrIn,
         bool isOrdered = true,
         bool isStronglyOrdered = true,
         bool isAllowed = true,
         bool isNextInInput = true,
         double probin = 1.0,
         History * mothin = 0)
    : state(statein),
      mother(mothin),
      selectedChild(-1),
      sumpath(0.0),
      sumGoodBranches(0.0),
      sumBadBranches(0.0),
      foundOrderedPath(false),
      foundStronglyOrderedPath(false),
      foundAllowedPath(false),
      foundCompletePath(false),
      scale(scalein),
      nextInInput(isNextInInput),
      prob(probin),
      clusterIn(c),
      iReclusteredOld(0),
      iReclusteredNew(),
      doInclude(true),
      mergingHooksPtr(mergingHooksPtrIn),
      beamA(beamAIn),
      beamB(beamBIn),
      particleDataPtr(particleDataPtrIn),
      infoPtr(infoPtrIn),
      loggerPtr(infoPtrIn->loggerPtr),
      showers(showersIn),
      coupSMPtr(coupSMPtrIn),
      probMaxSave(-1.),
      depth(depthIn),
      minDepthSave(-1)
    {

  // Initialise beam particles
  setupBeams();

  // Update probability with PDF ratio
  if (mother && mergingHooksPtr->includeRedundant()) prob *= pdfForSudakov();

  // Minimal scalar sum of pT used in Herwig to choose history
  // Keep track of scalar PT
  if (mother) {
    double acoll = (mother->state[clusterIn.emittor].isFinal())
                   ? mergingHooksPtr->herwigAcollFSR()
                   : mergingHooksPtr->herwigAcollISR();
    sumScalarPT = mother->sumScalarPT + acoll*scale;
  } else
    sumScalarPT = 0.0;

  // Remember reclustered radiator in lower multiplicity state
  if ( mother ) iReclusteredOld = mother->iReclusteredNew;

  // Check if more steps should be taken.
  int nFinalP = 0, nFinalW = 0, nFinalZ = 0;
  for ( int i = 0; i < int(state.size()); ++i )
    if ( state[i].isFinal() ) {
      if ( state[i].colType() != 0 )
        nFinalP++;
      if ( state[i].idAbs() == 23 )
        nFinalZ++;
      if ( state[i].idAbs() == 24 )
        nFinalW++;
    }
  if ( mergingHooksPtr->doWeakClustering()
    && nFinalP == 2 && nFinalW == 0 && nFinalZ == 0) depth = 0;

  // Stop clustering at 2->1 massive.
  // Stop clustering at 2->2 massless.

  bool qcd = ( nFinalP > mergingHooksPtr->hardProcess->nQuarksOut() );

  // If this is not the fully clustered state, try to find possible
  // QCD clusterings.
  vector<Clustering> clusterings;
  if ( qcd && depth > 0 ) clusterings = getAllQCDClusterings();

  bool dow = ( mergingHooksPtr->doWeakClustering()
    && nFinalP > 1 && nFinalW+nFinalZ > 0 );

  // If necessary, try to find possible EW clusterings.
  vector<Clustering> clusteringsEW;
  if ( depth > 0 && dow )
    clusteringsEW = getAllEWClusterings();
  if ( !clusteringsEW.empty() ) {
    clusterings.insert( clusterings.end(), clusteringsEW.begin(),
                        clusteringsEW.end() );
  }

  // If necessary, try to find possible SQCD clusterings.
  vector<Clustering> clusteringsSQCD;
  if ( depth > 0 && mergingHooksPtr->doSQCDClustering() )
    clusteringsSQCD = getAllSQCDClusterings();
  if ( !clusteringsSQCD.empty() )
    clusterings.insert( clusterings.end(), clusteringsSQCD.begin(),
                        clusteringsSQCD.end() );

  // If no clusterings were found, the recursion is done and we
  // register this node.
  if ( clusterings.empty() ) {
    // Multiply with hard process matrix element.
    prob *= hardProcessME(state);
    if (registerPath( *this, isOrdered, isStronglyOrdered, isAllowed,
      depth == 0 )) updateMinDepth(depth);
    return;
  }

  // We'll now order the clusterings in such a way that an ordered
  // history is found more rapidly. Following the branches with small pT is
  // a good heuristic, as is following ISR clusterings.
  multimap<double, Clustering *> sort;
  for (unsigned int i = 0; i < clusterings.size(); ++i) {
    double t = clusterings[i].pT();
    double index = t;
    //// This might be a marginally faster ordering.
    //double z = getCurrentZ(clusterings[i].emittor,
    //             clusterings[i].recoiler,
    //             clusterings[i].emitted,
    //             clusterings[i].flavRadBef);
    //double index = t/z;
    //if (!state[clusterings[i].emittor].isFinal())
    //  sort.insert(make_pair(-1./index, &clusterings[i]));
    //else
    //  sort.insert(make_pair(index, &clusterings[i]));
    sort.insert(make_pair(index, &clusterings[i]));
  }

  for ( multimap<double, Clustering *>::iterator it = sort.begin();
  it != sort.end(); ++it ) {

    double t = it->second->pT();
    // If this path is not strongly ordered and we already have found an
    // ordered path, then we don't need to continue along this path.
    bool stronglyOrdered = isStronglyOrdered;
    if ( mergingHooksPtr->enforceStrongOrdering()
      && ( !stronglyOrdered
         || ( mother && ( t <
                mergingHooksPtr->scaleSeparationFactor()*scale ) ))) {
      if ( onlyStronglyOrderedPaths()  ) continue;
      stronglyOrdered = false;
    }

    // Check if reclustering follows ordered sequence.
    bool ordered = isOrdered;
    if (  mergingHooksPtr->orderInRapidity()
      && mergingHooksPtr->orderHistories() ) {
      // Get new z value
      double z = getCurrentZ((*it->second).emittor,
                   (*it->second).recoiler,(*it->second).emitted,
                   (*it->second).flavRadBef);
      // Get z value of splitting that produced this state
      double zOld = (!mother) ? 0. : mother->getCurrentZ(clusterIn.emittor,
                       clusterIn.recoiler,clusterIn.emitted,
                       clusterIn.flavRadBef);
      // If this path is not ordered in pT and y, and we already have found
      // an ordered path, then we don't need to continue along this path.
      if ( !ordered || ( mother && (t < scale
         || t < pow(1. - z,2) / (z * (1. - zOld ))*scale ))) {
        if ( onlyOrderedPaths()  ) continue;
        ordered = false;
      }
    } else if ( mergingHooksPtr->orderHistories() ) {
      // If this path is not ordered in pT and we already have found an
      // ordered path, then we don't need to continue along this path, unless
      // we have not yet found an allowed path.
      if ( !ordered || ( mother && (t < scale) ) ) {
        if ( depth >= minDepth() && onlyOrderedPaths() && onlyAllowedPaths() )
          continue;
        ordered = false;
      }
    }

    // Check if reclustered state should be disallowed.
    bool doCut = mergingHooksPtr->canCutOnRecState()
              || mergingHooksPtr->allowCutOnRecState();
    bool allowed = isAllowed;
    if (  doCut
      && mergingHooksPtr->doCutOnRecState(cluster(*it->second)) ) {
      if ( onlyAllowedPaths()  ) continue;
      allowed = false;
    }

    // Skip if this branch is already strongly suppressed.
    double p = getProb(*it->second);
    if (abs(p)*prob < 1e-10*probMax()) continue;
    updateProbMax(abs(p)*prob,depth==0);

    // Skip clusterings with vanishing probability.
    if (p==0.) continue;

    // Create new state - already here, to catch errors when clustering.
    Event newState(cluster(*it->second));
    if (newState.size()<3) continue;

    // Perform the clustering and recurse and construct the next
    // history node.
    children.push_back(new History(depth - 1, t, newState,
           *it->second, mergingHooksPtr, beamA, beamB, particleDataPtr,
           infoPtr, showers, coupSMPtr, ordered, stronglyOrdered, allowed,
           true, prob*p, this ));
  }

}

//--------------------------------------------------------------------------

// Function to project all possible paths onto only the desired paths.

bool History::projectOntoDesiredHistories() {
  // At the moment, only trim histories.
  return trimHistories();
}

//--------------------------------------------------------------------------

// In the initial history node, select one of the paths according to
// the probabilities. This function should be called for the initial
// history node.
// IN  trialShower*    : Previously initialised trialShower object,
//                       to perform trial showering and as
//                       repository of pointers to initialise alphaS
//     PartonSystems* : PartonSystems object needed to initialise
//                      shower objects
// OUT double         : (Sukadov) , (alpha_S ratios) , (PDF ratios)

vector<double> History::weightCKKWL(PartonLevel* trial, AlphaStrong * asFSR,
  AlphaStrong * asISR, AlphaEM * aemFSR, AlphaEM * aemISR, double RN) {

  if ( mergingHooksPtr->canCutOnRecState() && !foundAllowedPath ) {
    loggerPtr->WARNING_MSG(
      "no allowed history found. Using disallowed history");
  }
  if ( mergingHooksPtr->orderHistories() && !foundOrderedPath ) {
    loggerPtr->WARNING_MSG(
      "no ordered history found. Using unordered history");
  }
  if ( mergingHooksPtr->canCutOnRecState()
    && mergingHooksPtr->orderHistories()
    && !foundAllowedPath && !foundOrderedPath ) {
    loggerPtr->WARNING_MSG("no allowed or ordered history found");
  }

  // Read alpha_S in ME calculation and maximal scale (eCM)
  double asME     = infoPtr->alphaS();
  double aemME    = infoPtr->alphaEM();
  double maxScale = (foundCompletePath) ? infoPtr->eCM()
                  : mergingHooksPtr->muFinME();

  // Select a path of clusterings
  History *  selected = select(RN);

  // Set scales in the states to the scales pythia would have set
  selected->setScalesInHistory();

  int nWgts = mergingHooksPtr->nWgts;
  // Get weight.
  vector<double> sudakov( nWgts, 1. );
  vector<double> asWeight( nWgts, 1. );
  vector<double> aemWeight( nWgts, 1. );
  vector<double> pdfWeight( nWgts, 1. );

  // Do trial shower, calculation of alpha_S ratios, PDF ratios
  sudakov  = selected->weightTree( trial, asME, aemME, maxScale,
    selected->clusterIn.pT(), asFSR, asISR, aemFSR, aemISR, asWeight,
    aemWeight, pdfWeight );

  // MPI no-emission probability
  int njetsMaxMPI = mergingHooksPtr->nMinMPI();
  vector<double> mpiwt = selected->weightTreeEmissions( trial, -1, 0,
      njetsMaxMPI, maxScale );

  // Set hard process renormalisation scale to default Pythia value.
  bool resetScales = mergingHooksPtr->resetHardQRen();

  // For pure QCD dijet events, evaluate the coupling of the hard process at
  // a more reasonable pT, rather than evaluation \alpha_s at a fixed
  // arbitrary scale.
  if ( resetScales
    && mergingHooksPtr->getProcessString().compare("pp>jj") == 0) {
    // Reset to a running coupling. Here we choose FSR for simplicity.
    double newQ2Ren = pow2( selected->hardRenScale(selected->state) );
    double runningCoupling = (*asFSR).alphaS(newQ2Ren) / asME;
    for (double& asW: asWeight) asW *= pow2(runningCoupling);
  } else if (isQCD2to2(selected->state)) {
    // Reset to a running coupling. Here we choose FSR for simplicity.
    double newQ2Ren = pow2( selected->hardRenScale(selected->state) );
    double runningCoupling = (*asFSR).alphaS(newQ2Ren) / asME;
    for (double& asW: asWeight) asW *= pow2(runningCoupling);
  }

  // For W clustering, correct the \alpha_em.
  if (isEW2to1(selected->state)) {
    // Reset to a running coupling. Here we choose FSR for simplicity.
    double newQ2Ren = pow2( selected->hardRenScale(selected->state) );
    double runningCoupling = (*aemFSR).alphaEM(newQ2Ren) / aemME;
    for (double& aemW: aemWeight) aemW *= runningCoupling;
  }

  // For prompt photon events, evaluate the coupling of the hard process at
  // a more reasonable pT, rather than evaluation \alpha_s at a fixed
  // arbitrary scale.
  if ( resetScales
    && mergingHooksPtr->getProcessString().compare("pp>aj") == 0) {
    // Reset to a running coupling. In prompt photon always ISR.
    double newQ2Ren = pow2( selected->hardRenScale(selected->state) );
    double runningCoupling =
      (*asISR).alphaS( newQ2Ren + pow(mergingHooksPtr->pT0ISR(),2) ) / asME;
    for (double& asW: asWeight) asW *= runningCoupling;
  }

  // Done
  vector<double> ret;
  for (int iVar = 0; iVar < nWgts; ++iVar)
    ret.push_back(sudakov[iVar]*asWeight[iVar]*aemWeight[iVar]*pdfWeight[iVar]*
        mpiwt[iVar]);
  return ret;

}

//--------------------------------------------------------------------------

// Function to return weight of virtual correction and subtractive events
// for NL3 merging

vector<double> History::weightNL3Loop(PartonLevel* trial, double RN ) {

  if ( mergingHooksPtr->canCutOnRecState() && !foundAllowedPath ) {
    loggerPtr->WARNING_MSG(
      "no allowed history found. Using disallowed history");
  }

  // Select a path of clusterings
  History *  selected = select(RN);
  // Set scales in the states to the scales pythia would have set
  selected->setScalesInHistory();

  // So far, no reweighting
  int nWgts = mergingHooksPtr->nWgts;
  vector<double> wt( nWgts, 1. );

  // Only reweighting with MPI no-emission probability
  double maxScale = (foundCompletePath) ? infoPtr->eCM()
                  : mergingHooksPtr->muFinME();
  int njetsMaxMPI = mergingHooksPtr->nMinMPI();
  vector<double> mpiwt = selected->weightTreeEmissions( trial, -1, 0,
      njetsMaxMPI, maxScale );
  wt = mpiwt;
  // Done
  return wt;
}

//--------------------------------------------------------------------------

// Function to calculate O(\alpha_s)-term of CKKWL-weight for NLO merging

vector<double> History::weightNL3First(PartonLevel* trial, AlphaStrong* asFSR,
  AlphaStrong* asISR, AlphaEM* , AlphaEM* , double RN,
  Rndm* rndmPtr ) {

  // Read alpha_S in ME calculation and maximal scale (eCM)
  double asME   = infoPtr->alphaS();
  double muR      = mergingHooksPtr->muRinME();
  double maxScale = (foundCompletePath)
                  ? infoPtr->eCM()
                  : mergingHooksPtr->muFinME();

  // Pick path of clusterings
  History *  selected = select(RN);
  // Set scales in the states to the scales pythia would have set
  selected->setScalesInHistory();

  int nSteps = mergingHooksPtr->getNumberOfClusteringSteps(state);

  // Get the lowest order k-factor and add first two terms in expansion
  double kFactor = asME * mergingHooksPtr->k1Factor(nSteps);

  // If using Bbar, which includes a tree-level part, subtract an
  // additional one, i.e. the O(\as^0) contribution as well
  double wt = 1. + kFactor;

  // Calculate sum of O(alpha) terms
  double wtFirst = selected->weightFirst(trial,asME, muR, maxScale, asFSR,
      asISR, rndmPtr );

  // Get starting scale for trial showers.
  double startingScale = (selected->mother) ? state.scale()
    : infoPtr->eCM();

  // Count emissions: New variant
  // Generate true average, not only one-point
  bool fixpdf = true;
  bool fixas  = true;
  double nWeight1 = 0.;
  for(int i=0; i < NTRIAL; ++i) {
    // Get number of emissions
    vector<double> unresolvedEmissionTerm = countEmissions( trial,
      startingScale, mergingHooksPtr->tms(), 2, asME, asFSR, asISR, 3,
      fixpdf, fixas );
    nWeight1 += unresolvedEmissionTerm[1];
  }

  wtFirst += nWeight1/double(NTRIAL);

  // Introduce vector to allow variation of coefficient
  int nWgts = mergingHooksPtr->nWgts;
  vector<double> wtVec({wt+wtFirst});

  // Use the varied scale in the coefficient around which we expand
  for (int iVar = 1; iVar < nWgts; ++iVar) {
    double asFix = asFSR->alphaS(pow2(muR*mergingHooksPtr->
          muRVarFactors[iVar-1])) / asME;
    wtVec.push_back( wt + asFix*wtFirst );
  }

  // Introduce variation of stong coupling that is not done in Born input
  for ( int iVar = 1; iVar < nWgts; ++iVar ) {
    double corrFac = std::pow(asFSR->alphaS(pow2(muR*mergingHooksPtr->
            muRVarFactors[iVar-1])) / asME, nSteps);
    wtVec[iVar] *= corrFac;
  }

  // Done
  return wtVec;

}

//--------------------------------------------------------------------------

vector<double> History::weightNL3Tree(PartonLevel* trial, AlphaStrong*
    asFSR, AlphaStrong * asISR, AlphaEM * aemFSR, AlphaEM * aemISR,
    double RN) {
  // No difference to CKKW-L. Recycle CKKW-L function.
  return weightCKKWL( trial, asFSR, asISR, aemFSR, aemISR, RN);
}

//--------------------------------------------------------------------------

vector<double> History::weightUMEPSTree(PartonLevel* trial, AlphaStrong*
    asFSR, AlphaStrong * asISR, AlphaEM * aemFSR, AlphaEM * aemISR,
    double RN) {
  // No difference to CKKW-L. Recycle CKKW-L function.
  return weightCKKWL( trial, asFSR, asISR, aemFSR, aemISR, RN);
}

//--------------------------------------------------------------------------

// Function to return weight of virtual correction events for NLO merging

vector<double> History::weightUMEPSSubt(PartonLevel* trial, AlphaStrong*
    asFSR, AlphaStrong * asISR, AlphaEM * aemFSR, AlphaEM * aemISR,
    double RN ) {

  // Read alpha_S in ME calculation and maximal scale (eCM)
  double asME     = infoPtr->alphaS();
  double aemME    = infoPtr->alphaEM();
  double maxScale = (foundCompletePath) ? infoPtr->eCM()
                  : mergingHooksPtr->muFinME();
  // Select a path of clusterings
  History *  selected = select(RN);
  // Set scales in the states to the scales pythia would have set
  selected->setScalesInHistory();

  // Get weight.
  int nWgts = mergingHooksPtr->nWgts;
  vector<double> sudakov( nWgts, 1.);
  vector<double> asWeight( nWgts, 1.);
  vector<double> aemWeight( nWgts, 1.);
  vector<double> pdfWeight( nWgts, 1.);

  // Do trial shower, calculation of alpha_S ratios, PDF ratios
  sudakov   = selected->weightTree(trial, asME, aemME, maxScale,
    selected->clusterIn.pT(), asFSR, asISR, aemFSR, aemISR, asWeight,
    aemWeight, pdfWeight);

  // MPI no-emission probability.
  int njetsMaxMPI = mergingHooksPtr->nMinMPI()+1;
  vector<double> mpiwt = selected->weightTreeEmissions( trial, -1, 0,
      njetsMaxMPI, maxScale );

  // Set hard process renormalisation scale to default Pythia value.
  bool resetScales = mergingHooksPtr->resetHardQRen();
  // For pure QCD dijet events, evaluate the coupling of the hard process at
  // a more reasonable pT, rather than evaluation \alpha_s at a fixed
  // arbitrary scale.
  if ( resetScales
    && mergingHooksPtr->getProcessString().compare("pp>jj") == 0) {
    // Reset to a running coupling. Here we choose FSR for simplicity.
    double newQ2Ren = pow2( selected->hardRenScale(selected->state) );
    double runningCoupling = (*asFSR).alphaS(newQ2Ren) / asME;
    for (double& asW: asWeight) asW *= pow(runningCoupling,2);
  }

  // For prompt photon events, evaluate the coupling of the hard process at
  // a more reasonable pT, rather than evaluation \alpha_s at a fixed
  // arbitrary scale.
  if ( resetScales
    && mergingHooksPtr->getProcessString().compare("pp>aj") == 0) {
    // Reset to a running coupling. In prompt photon always ISR.
    double newQ2Ren = pow2( selected->hardRenScale(selected->state) );
    double runningCoupling =
      (*asISR).alphaS( newQ2Ren + pow(mergingHooksPtr->pT0ISR(),2) ) / asME;
    for (double& asW: asWeight) asW *= runningCoupling;
  }

  // Done
  vector<double> ret;
  for (int iVar = 0; iVar < nWgts; ++iVar)
    ret.push_back(sudakov[iVar]*asWeight[iVar]*aemWeight[iVar]*pdfWeight[iVar]*
        mpiwt[iVar]);
  return ret;

}

//--------------------------------------------------------------------------

vector<double> History::weightUNLOPSTree(PartonLevel* trial, AlphaStrong*
    asFSR, AlphaStrong* asISR, AlphaEM * aemFSR, AlphaEM * aemISR, double RN,
    int depthIn) {

  if ( mergingHooksPtr->canCutOnRecState() && !foundAllowedPath ) {
    loggerPtr->WARNING_MSG(
      "no allowed history found. Using disallowed history");
  }
  if ( mergingHooksPtr->orderHistories() && !foundOrderedPath ) {
    loggerPtr->WARNING_MSG(
      "no ordered history found. Using unordered history");
  }
  if ( mergingHooksPtr->canCutOnRecState()
    && mergingHooksPtr->orderHistories()
    && !foundAllowedPath && !foundOrderedPath ) {
    loggerPtr->WARNING_MSG("no allowed or ordered history found");
  }

  // Read alpha_S in ME calculation and maximal scale (eCM)
  double asME     = infoPtr->alphaS();
  double aemME    = infoPtr->alphaEM();
  double maxScale = (foundCompletePath) ? infoPtr->eCM()
                  : mergingHooksPtr->muFinME();
  // Select a path of clusterings
  History *  selected = select(RN);
  // Set scales in the states to the scales pythia would have set
  selected->setScalesInHistory();

  // Get weight.
  int nWgts = mergingHooksPtr->nWgts;
  vector<double> asWeight( nWgts, 1. );
  vector<double> aemWeight( nWgts, 1. );
  vector<double> pdfWeight( nWgts, 1. );

  // Do trial shower, calculation of alpha_S ratios, PDF ratios
  vector<double> wt( nWgts, 1.);
  if (depthIn < 0) wt = selected->weightTree(trial, asME, aemME, maxScale,
    selected->clusterIn.pT(), asFSR, asISR, aemFSR, aemISR, asWeight,
    aemWeight, pdfWeight);
  else {
    wt   = selected->weightTreeEmissions( trial, 1, 0, depthIn, maxScale );
    if (wt[0] != 0.) {
      asWeight  = selected->weightTreeAlphaS( asME, asFSR, asISR, depthIn);
      aemWeight = selected->weightTreeAlphaEM( aemME, aemFSR, aemISR, depthIn);
      pdfWeight = selected->weightTreePDFs( maxScale,
                                            selected->clusterIn.pT(), depthIn);
    }
  }

  // MPI no-emission probability.
  int njetsMaxMPI = mergingHooksPtr->nMinMPI();
  vector<double> mpiwt = selected->weightTreeEmissions( trial, -1, 0,
      njetsMaxMPI, maxScale );

  // Set hard process renormalisation scale to default Pythia value.
  bool resetScales = mergingHooksPtr->resetHardQRen();
  // For pure QCD dijet events, evaluate the coupling of the hard process at
  // a more reasonable pT, rather than evaluation \alpha_s at a fixed
  // arbitrary scale.
  if ( resetScales
    && mergingHooksPtr->getProcessString().compare("pp>jj") == 0) {
    // Reset to a running coupling. Here we choose FSR for simplicity.
    double newQ2Ren = pow2( selected->hardRenScale(selected->state) );
    double runningCoupling = (*asFSR).alphaS(newQ2Ren) / asME;
    for (double& asW: asWeight) asW *= pow(runningCoupling,2);
  }

  // For prompt photon events, evaluate the coupling of the hard process at
  // a more reasonable pT, rather than evaluation \alpha_s at a fixed
  // arbitrary scale.
  if ( resetScales
    && mergingHooksPtr->getProcessString().compare("pp>aj") == 0) {
    // Reset to a running coupling. In prompt photon always ISR.
    double newQ2Ren = pow2( selected->hardRenScale(selected->state) );
    double runningCoupling =
      (*asISR).alphaS( newQ2Ren + pow(mergingHooksPtr->pT0ISR(),2) ) / asME;
    for (double& asW: asWeight) asW *= runningCoupling;
  }

  // Done
  vector<double> ret;
  for (int iVar = 0; iVar < nWgts; ++iVar)
    ret.push_back(wt[iVar]*asWeight[iVar]*aemWeight[iVar]*pdfWeight[iVar]*
        mpiwt[iVar]);

  // For tree level, undo as variation applied to ME component to avoid double
  // ratios when combining later.
  int nSteps = mergingHooksPtr->getNumberOfClusteringSteps(state);
  double muR = mergingHooksPtr->muRinME();
  for (int iVar = 1; iVar < nWgts; ++iVar)
    asWeight[iVar] *= std::pow((*asFSR).alphaS(muR*muR) /
        (*asFSR).alphaS(pow2(muR*mergingHooksPtr->muRVarFactors[iVar-1])),
        nSteps);

  // Save weight vectors internally for UNLOPS-P and -PC
  mergingHooksPtr->individualWeights.wtSave = wt;
  mergingHooksPtr->individualWeights.asWeightSave = asWeight;
  mergingHooksPtr->individualWeights.aemWeightSave = aemWeight;
  mergingHooksPtr->individualWeights.pdfWeightSave = pdfWeight;
  mergingHooksPtr->individualWeights.mpiWeightSave = mpiwt;

  return ret;

}

//--------------------------------------------------------------------------

vector<double> History::weightUNLOPSLoop(PartonLevel* trial, AlphaStrong*
    asFSR, AlphaStrong* asISR, AlphaEM * aemFSR, AlphaEM * aemISR, double RN,
    int depthIn) {
  // No difference to default NL3
  if (depthIn < 0) return weightNL3Loop(trial, RN);

  // Read alpha_S in ME calculation and maximal scale (eCM)
  double asME       = infoPtr->alphaS();
  double aemME      = infoPtr->alphaEM();
  double maxScale   = (foundCompletePath) ? infoPtr->eCM() :
                      mergingHooksPtr->muFinME();

  // Select a path of clusterings
  History * selected = select(RN);
  // Set scales in the status to the scales pythia would have set
  selected->setScalesInHistory();

  // Get weight.
  int nWgts = mergingHooksPtr->nWgts;
  vector<double> wt( nWgts, 1.);
  vector<double> asWeight( nWgts, 1.);
  vector<double> aemWeight( nWgts, 1.);
  vector<double> pdfWeight( nWgts, 1.);

  // Do trial shower, calculation of alpha_S ratios, PDF ratios.
  wt   = selected->weightTreeEmissions( trial, 1, 0, depthIn, maxScale );
  if (wt[0] != 0.) {
    asWeight  = selected->weightTreeAlphaS( asME, asFSR, asISR, depthIn,
                                            true);
    aemWeight = selected->weightTreeAlphaEM( aemME, aemFSR, aemISR, depthIn);
    pdfWeight = selected->weightTreePDFs( maxScale,
                                          selected->clusterIn.pT(), depthIn);
  }

  // MPI no-emission probability.
  int njetsMaxMPI = mergingHooksPtr->nMinMPI();
  vector<double> mpiwt = selected->weightTreeEmissions( trial, -1, 0,
      njetsMaxMPI, maxScale );

  // Set hard process renormalisation scale to default Pythia value.
  bool resetScales = mergingHooksPtr->resetHardQRen();
  // For pure QCD dijet events, evaluate the coupling of the hard process at
  // a more reasonable pT, rather than evaluation \alpha_s at a fixed
  // arbitrary scale.
  if ( resetScales
    && mergingHooksPtr->getProcessString().compare("pp>jj") == 0) {
    // Reset to a running coupling. Here we choose FSR for simplicity.
    double newQ2Ren = pow2( selected->hardRenScale(selected->state) );
    double runningCoupling = (*asFSR).alphaS(newQ2Ren) / asME;
    for (double& asW: asWeight) asW *= pow(runningCoupling,2);
  }

  // For prompt photon events, evaluate the coupling of the hard process at
  // a more reasonable pT, rather than evaluation \alpha_s at a fixed
  // arbitrary scale.
  if ( resetScales
    && mergingHooksPtr->getProcessString().compare("pp>aj") == 0) {
    // Reset to a running coupling. In prompt photon always ISR.
    double newQ2Ren = pow2( selected->hardRenScale(selected->state) );
    double runningCoupling =
      (*asISR).alphaS( newQ2Ren + pow(mergingHooksPtr->pT0ISR(),2) ) / asME;
    for (double& asW: asWeight) asW *= runningCoupling;
  }

  // Done
  vector<double> ret;
  for (int iVar = 0; iVar < nWgts; ++iVar)
    ret.push_back(wt[iVar]*asWeight[iVar]*aemWeight[iVar]*pdfWeight[iVar]*
        mpiwt[iVar]);

  // Save weight vectors interally for UNLOPS-P and -PC
  mergingHooksPtr->individualWeights.wtSave = wt;
  mergingHooksPtr->individualWeights.asWeightSave = asWeight;
  mergingHooksPtr->individualWeights.aemWeightSave = aemWeight;
  mergingHooksPtr->individualWeights.pdfWeightSave = pdfWeight;
  mergingHooksPtr->individualWeights.mpiWeightSave = mpiwt;

  return ret;

}

//--------------------------------------------------------------------------

vector<double> History::weightUNLOPSSubt(PartonLevel* trial, AlphaStrong*
    asFSR, AlphaStrong* asISR, AlphaEM * aemFSR, AlphaEM * aemISR, double RN,
  int depthIn) {

  // Select a path of clusterings
  History* selected = select(RN);
  // Set scales in the states to the scales pythia would have set
  selected->setScalesInHistory();

  // Read alpha_S in ME calculation and maximal scale (eCM)
  double asME     = infoPtr->alphaS();
  double aemME    = infoPtr->alphaEM();
  double maxScale = (foundCompletePath)
                  ? infoPtr->eCM()
                  : mergingHooksPtr->muFinME();

  int nWgts = mergingHooksPtr->nWgts;

  // Only allow two clusterings if all intermediate states above the
  // merging scale.
  int nSteps = mergingHooksPtr->getNumberOfClusteringSteps(state);
  if ( nSteps == 2 && mergingHooksPtr->nRecluster() == 2
    && ( !foundCompletePath
      || !selected->allIntermediateAboveRhoMS( mergingHooksPtr->tms() )) )
    return vector<double>( nWgts, 0. );

  // Get weights: alpha_S ratios and PDF ratios
  vector<double> asWeight( nWgts, 1.);
  vector<double> aemWeight( nWgts, 1.);
  vector<double> pdfWeight( nWgts, 1.);
  // Do trial shower, calculation of alpha_S ratios, PDF ratios
  vector<double> wt( nWgts, 1.);
  if (depthIn < 0)
    wt = selected->weightTree(trial, asME, aemME, maxScale,
      selected->clusterIn.pT(), asFSR, asISR, aemFSR, aemISR, asWeight,
      aemWeight, pdfWeight);
  else {
    wt = selected->weightTreeEmissions( trial, 1, 0, depthIn, maxScale );
    if (wt[0] > 0.) {
      asWeight  = selected->weightTreeAlphaS( asME, asFSR, asISR, depthIn);
      aemWeight = selected->weightTreeAlphaEM( aemME, aemFSR, aemISR, depthIn);
      pdfWeight = selected->weightTreePDFs( maxScale,
                                            selected->clusterIn.pT(), depthIn);
    }
  }

  // MPI no-emission probability.
  int njetsMaxMPI = mergingHooksPtr->nMinMPI()+1;
  vector<double> mpiwt = selected->weightTreeEmissions( trial, -1, 0,
      njetsMaxMPI, maxScale );

  // Set weight
  vector<double> ret;
  if (mergingHooksPtr->nRecluster() == 2 )
    ret = wt = asWeight = aemWeight = pdfWeight = mpiwt =
      vector<double>( nWgts, 1. );
  else {
    for (int iVar = 0; iVar < nWgts; ++iVar)
      ret.push_back(asWeight[iVar]*aemWeight[iVar]*pdfWeight[iVar]*
          wt[iVar]*mpiwt[iVar]);
  }

  // For tree level, undo as variation applied to ME component to avoid double
  // ratios when combining later.
  double muR = mergingHooksPtr->muRinME();
  for (int iVar = 1; iVar < nWgts; ++iVar)
    asWeight[iVar] *= std::pow((*asFSR).alphaS(muR*muR) /
        (*asFSR).alphaS(pow2(muR*mergingHooksPtr->muRVarFactors[iVar-1])),
        nSteps);

  // Save weight vectors interally for UNLOPS-P and -PC
  mergingHooksPtr->individualWeights.wtSave = wt;
  mergingHooksPtr->individualWeights.asWeightSave = asWeight;
  mergingHooksPtr->individualWeights.aemWeightSave = aemWeight;
  mergingHooksPtr->individualWeights.pdfWeightSave = pdfWeight;
  mergingHooksPtr->individualWeights.mpiWeightSave = mpiwt;

  // Done
  return ret;

}

//--------------------------------------------------------------------------

vector<double> History::weightUNLOPSSubtNLO(PartonLevel* trial, AlphaStrong*
    asFSR, AlphaStrong* asISR, AlphaEM * aemFSR, AlphaEM * aemISR, double RN,
    int depthIn) {

  // So far, no reweighting
  int nWgts = mergingHooksPtr->nWgts;
  vector<double> wt( nWgts, 1. );

  if (depthIn < 0) {

    // Select a path of clusterings
    History *  selected = select(RN);
    // Set scales in the states to the scales pythia would have set
    selected->setScalesInHistory();
    // Only reweighting with MPI no-emission probability
    double maxScale = (foundCompletePath) ? infoPtr->eCM()
                    : mergingHooksPtr->muFinME();
    int njetsMaxMPI = mergingHooksPtr->nMinMPI()+1;
    vector<double> mpiwt = selected->weightTreeEmissions
      ( trial, -1, 0, njetsMaxMPI, maxScale );
    wt = mpiwt;
    // Done
    return wt;
  }

  // Select a path of clusterings
  History* selected = select(RN);
  // Set scales in the states to the scales pythia would have set
  selected->setScalesInHistory();

  // Read alpha_S in ME calculation and maximal scale (eCM)
  double asME     = infoPtr->alphaS();
  double aemME    = infoPtr->alphaEM();
  double maxScale = (foundCompletePath)
                  ? infoPtr->eCM()
                  : mergingHooksPtr->muFinME();

  // Only allow two clusterings if all intermediate states above the
  // merging scale.
  double nSteps = mergingHooksPtr->getNumberOfClusteringSteps(state);
  if ( nSteps == 2 && mergingHooksPtr->nRecluster() == 2
    && ( !foundCompletePath
      || !selected->allIntermediateAboveRhoMS( mergingHooksPtr->tms() )) )
    return vector<double>( nWgts, 0. );

  // Get weights: alpha_S ratios and PDF ratios
  vector<double> asWeight( nWgts, 1.);
  vector<double> aemWeight( nWgts, 1.);
  vector<double> pdfWeight( nWgts, 1.);
  // Do trial shower, calculation of alpha_S ratios, PDF ratios
  wt = selected->weightTreeEmissions( trial, 1, 0, depthIn, maxScale );
  if (wt[0] > 0.) {
    asWeight  = selected->weightTreeAlphaS( asME, asFSR, asISR, depthIn,
                                            true);
    aemWeight = selected->weightTreeAlphaEM( aemME, aemFSR, aemISR, depthIn);
    pdfWeight = selected->weightTreePDFs( maxScale,
                                          selected->clusterIn.pT(), depthIn);
  }

  // MPI no-emission probability.
  int njetsMaxMPI = mergingHooksPtr->nMinMPI()+1;
  vector<double> mpiwt = selected->weightTreeEmissions( trial, -1, 0,
      njetsMaxMPI, maxScale );

  // Set weight
  vector<double> ret;
  if (mergingHooksPtr->nRecluster() == 2 )
    ret = wt = asWeight = aemWeight = pdfWeight = mpiwt =
      vector<double>( nWgts, 1. );
  else {
    for (int iVar = 0; iVar < nWgts; ++iVar)
      ret.push_back(asWeight[iVar]*aemWeight[iVar]*pdfWeight[iVar]*
          wt[iVar]*mpiwt[iVar]);
  }

  // Save weight vectors interally for UNLOPS-P and -PC
  mergingHooksPtr->individualWeights.wtSave = wt;
  mergingHooksPtr->individualWeights.asWeightSave = asWeight;
  mergingHooksPtr->individualWeights.aemWeightSave = aemWeight;
  mergingHooksPtr->individualWeights.pdfWeightSave = pdfWeight;
  mergingHooksPtr->individualWeights.mpiWeightSave = mpiwt;

  // Done
  return ret;
}

//--------------------------------------------------------------------------

// Function to calculate O(\alpha_s)-term of CKKWL-weight for NLO merging

vector<double> History::weightUNLOPSFirst( int order, PartonLevel*
  trial, AlphaStrong* asFSR, AlphaStrong* asISR, AlphaEM*, AlphaEM*,
  double RN, Rndm* rndmPtr ) {

  int nWgts = mergingHooksPtr->nWgts;

  // Already done if no correction should be calculated
  if ( order < 0 ) return vector<double>( nWgts, 0. );

  // Read alpha_S in ME calculation and maximal scale (eCM)
  double asME     = infoPtr->alphaS();
  //double aemME    = infoPtr->alphaEM();
  double muR      = mergingHooksPtr->muRinME();
  double maxScale = (foundCompletePath)
                  ? infoPtr->eCM()
                  : mergingHooksPtr->muFinME();

  // Pick path of clusterings
  History *  selected = select(RN);
  // Set scales in the states to the scales pythia would have set
  selected->setScalesInHistory();

  double nSteps = mergingHooksPtr->getNumberOfClusteringSteps(state);

  // Get the lowest order k-factor and add first two terms in expansion
  double kFactor = asME * mergingHooksPtr->k1Factor(nSteps);

  // If using Bbar, which includes a tree-level part, subtract an
  // additional one, i.e. the O(\as^0) contribution as well
  double wt = 1;
  // Set up vector for order == 0 case.
  vector<double> wtVec(nWgts, wt);

  if (order > 0) {
    // Start by adding the O(\alpha_s^1)-term of the k-factor.
    if ( mergingHooksPtr->orderHistories() && foundOrderedPath )
      wt += kFactor;

    // Calculate sum of O(\alpha_s^1)-terms of the ckkw-l weight WITHOUT
    // the O(\alpha_s^1)-term of the last no-emission probability.
    // Get first term in expansion of alpha_s ratios.
    double wA = selected->weightFirstAlphaS( asME, muR, asFSR, asISR );
    // Generate true average, not only one-point.
    double nWeight = 0.;
    for ( int i=0; i < NTRIAL; ++i ) {
      // Get average number of emissions.
      double wE   = selected->weightFirstEmissions(trial,asME, maxScale,
        asFSR, asISR, true, true );
      // Add average number of emissions off reconstructed states to weight.
      nWeight += wE;
      // Get first term in expansion of PDF ratios.
      double pscale = selected->clusterIn.pT();
      double wP   = selected->weightFirstPDFs(asME, maxScale, pscale, rndmPtr);
      // Add integral of DGLAP shifted PDF ratios from \alpha_s
      // expansion to wt.
      nWeight += wP;
    }

    // Introduce vector to allow variation of coefficient
    wtVec = vector<double>({wt + wA + nWeight/double(NTRIAL)});

    // Use the varied scale in the coefficient around which we expand
    for (int iVar = 1; iVar < nWgts; ++iVar) {
      double asFix = asFSR->alphaS(pow2(muR*mergingHooksPtr->
            muRVarFactors[iVar-1])) / asME;
      wtVec.push_back( wt + asFix*(wA + nWeight / double(NTRIAL)) );
    }
  }

  // Introduce variation of stong coupling that is not done in Born input
  mergingHooksPtr->individualWeights.bornAsVarFac =
    vector<double>( nWgts, 1. );
  for ( int iVar = 1; iVar < nWgts; ++iVar ) {
    double corrFac = std::pow(asFSR->alphaS(pow2(muR*mergingHooksPtr->
            muRVarFactors[iVar-1])) / asME, nSteps);
    wtVec[iVar] *= corrFac;
    mergingHooksPtr->individualWeights.bornAsVarFac[iVar] =
      corrFac;
  }

  // If O(\alpha_s^1)-term + O(\alpha_s^1)-term is to be calculated, done.
  if ( order <= 1 ) return wtVec;

  // So far, no calculation of  O(\alpha_s^2)-term
  return vector<double>( nWgts, 0. );

}

//--------------------------------------------------------------------------

// Function to set the state with complete scales for evolution.

void History::getStartingConditions( const double RN, Event& outState ) {

  // Select the history
  History *  selected = select(RN);

  // Set scales in the states to the scales pythia would have set
  selected->setScalesInHistory();

  // Get number of clustering steps.
  int nSteps = mergingHooksPtr->getNumberOfClusteringSteps(state);

  // Update the lowest order process.
  if (!selected->mother) {
    int nFinal = 0;
    for(int i=0; i < int(state.size()); ++i)
      if ( state[i].isFinal()) nFinal++;
    if (nFinal <=2)
      state.scale(mergingHooksPtr->muF());

    // Save information on last splitting, to allow the next
    // emission in the shower to have smaller rapidity with
    // respect to the last ME splitting.
    // For hard process, use dummy values.
    if (mergingHooksPtr->getNumberOfClusteringSteps(state) == 0) {
      infoPtr->zNowISR(0.5);
      infoPtr->pT2NowISR(pow(state[0].e(),2));
      infoPtr->hasHistory(true);
    // For incomplete process, try to use real values.
    } else {
      infoPtr->zNowISR(selected->zISR());
      infoPtr->pT2NowISR(pow(selected->pTISR(),2));
      infoPtr->hasHistory(true);
    }

    // Set QCD 2->2 starting scale different from arbitrary scale in LHEF!
    // --> Set to minimal mT of partons.
    int nFinalCol = 0;
    double muf = state[0].e();
    for ( int i=0; i < state.size(); ++i )
    if ( state[i].isFinal()
      && ( state[i].colType() != 0 || state[i].id() == 22 ) ) {
      nFinalCol++;
      muf = min( muf, abs(state[i].mT()) );
    }
    // For pure QCD dijet events (only!), set the process scale to the
    // transverse momentum of the outgoing partons.
    if ( nSteps == 0 && nFinalCol == 2
      && ( mergingHooksPtr->getProcessString().compare("pp>jj") == 0
        || mergingHooksPtr->getProcessString().compare("pp>aj") == 0) ) {
      state.scale(muf);
      for (int i = 3;i < state.size();++i)
        state[i].scale(muf);
    }
    // For weak inclusive merging, follow QCD 2->2 starting scale for dijet
    // events. Also, restore input input polarisations.
    if (nSteps == 0 && nFinalCol == 2 &&
        mergingHooksPtr->getProcessString().find("inc") != string::npos) {
        state.scale(muf);
      for (int i = 3;i < state.size();++i)
        state[i].scale(muf);
      for ( int i=0; i < min(state.size(),outState.size()); ++i )
        state[i].pol(outState[i].pol());
    }

  } else {

    // Save information on last splitting, to allow the next
    // emission in the shower to have smaller rapidity with
    // respect to the last ME splitting.
    infoPtr->zNowISR(selected->zISR());
    infoPtr->pT2NowISR(pow(selected->pTISR(),2));
    infoPtr->hasHistory(true);

  }

  // Copy the output state.
  outState = state;

  // Save MPI starting scale.
  if (nSteps == 0)
    mergingHooksPtr->muMI(infoPtr->eCM());
  else
    mergingHooksPtr->muMI(outState.scale());

  // Setup the weak shower if W clustering is enabled.
  if (mergingHooksPtr->doWeakClustering()) setupSimpleWeakShower(0);

  mergingHooksPtr->setShowerStoppingScale( 0.0 );
}

//--------------------------------------------------------------------------

// Function to print the history that would be chosen from the number RN.

void History::printHistory( const double RN ) {
  History *  selected = select(RN);
  selected->printStates();
  // Done
}

//--------------------------------------------------------------------------

// Function to print the states in a history, starting from the hard process.

void History::printStates() {
  if ( !mother ) {
    cout << scientific << setprecision(6) << "Probability=" << prob << endl;
    state.list();
    return;
  }

  // Print.
  double p = prob/mother->prob;
  cout << scientific << setprecision(6) << "Probability=" << p
       << " scale=" << clusterIn.pT() << endl;
  state.list();
  // Recurse
  mother->printStates();
  // Done
  return;
}

//--------------------------------------------------------------------------

// Function to set the state with complete scales for evolution.

bool History::getClusteredEvent( const double RN, int nSteps,
                Event& outState) {

  // Select history
  History *  selected = select(RN);
  // Set scales in the states to the scales pythia would have set
  // (Only needed if not done before in calculation of weights or
  //  setting of starting conditions)
  selected->setScalesInHistory();
  // If the history does not allow for nSteps clusterings (e.g. because the
  // history is incomplete), return false
  if (nSteps > selected->nClusterings()) return false;
  // Return event with nSteps-1 additional partons (i.e. recluster the last
  // splitting) and copy the output state
  outState = selected->clusteredState(nSteps-1);
  // Done.
  return true;

}

//--------------------------------------------------------------------------

bool History::getFirstClusteredEventAboveTMS( const double RN, int nDesired,
                Event& process, int& nPerformed, bool doUpdate ) {

  // Do reclustering (looping) steps. Remember process scale.
  int nTried  = nDesired - 1;
  // Get number of clustering steps.
  int nSteps   = select(RN)->nClusterings();
  // Set scales in the states to the scales pythia would have set.
  select(RN)->setScalesInHistory();

  // Recluster until reclustered event is above the merging scale.
  Event dummy = Event();
  do {
    // Initialise temporary output of reclustering.
    dummy.clear();
    dummy.init( "(hard process-modified)", particleDataPtr );
    dummy.clear();
    // Recluster once more.
    nTried++;
    // If reclustered event does not exist, exit.
    if ( !getClusteredEvent( RN, nSteps-nTried+1, dummy ) ) return false;
    if ( nTried >= nSteps ) break;

    // Continue loop if reclustered event has unresolved partons.
  } while ( mergingHooksPtr->getNumberOfClusteringSteps(dummy) > 0
         && mergingHooksPtr->tmsNow( dummy) < mergingHooksPtr->tms() );

  // Update the hard process.
  if ( doUpdate ) process = dummy;

  // Failed to produce output state.
  if ( nTried > nSteps ) return false;

  nPerformed = nTried;
  if ( doUpdate ) {
    // Update to the actual number of steps.
    mergingHooksPtr->nReclusterSave = nPerformed;
    // Save MPI starting scale
    if (mergingHooksPtr->getNumberOfClusteringSteps(state) == 0)
      mergingHooksPtr->muMI(infoPtr->eCM());
    else
      mergingHooksPtr->muMI(state.scale());
  }

  // Done
  return true;

}

//--------------------------------------------------------------------------

// Calculate and return pdf ratio.

double History::getPDFratio( int side, bool forSudakov, bool useHardPDFs,
                    int flavNum, double xNum, double muNum,
                    int flavDen, double xDen, double muDen) {

  // Do nothing for e+e- beams
  if ( abs(flavNum) > 10 && flavNum != 21 ) return 1.0;
  if ( abs(flavDen) > 10 && flavDen != 21 ) return 1.0;

  // Now calculate PDF ratio if necessary
  double pdfRatio = 1.0;

  // Get mother and daughter pdfs
  double pdfNum = 0.0;
  double pdfDen = 0.0;

  // Use hard process PDFs (i.e. PDFs NOT used in ISR, FSR or MPI).
  if ( useHardPDFs ) {
    if (side == 1) {
      if (forSudakov)
        pdfNum = mother->beamA.xfHard( flavNum, xNum, muNum*muNum);
      else
        pdfNum = beamA.xfHard( flavNum, xNum, muNum*muNum);
      pdfDen = max(1e-10, beamA.xfHard( flavDen, xDen, muDen*muDen));
    } else {
      if (forSudakov)
        pdfNum = mother->beamB.xfHard( flavNum, xNum, muNum*muNum);
      else
        pdfNum = beamB.xfHard( flavNum, xNum, muNum*muNum);
      pdfDen = max(1e-10,beamB.xfHard( flavDen, xDen, muDen*muDen));
    }

  // Use rescaled PDFs in the presence of multiparton interactions
  } else {
    if (side == 1) {
      if (forSudakov)
        pdfNum = mother->beamA.xfISR(0, flavNum, xNum, muNum*muNum);
      else
        pdfNum = beamA.xfISR(0, flavNum, xNum, muNum*muNum);
      pdfDen = max(1e-10, beamA.xfISR(0, flavDen, xDen, muDen*muDen));

    } else {
      if (forSudakov)
        pdfNum = mother->beamB.xfISR(0, flavNum, xNum, muNum*muNum);
      else
        pdfNum = beamB.xfISR(0, flavNum, xNum, muNum*muNum);
      pdfDen = max(1e-10,beamB.xfISR(0, flavDen, xDen, muDen*muDen));
    }
  }

  // Cut out charm threshold.
  if ( forSudakov && abs(flavNum) ==4 && abs(flavDen) == 4 && muDen == muNum
    && muNum < particleDataPtr->m0(4))
    pdfDen = pdfNum = 1.0;

  // Return ratio of pdfs
  if ( pdfNum > 1e-15 && pdfDen > 1e-10 ) {
    pdfRatio *= pdfNum / pdfDen;
  } else if ( pdfNum < pdfDen ) {
    pdfRatio = 0.;
  } else if ( pdfNum > pdfDen ) {
    pdfRatio = 1.;
  }

  // Done
  return pdfRatio;

}

//--------------------------------------------------------------------------

/*--------------- METHODS USED FOR ONLY ONE PATH OF HISTORY NODES ------- */

// Function to set all scales in the sequence of states. This is a
// wrapper routine for setScales and setEventScales methods

void History::setScalesInHistory() {
  // Find correct links from n+1 to n states (mother --> child), as
  // needed for enforcing ordered scale sequences
  vector<int> ident;
  findPath(ident);

  // Set production scales in the states to the scales pythia would
  // have set and enforce ordering
  setScales(ident,true);

  // Set the overall event scales to the scale of the last branching
  setEventScales();

}

//--------------------------------------------------------------------------

// Setup function that call the real getWeakProb.

double History::getWeakProb() {
  vector<int> modes, fermionLines;
  vector<Vec4> mom;
  return getWeakProb(modes, mom, fermionLines);
}

//--------------------------------------------------------------------------

// Recursive function that returns the weak probability for the given path.
// mode refers to which ME correction to use, 1 = sChannel, 2 = gluon channel,
// 3 = double quark t-channel, 4 is double quark u-channel.

double History::getWeakProb(vector<int> &mode, vector<Vec4> &mom,
  vector<int> fermionLines) {

  // If at end, return 1.
  if (!mother) return 1.;

  // Find the transfer map given the splitting.
  map<int,int> stateTransfer;
  findStateTransfer(stateTransfer);

  // Setup hard process.
  if (mode.empty()) setupWeakHard(mode,fermionLines,mom);

  // Update modes and fermionLines.
  vector<int> modeNew = updateWeakModes(mode, stateTransfer);
  vector<int> fermionLinesNew = updateWeakFermionLines(fermionLines,
    stateTransfer);

  // Get the probability if it is a weak emission.
  if (mother->state[clusterIn.emitted].idAbs() == 24 ||
      mother->state[clusterIn.emitted].idAbs() == 23)
    return getSingleWeakProb(modeNew, mom, fermionLinesNew) *
      mother->getWeakProb(modeNew, mom, fermionLinesNew);
  else return mother->getWeakProb(modeNew, mom, fermionLinesNew);
}

//--------------------------------------------------------------------------

double History::getSingleWeakProb(vector<int> &mode, vector<Vec4> &mom,
  vector<int> fermionLines) {

  // Find the correct coupling coefficient.
  double weakCoupling = 0.0;
  if (mother->state[clusterIn.emitted].idAbs() == 24) {
    // No emissions from right handed particles.
    if (clusterIn.spinRadBef == 1) return 0.0;
    else if (clusterIn.spinRadBef == -1)
      weakCoupling = 4.*M_PI/ coupSMPtr->sin2thetaW()
        * coupSMPtr->V2CKMid(abs(clusterIn.flavRadBef),
        mother->state[clusterIn.emittor].idAbs());
    else {
      loggerPtr->WARNING_MSG(
        "spin not properly configurated. Skipping history");
      return 0.0;
    }
  } else if (mother->state[clusterIn.emitted].idAbs() == 23) {
    // No emissions from right handed particles.
    if (clusterIn.spinRadBef == 1)
      weakCoupling = 4.*M_PI*pow2(coupSMPtr->rf( abs(clusterIn.flavRadBef)))
        / (coupSMPtr->sin2thetaW() * coupSMPtr->cos2thetaW()) ;
    else if (clusterIn.spinRadBef == -1)
      weakCoupling = 4.*M_PI*pow2(coupSMPtr->lf( abs(clusterIn.flavRadBef)))
        / (coupSMPtr->sin2thetaW() * coupSMPtr->cos2thetaW()) ;
    else {
      loggerPtr->WARNING_MSG(
        "spin not properly configurated. Skipping history");
      return 0.0;
    }
  } else {
    loggerPtr->WARNING_MSG("did not emit W/Z. Skipping history");
    return 0.0;
  }

  // Find and store kinematics (e.g. z, pT, k1, k3).

  // Store momenta.
  Vec4 pRadAft = mother->state[clusterIn.emittor].p();
  Vec4 pEmtAft = mother->state[clusterIn.emitted].p();
  Vec4 pRecAft = mother->state[clusterIn.recoiler].p();
  Vec4 pSum = pRadAft + pEmtAft + pRecAft;
  double m2sum = pSum.m2Calc();
  double Qsq = (pRadAft + pEmtAft).m2Calc();

  double m2Rad0 = pRadAft.m2Calc();
  double m2Emt0 = pEmtAft.m2Calc();
  double lambda13 = sqrt( pow2(Qsq - m2Rad0 - m2Emt0 ) - 4. * m2Rad0*m2Emt0 );
  double k1 = ( Qsq - lambda13 + (m2Emt0 - m2Rad0 ) ) / ( 2. * Qsq );
  double k3 = ( Qsq - lambda13 - (m2Emt0 - m2Rad0 ) ) / ( 2. * Qsq );

  double z = mother->getCurrentZ(clusterIn.emittor, clusterIn.recoiler,
    clusterIn.emitted, clusterIn.flavRadBef);
  double pT2 = pow2(clusterIn.pTscale);

  double x1 = 2. * pRadAft * pSum / m2sum;
  double x2 = 2. * pRecAft * pSum / m2sum;
  double x3 = 2. * pEmtAft * pSum / m2sum;

  // Final state clustering.
  if ( state[clusterIn.radBef].status() > 0) {
     // s-channel
    if (mode[clusterIn.emittor] == 1) {
      // Calculate variables.
      double eCMME = pSum.mCalc();
      double r1 = mother->state[clusterIn.emittor].m() / eCMME;
      double r2 = mother->state[clusterIn.recoiler].m() / eCMME;
      double r3 = mother->state[clusterIn.emitted].m() / eCMME;
      double x1s    = x1 * x1;
      double x2s    = x2 * x2;
      double r1s    = r1 * r1;
      double r2s    = r2 * r2;
      double r3s    = r3 * r3;
      double prop1  = 1. + r1s - r2s - x1;
      double prop2  = 1. + r2s - r1s - x2;
      double prop1s = prop1 * prop1;
      double prop2s = prop2 * prop2;
      double prop12 = prop1 * prop2;

      // Calculate Jacobian.
      double jac = 1./(1.-z) * 1./pT2 * (1-x2+r2-r1)*(x3 - k1*(x1+x3))
        * (1.-x1+r1-r2) / x3;
      return jac * weakCoupling * ((2. * r3s * r3s + 2. * r3s *
        (x1 + x2) + x1s + x2s) / prop12 - r3s / prop1s - r3s / prop2s);
    }
    // t-channel.
    else {
      // Store momentas needed.
      Vec4 p1 = mother->state[clusterIn.emittor].p();
      Vec4 p2 = mother->state[clusterIn.recoiler].p();
      Vec4 p3 = mother->state[clusterIn.emitted].p();
      Vec4 radBef = state[clusterIn.radBef].p();
      Vec4 recBef = state[clusterIn.recBef].p();
      Vec4 pIn1 = mom[0];
      Vec4 pIn2 = mom[1];

      // Check if a swap is needed.
      if (fermionLines[2] == clusterIn.emittor);
      else if (fermionLines[3] == clusterIn.emittor) swap(pIn1, pIn2);

      // Rescaling of incoming partons p3 and p4.
      double scaleFactor2 = (p1 + p2 + p3).m2Calc() / (pIn1 + pIn2).m2Calc();
      double scaleFactor = sqrt(scaleFactor2);
      pIn1 *= scaleFactor;
      pIn2 *= scaleFactor;

      // Longitudinal boost to rest frame of incoming partons of
      // hard interaction.
      RotBstMatrix rot2to2frame;
      rot2to2frame.bstback(pIn1 + pIn2);
      pIn1.rotbst(rot2to2frame);
      pIn2.rotbst(rot2to2frame);
      p1.rotbst(rot2to2frame);
      p2.rotbst(rot2to2frame);
      p3.rotbst(rot2to2frame);
      recBef.rotbst(rot2to2frame);
      radBef.rotbst(rot2to2frame);

      // Further boost to rest frame of outgoing state.
      RotBstMatrix rot2to3frame;
      rot2to3frame.bstback(p1 + p2 + p3);
      p1.rotbst(rot2to3frame);
      p2.rotbst(rot2to3frame);
      p3.rotbst(rot2to3frame);
      recBef.rotbst(rot2to3frame);
      radBef.rotbst(rot2to3frame);

      // Calculate variables;
      double sHat = (pIn1 + pIn2).m2Calc();
      double tHat = (radBef - pIn1).m2Calc();
      double uHat = (recBef - pIn1).m2Calc();
      double localProb = 0;
      double Q2   = pT2 / (z*(1.-z));
      double jac = 1./(4. * M_PI) * 1./( (1.-z) * z ) * sHat / (sHat - Q2)
        * (1. - k1 - k3);

      // Calculate the ME depending on the top of process.
      if (mode[clusterIn.emittor] == 2)
        localProb = simpleWeakShowerMEs.getMEqg2qgZ( pIn1, pIn2, p2, p3, p1)
          / simpleWeakShowerMEs.getMEqg2qg( sHat, tHat, uHat);
      else if (mode[clusterIn.emittor] == 3)
        localProb = simpleWeakShowerMEs.getMEqq2qqZ( pIn1, pIn2, p3, p2, p1)
          / simpleWeakShowerMEs.getMEqq2qq( sHat, tHat, uHat, false);
      else if (mode[clusterIn.emittor] == 4)
        localProb = simpleWeakShowerMEs.getMEqq2qqZ( pIn1, pIn2, p3, p2, p1)
          / simpleWeakShowerMEs.getMEqq2qq( sHat, tHat, uHat, true);
      else {
        loggerPtr->WARNING_MSG(
          "wrong mode setup. Setting probability for path to zero");
      }

      // Split matrix element according to propagaters.
      localProb *=  abs((-p3 + pIn1).m2Calc())
               / ((p3 + p1).m2Calc() + abs((-pIn1 + p3).m2Calc()));

      return jac * weakCoupling * localProb;
    }
  }
  // Initial clustering.
  else {
    // s-channel
    if (mode[clusterIn.emittor] == 1) {
      Vec4 pIn1 = mother->state[clusterIn.emittor].p();
      Vec4 pIn2 = mother->state[clusterIn.recoiler].p();
      Vec4 p1 = mother->state[clusterIn.emitted].p();
      Vec4 p2 = pIn1 + pIn2 -p1;

      double sH  = (pIn1 + pIn2).m2Calc();
      double tH  = (p1 - pIn1).m2Calc();
      double uH  = (p1 - pIn2).m2Calc();
      double m3s = p1.m2Calc();
      double m4s = p2.m2Calc();

      double jac = 1./sH * tH*uH / ( tH * (tH + uH) );
      return jac * weakCoupling * ((uH*uH + tH*tH + 2 * sH * (m3s + m4s))
        / (uH*tH) - m3s * m4s * (1/(tH*tH) + 1/(uH*uH)));
    }
    else {

      // Store momenta.
      Vec4 pIn1 = mother->state[clusterIn.emittor].p();
      Vec4 pIn2 = mother->state[clusterIn.recoiler].p();
      Vec4 p3 = mother->state[clusterIn.emitted].p();
      Vec4 p1 = mom[2];
      Vec4 p2 = mom[3];

      // Check if radiator is from beam one or two.
      if (fermionLines[0] == clusterIn.emittor);
      else if (fermionLines[1] == clusterIn.emittor)
        swap(p1, p2);


      Vec4 pDaughter, pRecoiler;
      int signBeam = (pIn1.pz() > 0.) ? 1 : -1;
      double eCM = state[0].e(), phi = 0;

      // Undo the ISR boost.
      reverseBoostISR(pIn1, p3, pIn2, pDaughter, pRecoiler, signBeam,
        eCM, phi);

      // Scale outgoing vectors to conserve energy / momentum.
      //double scaleFactor2 = (pIn1 + pIn2 - p3).m2Calc() / (p1 + p2).m2Calc();
      double scaleFactor2 = (pIn1 + pIn2 - p3).m2Calc() / (p1 + p2).m2Calc();
      double scaleFactor  = sqrt(scaleFactor2);
      RotBstMatrix rot2to2frame;
      rot2to2frame.bstback(p1 + p2);
      p1.rotbst(rot2to2frame);
      p2.rotbst(rot2to2frame);
      p1 *= scaleFactor;
      p2 *= scaleFactor;

      // Find 2 to 2 rest frame for incoming particles.
      // This is done before one of the two are made virtual (Q^2 mass).
      Vec4 radBef = state[clusterIn.radBef].p();
      Vec4 recBef = state[clusterIn.recBef].p();

      RotBstMatrix rot2to2frameInc;
      rot2to2frameInc.bstback(radBef + recBef);
      radBef.rotbst(rot2to2frameInc);
      recBef.rotbst(rot2to2frameInc);
      double sHat = (p1 + p2).m2Calc();
      double tHat = (p1 - radBef).m2Calc();
      double uHat = (p1 - recBef).m2Calc();
      double localProb = 0;
      p1.rot(0., -phi);
      p2.rot(0., -phi);

      // Calculating the Jacobian
      double jac = z / (4.*M_PI);

      if (mode[clusterIn.emittor] == 2)
        localProb = simpleWeakShowerMEs.getMEqg2qgZ(pIn1, pIn2, p2, p3, p1)
          / simpleWeakShowerMEs.getMEqg2qg(sHat, tHat, uHat);
      else if (mode[clusterIn.emittor] == 4)
        localProb = simpleWeakShowerMEs.getMEqq2qqZ(pIn1, pIn2, p3, p2, p1)
          / simpleWeakShowerMEs.getMEqq2qq(sHat, tHat, uHat, true);
      else if (mode[clusterIn.emittor] == 3)
        localProb = simpleWeakShowerMEs.getMEqq2qqZ(pIn1, pIn2, p3, p2, p1)
          / simpleWeakShowerMEs.getMEqq2qq(sHat, tHat, uHat, false);
      else {
        loggerPtr->WARNING_MSG(
          "wrong mode setup. Setting probability for path to zero");
      }

      // Split of ME into an ISR part and FSR part.
      localProb *= (p3 + p1).m2Calc() / ( (p3 + p1).m2Calc()
                 + abs((-pIn1 + p3).m2Calc()) );

      return jac * weakCoupling * localProb;
    }
  }

}

//--------------------------------------------------------------------------

// Check if the weak recoil structure is allowed.
bool History::checkWeakRecoils(map<int,int> &allowedRecoils, bool isFirst) {
  if (!mother) return true;

  // Setup if first
  if (isFirst) {
    // Drell-Yan production.
    if (state.size() != 8) {
      if (state[3].isQuark() || state[3].isLepton())
        allowedRecoils.insert(pair<int,int>(3,4));
      if (state[4].isQuark() || state[4].isLepton())
        allowedRecoils.insert(pair<int,int>(4,3));

    } else {
      if (state[3].isQuark() || state[3].isLepton())
        allowedRecoils.insert(pair<int,int>(3,4));
      if (state[4].isQuark() || state[4].isLepton())
        allowedRecoils.insert(pair<int,int>(4,3));
      if (state[5].isQuark() || state[5].isLepton())
        allowedRecoils.insert(pair<int,int>(5,6));
      if (state[6].isQuark() || state[6].isLepton())
        allowedRecoils.insert(pair<int,int>(6,5));
    }
  }

  // Find the transfer map.
  map<int,int> transfer;
  findStateTransfer(transfer);

  // Copy the new allowed recoils.
  map<int,int> allowedRecoilsNew;
  for (map<int,int>::iterator it = allowedRecoils.begin();
       it != allowedRecoils.end(); ++it) {

    // Start by considering final state splittings.
    if (state[clusterIn.radBef].status() > 0) {
      // If the dipole was not connected to current splitting.
      if (it->first  != clusterIn.radBef &&
          it->second != clusterIn.radBef)
        allowedRecoilsNew.insert(pair<int,int>(transfer[it->first],
                                               transfer[it->second]));
      // If the recoiler is splitted into two.
      else if (it->second == clusterIn.radBef) {
        // Follow fermion line.
        if (state[clusterIn.recBef].isQuark() ||
            state[clusterIn.recBef].isLepton()) {
          if (mother->state[clusterIn.emittor].isQuark() ||
              mother->state[clusterIn.emittor].isLepton())
            allowedRecoilsNew.insert(pair<int,int>(transfer[it->first],
                                                   clusterIn.emittor));
          else
            allowedRecoilsNew.insert(pair<int,int>(transfer[it->first],
                                                   clusterIn.emitted));
        }
        // If no fermion line to follow, choose the largest invariant mass.
        else {
          double mEmittor = (mother->state[clusterIn.emittor].p() +
                             mother->state[transfer[it->first]].p()).mCalc();
          double mEmitted = (mother->state[clusterIn.emitted].p() +
                             mother->state[transfer[it->first]].p()).mCalc();
          if (mEmitted > mEmittor)
            allowedRecoilsNew.insert(pair<int,int>(transfer[it->first],
                                                   clusterIn.emitted));
          else
            allowedRecoilsNew.insert(pair<int,int>(transfer[it->first],
                                                   clusterIn.emittor));
        }
      }
      // If the radiator is splitted into two.
      if (mother->state[clusterIn.emittor].isQuark() ||
          mother->state[clusterIn.emittor].isLepton())
        allowedRecoilsNew.insert(pair<int,int>(clusterIn.emittor,
                                               transfer[it->second]));
      else
        allowedRecoilsNew.insert(pair<int,int>(clusterIn.emitted,
                                               transfer[it->second]));
    }

    // Look at initial splittings.
    else {
      // If not involved in the splitting.
      if (it->first  != clusterIn.radBef &&
          it->second != clusterIn.radBef)
        allowedRecoilsNew.insert(pair<int,int>(transfer[it->first],
                                               transfer[it->second]));

      // If the recoiler is splitted, always choose the emittor.
      else if (it->second == clusterIn.radBef)
         allowedRecoilsNew.insert(pair<int,int>(transfer[it->first],
                                                   clusterIn.emittor));

      // If the radiator splits into two.
      else {
        // If the the fermion line continues to be the beam particle.
         if (mother->state[clusterIn.emittor].isQuark() ||
              mother->state[clusterIn.emittor].isLepton())
           allowedRecoilsNew.insert(pair<int,int>(clusterIn.emittor,
                                                  clusterIn.recoiler));

         // If the fermion line is emitted, find recoiler in final state.
         else
           allowedRecoilsNew.insert(pair<int,int>(clusterIn.emittor,
                                                  findISRRecoiler()));
      }
    }
  }

  // If a gluon/phton is split into a quark-antiquark pair, add two new
  // possible configurations.
  if ( (state[clusterIn.radBef].idAbs() == 22 ||
        state[clusterIn.radBef].idAbs() == 21) &&
       (mother->state[clusterIn.emittor].isQuark() ||
        mother->state[clusterIn.emittor].isLepton() ) ) {
    // If it is a final splitting, just add the two.
    if (state[clusterIn.radBef].status() > 0) {
      allowedRecoilsNew.insert(pair<int,int>(clusterIn.emittor,
                                             clusterIn.emitted));
      allowedRecoilsNew.insert(pair<int,int>(clusterIn.emitted,
                                             clusterIn.emittor));
    }

    // If it is an initial splitting.
    else {
      allowedRecoilsNew.insert(pair<int,int>(clusterIn.emittor,
                                             clusterIn.recoiler));
      allowedRecoilsNew.insert(pair<int,int>(clusterIn.emitted,
                                             findISRRecoiler()));
    }
  }

  // allowedRecoilsNew is now properly setup, so ready to check
  // if recoil works.

  // If weak emission, do the check.
  if (mother->state[clusterIn.emitted].idAbs() == 24 ||
      mother->state[clusterIn.emitted].idAbs() == 23)
    if ( clusterIn.recoiler != allowedRecoilsNew[clusterIn.emittor])
      return false;

  // check the mother.
  return mother->checkWeakRecoils(allowedRecoilsNew);

}

//--------------------------------------------------------------------------

// Find the recoiler for an ISR scattered weak particle.
// Always use 1 as weak weight, even though the shower uses a slightly
// different value for Z emissions.
int History::findISRRecoiler() {

  int flavRad = mother->state[clusterIn.emitted].id();
  Vec4 pRad = mother->state[clusterIn.emitted].p();
  double mRad = mother->state[clusterIn.emitted].m();
  int iRad = clusterIn.emitted;
  int iRec = 0;
  double ppMin = 1E20;
  for (int i = 0;i < mother->state.size(); ++i) {
    if (i == iRad) continue;
    if (mother->state[i].isFinal() && mother->state[i].id() == - flavRad) {
      double ppNow = mother->state[i].p() * pRad
                   - mother->state[i].m() - mRad;
      if (ppNow < ppMin) {
        ppMin = ppNow;
        iRec = i;
      }
    }
  }
  if (iRec) return iRec;

  // Find nearest recoiler weak-charge-squared-weighted.
  for (int i = 0;i < mother->state.size(); ++i) {
    if (i == iRad) continue;
    if (mother->state[i].isFinal() && mother->state[i].idAbs() < 20) {
      double weakCoupNow = 1.;
      double ppNow = (mother->state[i].p() * pRad
        - mother->state[i].m() - mRad) / weakCoupNow;
      if (ppNow < ppMin) {
        ppMin = ppNow;
        iRec = i;
      }
    }
  }
  if (iRec) return iRec;

   // Find nearest recoiler in final state.
  for (int i = 0;i < mother->state.size(); ++i) {
    if (i == iRad) continue;
    if (mother->state[i].isFinal()) {
      double ppNow = mother->state[i].p() * pRad
                   - mother->state[i].m() - mRad;
      if (ppNow < ppMin) {
        ppMin = ppNow;
        iRec = i;
      }
    }
  }
  if (iRec) return iRec;

  return 0;
}

//--------------------------------------------------------------------------

// Find map between indecies in the current state and the state after
// the splitting.
// NOT IMPLEMENTED FOR MULTIPLE W/Z/GAMMA (NEED TO HAVE A WAY TO IDENTIFY THEM)
void History::findStateTransfer(map<int,int> &transfer) {
  // No need to transfer if already at highest multiplicity.
  if (!mother) return;
  transfer.clear();

  // Directly assign the 3 first particles (system, beam1, beam2);
  for(int i = 0;i < 3; ++i)
    transfer.insert(pair<int,int>(i,i));

  transfer.insert(pair<int,int>(clusterIn.radBef, clusterIn.emittor));
  transfer.insert(pair<int,int>(clusterIn.recBef, clusterIn.recoiler));

  // Handle all particles that are not part of the clustering.
  for (int i = 0; i < int(mother->state.size()); ++i) {
    if (clusterIn.emitted == i ||
        clusterIn.emittor == i ||
        clusterIn.recoiler == i)
      continue;

    for (int j = 0;j < int(state.size()); ++j) {
      if (mother->state[i].id()            == state[j].id()
          && mother->state[i].colType()    == state[j].colType()
          && mother->state[i].chargeType() == state[j].chargeType()
          && mother->state[i].col()        == state[j].col()
          && mother->state[i].acol()       == state[j].acol()
          && mother->state[i].status()     == state[j].status()) {
        transfer.insert(pair<int,int>(j,i));
        break;
      }
    }
  }
}

//--------------------------------------------------------------------------

// Function to find the index (in the mother histories) of the
// child history, thus providing a way access the path from both
// initial history (mother == 0) and final history (all children == 0)
// IN vector<int> : The index of each child in the children vector
//                  of the current history node will be saved in
//                  this vector
// NO OUTPUT

void History::findPath(vector<int>& out) {

  // If the initial and final nodes are identical, return
  if (!mother && int(children.size()) < 1) return;
  // Find the child by checking the children vector for the perfomed
  // clustering
  int iChild=-1;
  if ( mother ) {
    int size = int(mother->children.size());
    // Loop through children and identify child chosen
    for ( int i=0; i < size; ++i) {
      if ( mother->children[i]->scale == scale
        && mother->children[i]->prob  == prob
        && equalClustering(mother->children[i]->clusterIn,clusterIn)) {
        iChild = i;
        break;
      }
    }
    // Save the index of the child in the children vector and recurse
    if (iChild >-1)
      out.push_back(iChild);
    mother->findPath(out);
  }
}

//--------------------------------------------------------------------------

// Functions to set the  parton production scales and enforce
// ordering on the scales of the respective clusterings stored in
// the History node:
// Method will start from lowest multiplicity state and move to
// higher states, setting the production scales the shower would
// have used.
// When arriving at the highest multiplicity, the method will switch
// and go back in direction of lower states to check and enforce
// ordering for unordered histories.
// IN vector<int> : Vector of positions of the chosen child
//                  in the mother history to allow to move
//                  in direction initial->final along path
//    bool        : True: Move in direction low->high
//                       multiplicity and set production scales
//                  False: Move in direction high->low
//                       multiplicity and check and enforce
//                       ordering
// NO OUTPUT

void History::setScales( vector<int> index, bool forward) {

  // First, set the scales of the hard process to the kinematial
  // limit (=s)
  if ( children.empty() && forward ) {
    // New "incomplete" configurations showered from mu
    if (!mother) {
      double scaleNew = 1.;
      if (mergingHooksPtr->incompleteScalePrescip()==0) {
        scaleNew = mergingHooksPtr->muF();
      } else if (mergingHooksPtr->incompleteScalePrescip()==1) {
        Vec4 pOut;
        pOut.p(0.,0.,0.,0.);
        for(int i=0; i<int(state.size()); ++i)
          if (state[i].isFinal())
            pOut += state[i].p();
        scaleNew = pOut.mCalc();
      } else if (mergingHooksPtr->incompleteScalePrescip()==2) {
        scaleNew = state[0].e();
      }

      scaleNew = max( mergingHooksPtr->pTcut(), scaleNew);

      state.scale(scaleNew);
      for(int i=3; i < int(state.size());++i)
        if (state[i].colType() != 0)
          state[i].scale(scaleNew);
    } else {
      // 2->2 with non-parton particles showered from eCM
      state.scale( state[0].e() );
      // Count final partons
      bool isLEP = ( state[3].isLepton() && state[4].isLepton() );
      int nFinal = 0;
      int nFinalPartons = 0;
      int nFinalPhotons = 0;
      for ( int i=0; i < int(state.size()); ++i ) {
        if ( state[i].isFinal() ) {
          nFinal++;
          if ( state[i].colType() != 0 ) nFinalPartons++;
          if ( state[i].id() == 22 )     nFinalPhotons++;
        }
      }
      bool isQCD = ( nFinal == 2 && nFinal == nFinalPartons );
      bool isPPh = ( nFinal == 2 && nFinalPartons == 1 && nFinalPhotons == 1);
      // If 2->2, purely partonic, set event scale to kinematic pT
      if ( !isLEP && ( isQCD || isPPh ) ) {
        double scaleNew = hardFacScale(state);
        state.scale( scaleNew );
      }
    }
  }
  // Set all particle production scales, starting from lowest
  // multiplicity (final) state
  if (mother && forward) {
    // When choosing splitting scale, beware of unordered splittings:
    double scaleNew = 1.;
    if (mergingHooksPtr->unorderedScalePrescip() == 0) {
      // Use larger scale as common splitting scale for mother and child
      scaleNew = max( mergingHooksPtr->pTcut(), max(scale,mother->scale));
    } else if (mergingHooksPtr->unorderedScalePrescip() == 1) {
      // Use smaller scale as common splitting scale for mother and child
      if (scale < mother->scale)
        scaleNew *= max( mergingHooksPtr->pTcut(), min(scale,mother->scale));
      else
        scaleNew *= max( mergingHooksPtr->pTcut(), max(scale,mother->scale));
    }

    // Rescale the mother state partons to the clustering scales
    // that have been found along the path
    mother->state[clusterIn.emitted].scale(scaleNew);
    mother->state[clusterIn.emittor].scale(scaleNew);
    mother->state[clusterIn.recoiler].scale(scaleNew);

    // Find unchanged copies of partons in higher multiplicity states
    // and rescale those
    mother->scaleCopies(clusterIn.emitted, mother->state, scaleNew);
    mother->scaleCopies(clusterIn.emittor, mother->state, scaleNew);
    mother->scaleCopies(clusterIn.recoiler, mother->state, scaleNew);

    // Recurse
    mother->setScales(index,true);
  }

  // Now, check and correct ordering from the highest multiplicity
  // state backwards to all the clustered states
  if (!mother || !forward) {
    // Get index of child along the path
    int iChild = -1;
    if ( int(index.size()) > 0 ) {
      iChild = index.back();
      index.pop_back();
    }

    // Check that the reclustered scale is above the shower cut
    if (mother) {
      scale = max(mergingHooksPtr->pTcut(), scale);
    }
    // If this is NOT the 2->2 process, check and enforce ordering
    if (iChild != -1 && !children.empty()) {
      if (scale > children[iChild]->scale ) {
        if (mergingHooksPtr->unorderedScalePrescip() == 0) {
          // Use larger scale as common splitting scale for mother and child
          double scaleNew = max( mergingHooksPtr->pTcut(),
                              max(scale,children[iChild]->scale));
          // Enforce ordering in particle production scales
          for( int i = 0; i < int(children[iChild]->state.size()); ++i)
            if (children[iChild]->state[i].scale() == children[iChild]->scale)
              children[iChild]->state[i].scale(scaleNew);
          // Enforce ordering in saved clustering scale
          children[iChild]->scale = scaleNew;

        } else if ( mergingHooksPtr->unorderedScalePrescip() == 1) {
           // Use smaller scale as common splitting scale for mother & child
           double scaleNew = max(mergingHooksPtr->pTcut(),
                               min(scale,children[iChild]->scale));
           // Enforce ordering in particle production scales
           for( int i = 0; i < int(state.size()); ++i)
             if (state[i].scale() == scale)
               state[i].scale(scaleNew);
           // Enforce ordering in saved clustering scale
           scale = scaleNew;
        }
      // Just set the overall event scale to the minimal scale
      } else {
        double scalemin = state[0].e();
        for( int i = 0; i < int(state.size()); ++i)
          if (state[i].colType() != 0)
            scalemin = max(mergingHooksPtr->pTcut(),
                         min(scalemin,state[i].scale()));
        state.scale(scalemin);
        scale = max(mergingHooksPtr->pTcut(), scale);
      }
      //Recurse
      children[iChild]->setScales(index, false);
    }
  }

}

//--------------------------------------------------------------------------

// Function to find a particle in all higher multiplicity events
// along the history path and set its production scale to the input
// scale
// IN  int iPart       : Parton in refEvent to be checked / rescaled
//     Event& refEvent : Reference event for iPart
//     double scale    : Scale to be set as production scale for
//                       unchanged copies of iPart in subsequent steps

void History::scaleCopies(int iPart, const Event& refEvent, double rho) {

  // Check if any parton recently rescaled is found unchanged:
  // Same charge, colours in mother->state
  if ( mother ) {
    for( int i=0; i < mother->state.size(); ++i) {
      if ( ( mother->state[i].id()         == refEvent[iPart].id()
          && mother->state[i].colType()    == refEvent[iPart].colType()
          && mother->state[i].chargeType() == refEvent[iPart].chargeType()
          && mother->state[i].col()        == refEvent[iPart].col()
          && mother->state[i].acol()       == refEvent[iPart].acol() )
         ) {
        // Rescale the unchanged parton
        mother->state[i].scale(rho);
        // Recurse
         if (mother->mother)
          mother->scaleCopies( iPart, refEvent, rho );
       } // end if found unchanged parton case
    } // end loop over particle entries in event
  }
}

//--------------------------------------------------------------------------

// Functions to set the OVERALL EVENT SCALES [=state.scale()] to
// the scale of the last clustering
// NO INPUT
// NO OUTPUT

void History::setEventScales() {
  // Set the event scale to the scale of the last clustering,
  // except for the very lowest multiplicity state
  if (mother) {
    mother->state.scale(scale);
    // Recurse
    mother->setEventScales();
  }
}

//--------------------------------------------------------------------------

// Functions to return the z value of the last ISR splitting
// NO INPUT
// OUTPUT double : z value of last ISR splitting in history

double History::zISR() {

  // Do nothing for ME level state
  if (!mother) return 0.0;
  // Skip FSR splitting
  if (mother->state[clusterIn.emittor].isFinal()) return mother->zISR();
  // Calculate z
  int rad = clusterIn.emittor;
  int rec = clusterIn.recoiler;
  int emt = clusterIn.emitted;
  double z = (mother->state[rad].p() + mother->state[rec].p()
            - mother->state[emt].p()).m2Calc()
    / (mother->state[rad].p() + mother->state[rec].p()).m2Calc();
  // Recurse
  double znew = mother->zISR();
  // Update z
  if (znew > 0.) z = znew;

  return z;
}

//--------------------------------------------------------------------------

// Functions to return the z value of the last FSR splitting
// NO INPUT
// OUTPUT double : z value of last FSR splitting in history

double History::zFSR() {

  // Do nothing for ME level state
  if (!mother) return 0.0;
  // Skip ISR splitting
  if (!mother->state[clusterIn.emittor].isFinal()) return mother->zFSR();
  // Calculate z
  int rad = clusterIn.emittor;
  int rec = clusterIn.recoiler;
  int emt = clusterIn.emitted;
  // Construct 2->3 variables for FSR
  Vec4   sum = mother->state[rad].p() + mother->state[rec].p()
             + mother->state[emt].p();
  double m2Dip = sum.m2Calc();
  double x1 = 2. * (sum * mother->state[rad].p()) / m2Dip;
  double x3 = 2. * (sum * mother->state[emt].p()) / m2Dip;
  // Calculate z of splitting for FSR
  double z = x1/(x1+x3);
  // Recurse
  double znew = mother->zFSR();
  // Update z
  if (znew > 0.) z = znew;

  return z;
}

//--------------------------------------------------------------------------

// Functions to return the pT scale of the last FSR splitting
// NO INPUT
// OUTPUT double : pT scale of last FSR splitting in history

double History::pTISR() {
  // Do nothing for ME level state
  if (!mother) return 0.0;
  // Skip FSR splitting
  if (mother->state[clusterIn.emittor].isFinal()) return mother->pTISR();
  double pT = mother->state.scale();
  // Recurse
  double pTnew = mother->pTISR();
  // Update pT
  if (pTnew > 0.) pT = pTnew;

  return pT;
}

//--------------------------------------------------------------------------

// Functions to return the pT scale of the last FSR splitting
// NO INPUT
// OUTPUT double : pT scale of last FSR splitting in history

double History::pTFSR() {

  // Do nothing for ME level state
  if (!mother) return 0.0;
  // Skip ISR splitting
  if (!mother->state[clusterIn.emittor].isFinal()) return mother->pTFSR();
  double pT = mother->state.scale();
  // Recurse
  double pTnew = mother->pTFSR();
  // Update pT
  if (pTnew > 0.) pT = pTnew;
  return pT;
}

//--------------------------------------------------------------------------

// Function to return the depth of the history (i.e. the number of
// reclustered splittings)
// NO INPUT
// OUTPUT int  : Depth of history

int History::nClusterings() {
  if (!mother) return 0;
  int w = mother->nClusterings();
  w += 1;
  return w;
}

//--------------------------------------------------------------------------

// Functions to return the event after nSteps splittings of the 2->2 process
// Example: nSteps = 1 -> return event with one additional parton
// INPUT  int   : Number of splittings in the event,
//                as counted from core 2->2 process
// OUTPUT Event : event with nSteps additional partons

Event History::clusteredState(int nSteps) {

  // Save state
  Event outState = state;
  // As long as there are steps to do, recursively save state
  if (mother && nSteps > 0)
    outState = mother->clusteredState(nSteps - 1);
  // Done
  return outState;

}

//--------------------------------------------------------------------------

// Function to choose a path from all paths in the tree
// according to their splitting probabilities
// IN double    : Random number
// OUT History* : Leaf of history path chosen

History * History::select(double rnd) {

  // No need to choose if no paths have been constructed.
  if ( goodBranches.empty() && badBranches.empty() ) return this;

  // Choose amongst paths allowed by projections.
  double sum = 0.;
  map<double, History*> selectFrom;
  if ( !goodBranches.empty() ) {
    selectFrom = goodBranches;
    sum        = sumGoodBranches;
  } else {
    selectFrom = badBranches;
    sum        = sumBadBranches;
  }

  if (mergingHooksPtr->pickBySumPT()) {
    // Find index of history with minimal sum of scalar pT
    int nFinal = 0;
    for (int i=0; i < state.size(); ++i)
      if (state[i].isFinal())
        nFinal++;
    double iMin = 0.;
    double sumMin = (nFinal-2)*state[0].e();
    for ( map<double, History*>::iterator it = selectFrom.begin();
      it != selectFrom.end(); ++it ) {

      if (it->second->sumScalarPT < sumMin) {
        sumMin = it->second->sumScalarPT;
        iMin = it->first;
      }
    }
    // Choose history with smallest sum of scalar pT
    return selectFrom.lower_bound(iMin)->second;
  } else {
    // Choose history according to probability, be careful about upper bound
    if ( rnd != 1. ) {
      return selectFrom.upper_bound(sum*rnd)->second;
    } else {
      return selectFrom.lower_bound(sum*rnd)->second;
    }
  }
  // Done
}

//--------------------------------------------------------------------------

// Function to project paths onto desired paths.

bool History::trimHistories() {
  // Do nothing if no paths have been constructed.
  if ( paths.empty() ) return false;
  // Loop through all constructed paths. Check all removal conditions.
  for ( map<double, History*>::iterator it = paths.begin();
    it != paths.end(); ++it ) {
    // Check if history is allowed.
    if ( it->second->keep() && !it->second->keepHistory() )
      it->second->remove();
  }
  // Project onto desired / undesired branches.
  double sumold, sumnew, mismatch;
  sumold = mismatch = 0.;
  // Loop through all constructed paths and store allowed paths.
  // Skip undesired paths.
  for ( map<double, History*>::iterator it = paths.begin();
    it != paths.end(); ++it ) {
    // Update index
    sumnew = it->first;
    if ( it->second->keep() ) {
      // Fill branches with allowed paths.
      goodBranches.insert( make_pair( sumnew - mismatch, it->second) );
      // Add probability of this path.
      sumGoodBranches = sumnew - mismatch;
    } else {
      // Update mismatch in probabilities resulting from not including this
      // path
      double mismatchOld = mismatch;
      mismatch += sumnew - sumold;
      // Fill branches with allowed paths.
      badBranches.insert( make_pair( mismatchOld + sumnew - sumold,
        it->second ) );
      // Add probability of this path.
      sumBadBranches = mismatchOld  + sumnew - sumold;
    }
    // remember index of this path in order to caclulate probability of
    // subsequent path.
    sumold = it->first;
  }

  // Done.
  return !goodBranches.empty();
}

//--------------------------------------------------------------------------

// Function implementing checks on a paths, deciding if the path is valid.

bool History::keepHistory() {
  bool keepPath = true;

  // Tag unordered paths for removal.
  if ( mergingHooksPtr->getProcessString().compare("pp>jj") == 0
    || mergingHooksPtr->getProcessString().compare("pp>aj") == 0
    || isQCD2to2(state)   ) {
    // Tag unordered paths for removal. Include scale of hard 2->2 process
    // into the ordering definition.
    double maxScale = hardFacScale(state);
    return isOrderedPath( maxScale );
  }

  // Set starting scale to mass of Drell-Yan for 2->1.
  if (isEW2to1(state)) {
    Vec4 pSum(0,0,0,0);
    for (int i = 0;i < state.size(); ++i)
      if (state[i].isFinal()) pSum += state[i].p();
    return isOrderedPath( pSum.mCalc());
  }
  keepPath = isOrderedPath( infoPtr->eCM() );

  // More stringent criterion.
  //keepPath = allIntermediateAboveRhoMS( mergingHooksPtr->tms() );

  // Do not keep extremely unlikely paths.
  if (probMax() > 0. && abs(prob) < 1e-10*probMax()) keepPath = false;

  //Done
  return keepPath;
}

//--------------------------------------------------------------------------

// Function to check if a path is ordered in evolution pT.

bool History::isOrderedPath( double maxscale ) {
  double newscale = clusterIn.pT();
  if ( !mother ) return true;
  if ( mother->state[clusterIn.emittor].idAbs() == 21
    && mother->state[clusterIn.emitted].idAbs() == 5
    && !mother->state[clusterIn.emittor].isFinal())
    newscale=maxscale;
  bool ordered = mother->isOrderedPath(newscale);
  if ( !ordered || maxscale < newscale) return false;
  return ordered;
}

//--------------------------------------------------------------------------

// Function to check if all reconstucted states in a path pass the merging
// scale cut.

bool History::allIntermediateAboveRhoMS( double rhoms, bool good ) {
  // If one state below the merging scale has already been found, no need to
  // check further.
  if ( !good ) return false;
  // Check merging scale for states with more than 0 jets
  int nFinal = 0;
  for ( int i = 0; i < state.size(); ++i )
    if ( state[i].isFinal() && state[i].colType() != 0 )
      nFinal++;
  double rhoNew = (nFinal > 0 ) ? mergingHooksPtr->tmsNow( state )
                : state[0].e();
  // Assume state from ME generator passes merging scale cut.
  if ( !mother ) return good;
  // Recurse.
  return mother->allIntermediateAboveRhoMS( rhoms, (rhoNew > rhoms) );
}

//--------------------------------------------------------------------------

// Function to check if any ordered paths were found (and kept).

bool History::foundAnyOrderedPaths() {
  //Do nothing if no paths were found
  if ( paths.empty() ) return false;
  double maxscale = infoPtr->eCM();
  // Loop through paths. Divide probability into ordered and unordered pieces.
  for ( map<double, History*>::iterator it = paths.begin();
    it != paths.end(); ++it )
    if ( it->second->isOrderedPath(maxscale) )
      return true;
  // Done
  return false;
}

//--------------------------------------------------------------------------

// For a full path, find the weight calculated from the ratio of
// couplings, the no-emission probabilities, and possible PDF
// ratios. This function should only be called for the last history
// node of a full path.
// IN  TimeShower : Already initialised shower object to be used as
//                  trial shower
//     double     : alpha_s value used in ME calculation
//     double     : Maximal mass scale of the problem (e.g. E_CM)
//     AlphaStrong: Initialised shower alpha_s object for FSR
//                  alpha_s ratio calculation
//     AlphaStrong: Initialised shower alpha_s object for ISR
//                  alpha_s ratio calculation (can be different from previous)

vector<double> History::weightTree(PartonLevel* trial, double as0, double aem0,
  double maxscale, double pdfScale, AlphaStrong * asFSR, AlphaStrong * asISR,
  AlphaEM * aemFSR, AlphaEM * aemISR, vector<double>& asWeight,
  vector<double>& aemWeight, vector<double>& pdfWeight) {

  // Use correct scale
  double newScale = scale;

  int nWgts = mergingHooksPtr->nWgts;

  // For ME state, just multiply by PDF ratios
  if ( !mother ) {

    int sideRad = (state[3].pz() > 0) ? 1 :-1;
    int sideRec = (state[4].pz() > 0) ? 1 :-1;

    // Calculate PDF first leg
    if (state[3].colType() != 0) {
      // Find x value and flavour
      double x = 2.*state[3].e() / state[0].e();
      int flav = state[3].id();
      // Find numerator/denominator scale
      double scaleNum = (children.empty()) ? hardFacScale(state) : maxscale;
      double scaleDen = mergingHooksPtr->muFinME();
      // For initial parton, multiply by PDF ratio
      double ratio = getPDFratio(sideRad, false, false, flav, x, scaleNum,
                       flav, x, scaleDen);
      for (double& pdfW: pdfWeight) pdfW *= ratio;
    }

    // Calculate PDF ratio for second leg
    if (state[4].colType() != 0) {
      // Find x value and flavour
      double x = 2.*state[4].e() / state[0].e();
      int flav = state[4].id();
      // Find numerator/denominator scale
      double scaleNum = (children.empty()) ? hardFacScale(state) : maxscale;
      double scaleDen = mergingHooksPtr->muFinME();
      // For initial parton, multiply with PDF ratio
      double ratio = getPDFratio(sideRec, false, false, flav, x, scaleNum,
                       flav, x, scaleDen);
      for (double& pdfW: pdfWeight) pdfW *= ratio;
    }
    return vector<double>(nWgts,1.);
  }

  // Remember new PDF scale n case true scale should be used for un-ordered
  // splittings.
  double newPDFscale = newScale;
  if (mergingHooksPtr->unorderedPDFscalePrescip() == 1)
    newPDFscale = clusterIn.pT();

  // Recurse
  vector<double> w = mother->weightTree(trial, as0, aem0, newScale,
      newPDFscale, asFSR, asISR, aemFSR, aemISR, asWeight, aemWeight,
      pdfWeight);

  // Do nothing for empty state
  if (state.size() < 3) return vector<double>(nWgts,1.);
  // If up to now, trial shower was not successful, return zero
  if ( w[0] < 1e-12 ) return vector<double>(nWgts,0.);
  // Do trial shower on current state, return zero if not successful
  vector<double> wTrial = doTrialShower(trial, 1, maxscale);
  for (int iVar = 0; iVar < nWgts; ++iVar)
    w[iVar] *= wTrial[iVar];
  if ( w[0] < 1e-12 ) return vector<double>( nWgts, 0. );

  int emtType = mother->state[clusterIn.emitted].colType();
  // Calculate alpha_s ratio for current state.
  if ( asFSR && asISR && emtType != 0) {
    double asScale = pow2( newScale );
    if (mergingHooksPtr->unorderedASscalePrescip() == 1)
      asScale = pow2( clusterIn.pT() );

    // Add regularisation scale to initial state alpha_s.
    bool FSR = mother->state[clusterIn.emittor].isFinal();
    if (!FSR) asScale += pow2(mergingHooksPtr->pT0ISR());

    // Directly get argument of running alpha_s from shower plugin.
    if (mergingHooksPtr->useShowerPlugin() )
      asScale = getShowerPluginScale(mother->state, clusterIn.emittor,
        clusterIn.emitted, clusterIn.recoiler, "scaleAS", asScale);

    double alphaSinPS = (FSR) ? (*asFSR).alphaS(asScale)
                              : (*asISR).alphaS(asScale);
    asWeight[0] *= alphaSinPS / as0;

    // Scale variations
    for (int iVar = 1; iVar < nWgts; ++iVar) {
      alphaSinPS = (FSR) ?
        asFSR->alphaS(pow2(mergingHooksPtr->muRVarFactors[iVar-1])*asScale) :
        asISR->alphaS(pow2(mergingHooksPtr->muRVarFactors[iVar-1])*asScale);
      asWeight[iVar] *= alphaSinPS / as0;
    }
  }

  // Calculate alpha_em ratio for current state.
  if ( aemFSR && aemISR && emtType == 0 ) {
    double aemScale = pow2( newScale );
    if (mergingHooksPtr->unorderedASscalePrescip() == 1)
      aemScale = pow2( clusterIn.pT() );

    // Add regularisation scale to initial state alpha_s.
    bool FSR = mother->state[clusterIn.emittor].isFinal();
    if (!FSR) aemScale += pow2(mergingHooksPtr->pT0ISR());

    // Directly get argument of running alpha_em from shower plugin.
    if (mergingHooksPtr->useShowerPlugin() )
      aemScale = getShowerPluginScale(mother->state, clusterIn.emittor,
        clusterIn.emitted, clusterIn.recoiler, "scaleEM", aemScale);

    double alphaEMinPS = (FSR) ? (*aemFSR).alphaEM(aemScale)
                               : (*aemISR).alphaEM(aemScale);
    for (double& aemW: aemWeight) aemW *= alphaEMinPS / aem0;
  }

  // Calculate pdf ratios: Get both sides of event
  int inP = 3;
  int inM = 4;
  int sideP = (mother->state[inP].pz() > 0) ? 1 :-1;
  int sideM = (mother->state[inM].pz() > 0) ? 1 :-1;

  if ( mother->state[inP].colType() != 0 ) {
    // Find x value and flavour
    double x = getCurrentX(sideP);
    int flav = getCurrentFlav(sideP);
    // Find numerator scale
    double scaleNum = (children.empty())
                    ? hardFacScale(state)
                    : ( (mergingHooksPtr->unorderedPDFscalePrescip() == 1)
                      ? pdfScale : maxscale );
    double scaleDen = (mergingHooksPtr->unorderedPDFscalePrescip() == 1)
                    ? clusterIn.pT() : newScale;
    // Multiply PDF ratio
    double ratio = getPDFratio(sideP, false, false, flav, x, scaleNum,
                     flav, x, scaleDen);
    for (double& pdfW: pdfWeight) pdfW *= ratio;
  }

  if ( mother->state[inM].colType() != 0 ) {
    // Find x value and flavour
    double x = getCurrentX(sideM);
    int flav = getCurrentFlav(sideM);
    // Find numerator scale
    double scaleNum = (children.empty())
                    ? hardFacScale(state)
                    : ( (mergingHooksPtr->unorderedPDFscalePrescip() == 1)
                      ? pdfScale : maxscale );
    double scaleDen = (mergingHooksPtr->unorderedPDFscalePrescip() == 1)
                    ? clusterIn.pT() : newScale;
    // Multiply PDF ratio
    double ratio = getPDFratio(sideM, false, false, flav, x, scaleNum,
                     flav, x, scaleDen);
    for (double& pdfW: pdfWeight) pdfW *= ratio;
  }

  // Done
  return w;
}

//--------------------------------------------------------------------------

// Function to return the \alpha_s-ratio part of the CKKWL weight of a path.

vector<double> History::weightTreeAlphaS( double as0, AlphaStrong * asFSR,
  AlphaStrong * asISR, int njetMax, bool asVarInME ) {

  int nWgts = mergingHooksPtr->nWgts;

  // For ME state, do nothing.
  if ( !mother ) return vector<double>(nWgts,1.);
  // Recurse
  vector<double> w = mother->weightTreeAlphaS( as0, asFSR, asISR, njetMax,
     asVarInME );
  // Do nothing for empty state
  if (state.size() < 3) return w;

  // If this node has too many jets, no not calculate no-emission probability.
  int njetNow = mergingHooksPtr->getNumberOfClusteringSteps( state) ;
  if (njetNow >= njetMax) return vector<double>( nWgts, 1.0 );

  // Store variables for easy use.
  bool FSR = mother->state[clusterIn.emittor].isFinal();
  int emtID = mother->state[clusterIn.emitted].id();

  // Do not correct alphaS if it is an EW emission.
  if (abs(emtID) == 22 || abs(emtID) == 23 || abs(emtID) == 24) return w;

  // Calculate alpha_s ratio for current state
  if ( asFSR && asISR ) {
    double asScale = pow2( scale );
    if (mergingHooksPtr->unorderedASscalePrescip() == 1)
      asScale = pow2( clusterIn.pT() );

    // Add regularisation scale to initial state alpha_s.
    if (!FSR) asScale += pow2(mergingHooksPtr->pT0ISR());

    // Directly get argument of running alpha_s from shower plugin.
    if (mergingHooksPtr->useShowerPlugin() )
      asScale = getShowerPluginScale(mother->state, clusterIn.emittor,
        clusterIn.emitted, clusterIn.recoiler, "scaleAS", asScale);

    double alphaSinPS = (FSR) ? (*asFSR).alphaS(asScale)
                              : (*asISR).alphaS(asScale);
    w[0] *= alphaSinPS / as0;

    // Scale variations
    for (int iVar = 1; iVar < nWgts; ++iVar) {
      alphaSinPS = (FSR) ?
        asFSR->alphaS(pow2(mergingHooksPtr->muRVarFactors[iVar-1])*asScale) :
        asISR->alphaS(pow2(mergingHooksPtr->muRVarFactors[iVar-1])*asScale);
      // Respect variations in ME if present (NLO input)
      double muR2 = pow2(mergingHooksPtr->muRinMESave);
      double alphaSinME = (!asVarInME) ? as0 : ((FSR) ?
          asFSR->alphaS(muR2*pow2(mergingHooksPtr->muRVarFactors[iVar-1])) :
          asISR->alphaS(muR2*pow2(mergingHooksPtr->muRVarFactors[iVar-1])));
      w[iVar] *= alphaSinPS / alphaSinME;
    }
  }

  // Done
  return w;
}

//--------------------------------------------------------------------------

// Function to return the \alpha_em-ratio part of the CKKWL weight of a path.

vector<double> History::weightTreeAlphaEM( double aem0, AlphaEM * aemFSR,
  AlphaEM * aemISR, int njetMax ) {

  int nWgts = mergingHooksPtr->nWgts;

  // For ME state, do nothing.
  if ( !mother ) return vector<double>( nWgts, 1. );
  // Recurse
  vector<double> w = mother->weightTreeAlphaEM( aem0, aemFSR, aemISR,
      njetMax );
  // Do nothing for empty state
  if (state.size() < 3) return w;

  // If this node has too many jets, no not calculate no-emission probability.
  int njetNow = mergingHooksPtr->getNumberOfClusteringSteps( state) ;
  if (njetNow >= njetMax) return vector<double>( nWgts, 1.0 );

  // Store variables for easy use.
  bool FSR = mother->state[clusterIn.emittor].isFinal();
  int emtID = mother->state[clusterIn.emitted].id();

  // Do not correct alpha EM if it not an EW emission.
  if (!(abs(emtID) == 22 || abs(emtID) == 23 || abs(emtID) == 24)) return w;

  // Calculate alpha_s ratio for current state
  if ( aemFSR && aemISR ) {
    double aemScale = pow2( scale );
    if (mergingHooksPtr->unorderedASscalePrescip() == 1)
      aemScale = pow2( clusterIn.pT() );

    // Add regularisation scale to initial state alpha_em.
    if (!FSR) aemScale += pow2(mergingHooksPtr->pT0ISR());

    // Directly get argument of running alpha_em from shower plugin.
    if (mergingHooksPtr->useShowerPlugin() )
      aemScale = getShowerPluginScale(mother->state, clusterIn.emittor,
        clusterIn.emitted, clusterIn.recoiler, "scaleEM", aemScale);

    double alphaEMinPS = (FSR) ? (*aemFSR).alphaEM(aemScale)
                               : (*aemISR).alphaEM(aemScale);
    for (double& wi: w) wi *= alphaEMinPS / aem0;
  }

  // Done
  return w;
}

//--------------------------------------------------------------------------

// Function to return the PDF-ratio part of the CKKWL weight of a path.

vector<double> History::weightTreePDFs( double maxscale, double pdfScale,
  int njetMax ) {

  // Use correct scale
  double newScale = scale;

  double nWgts = mergingHooksPtr->nWgts;

  // For ME state, just multiply by PDF ratios
  if ( !mother ) {

    // If this node has too many jets, do not calculate PDF ratio.
    int njet = mergingHooksPtr->getNumberOfClusteringSteps( state);
    if (njet > njetMax) return vector<double>( nWgts, 1.0 );

    vector<double> wt( nWgts, 1. );
    int sideRad = (state[3].pz() > 0) ? 1 :-1;
    int sideRec = (state[4].pz() > 0) ? 1 :-1;

    // Calculate PDF first leg
    if (state[3].colType() != 0) {
      // Find x value and flavour
      double x = 2.*state[3].e() / state[0].e();
      int flav = state[3].id();
      // Find numerator/denominator scale
      double scaleNum = (children.empty()) ? hardFacScale(state) : maxscale;
      double scaleDen = mergingHooksPtr->muFinME();
      // For initial parton, multiply by PDF ratio
      double ratio = getPDFratio(sideRad, false, false, flav, x, scaleNum,
          flav, x, scaleDen);
      for (double& w: wt) w *= ratio;
    }

    // Calculate PDF ratio for second leg
    if (state[4].colType() != 0) {
      // Find x value and flavour
      double x = 2.*state[4].e() / state[0].e();
      int flav = state[4].id();
      // Find numerator/denominator scale
      double scaleNum = (children.empty()) ? hardFacScale(state) : maxscale;
      double scaleDen = mergingHooksPtr->muFinME();
      // For initial parton, multiply with PDF ratio
      double ratio = getPDFratio(sideRec, false, false, flav, x, scaleNum,
          flav, x, scaleDen);
      for (double& w: wt) w *= ratio;
    }

    return wt;
  }

  // Remember new PDF scale n case true scale should be used for un-ordered
  // splittings.
  double newPDFscale = newScale;
  if ( mergingHooksPtr->unorderedPDFscalePrescip() == 1)
    newPDFscale = clusterIn.pT();

  // Recurse
  vector<double> w = mother->weightTreePDFs( newScale, newPDFscale, njetMax );

  // Do nothing for empty state
  if (state.size() < 3) return w;

  // If this node has too many jets, do not calculate PDF ratio.
  int njetNow = mergingHooksPtr->getNumberOfClusteringSteps( state) ;
  if (njetNow > njetMax) return vector<double>( nWgts, 1. );

  // Calculate pdf ratios: Get both sides of event
  int inP = 3;
  int inM = 4;
  int sideP = (mother->state[inP].pz() > 0) ? 1 :-1;
  int sideM = (mother->state[inM].pz() > 0) ? 1 :-1;

  if ( mother->state[inP].colType() != 0 ) {
    // Find x value and flavour
    double x = getCurrentX(sideP);
    int flav = getCurrentFlav(sideP);
    // Find numerator scale
    double scaleNum = (children.empty())
                    ? hardFacScale(state)
                    : ( (mergingHooksPtr->unorderedPDFscalePrescip() == 1)
                      ? pdfScale : maxscale );
    double scaleDen = (mergingHooksPtr->unorderedPDFscalePrescip() == 1)
                    ? clusterIn.pT() : newScale;

    double xDen = (njetNow == njetMax) ? mother->getCurrentX(sideP) : x;
    int flavDen = (njetNow == njetMax) ? mother->getCurrentFlav(sideP) : flav;
    double sDen = (njetNow == njetMax) ? mergingHooksPtr->muFinME() : scaleDen;
    double ratio = getPDFratio(sideP, false, false, flav, x, scaleNum,
                     flavDen, xDen, sDen);
    for (double& wi: w) wi *= ratio;
  }

  if ( mother->state[inM].colType() != 0 ) {
    // Find x value and flavour
    double x = getCurrentX(sideM);
    int flav = getCurrentFlav(sideM);
    // Find numerator scale
    double scaleNum = (children.empty())
                    ? hardFacScale(state)
                    : ( (mergingHooksPtr->unorderedPDFscalePrescip() == 1)
                      ? pdfScale : maxscale );
    double scaleDen = (mergingHooksPtr->unorderedPDFscalePrescip() == 1)
                    ? clusterIn.pT() : newScale;

    double xDen = (njetNow == njetMax) ? mother->getCurrentX(sideM) : x;
    int flavDen = (njetNow == njetMax) ? mother->getCurrentFlav(sideM) : flav;
    double sDen = (njetNow == njetMax) ? mergingHooksPtr->muFinME() : scaleDen;
    double ratio = getPDFratio(sideM, false, false, flav, x, scaleNum,
                     flavDen, xDen, sDen);
    for (double& wi: w) wi *= ratio;
  }

  // Done
  return w;
}

//--------------------------------------------------------------------------

// Function to return the no-emission probability part of the CKKWL weight.

vector<double> History::weightTreeEmissions( PartonLevel* trial, int type,
  int njetMin, int njetMax, double maxscale ) {

  int nWgts = mergingHooksPtr->nWgts;

  if (type == -1 && !mergingHooksPtr->settingsPtr->flag("PartonLevel:MPI"))
    return vector<double>( nWgts, 1. );

  // Use correct scale
  double newScale = scale;
  // For ME state, just multiply by PDF ratios

  if ( !mother ) return vector<double>( nWgts, 1.0 );
  // Recurse
  vector<double> w = mother->weightTreeEmissions( trial, type, njetMin,
      njetMax, newScale );
  // Do nothing for empty state
  if (state.size() < 3) return vector<double>( nWgts, 1.0 );
  // If up to now, trial shower was not successful, return zero
  if ( w[0] < 1e-12 ) return vector<double>( nWgts, 0.0 );
  // If this node has too many jets, do not calculate no-emission probability.
  int njetNow = mergingHooksPtr->getNumberOfClusteringSteps( state) ;
  if (njetNow >= njetMax) return vector<double>( nWgts, 1.0);
  // Do trial shower on current state, return zero if not successful
  else {
    vector<double> wTrial = doTrialShower( trial, type, maxscale );
    for (int iVar = 0; iVar < nWgts; ++iVar) w[iVar] *= wTrial[iVar];
  }
  if ( w[0] < 1e-12 ) return vector<double>( nWgts, 0.0 );
  // Done
  return w;

}

//--------------------------------------------------------------------------

// Function to generate the O(\alpha_s)-term of the CKKWL-weight.

double History::weightFirst(PartonLevel* trial, double as0, double muR,
  double maxscale, AlphaStrong * asFSR, AlphaStrong * asISR, Rndm* rndmPtr ) {

  // Use correct scale
  double newScale = scale;

  if ( !mother ) {

    double weight = 0.;

    // Calculate PDF first leg
    if (state[3].colType() != 0) {
      // Find x value and flavour
      double x = 2.*state[3].e() / state[0].e();
      int flav = state[3].id();
      // Find numerator/denominator scale
      double scaleNum = (children.empty()) ? hardFacScale(state) : maxscale;
      double scaleDen = mergingHooksPtr->muFinME();
      // Monte Carlo integrand.
      double intPDF4 = monteCarloPDFratios(flav, x, scaleNum, scaleDen,
                         mergingHooksPtr->muFinME(), as0, rndmPtr);
      weight += intPDF4;
    }

    // Calculate PDF ratio for second leg
    if (state[4].colType() != 0) {
      // Find x value and flavour
      double x = 2.*state[4].e() / state[0].e();
      int flav = state[4].id();
      // Find numerator/denominator scale
      double scaleNum = (children.empty()) ? hardFacScale(state) : maxscale;
      double scaleDen = mergingHooksPtr->muFinME();
      // Monte Carlo integrand.
      double intPDF4 = monteCarloPDFratios(flav, x, scaleNum, scaleDen,
                         mergingHooksPtr->muFinME(), as0, rndmPtr);
      weight += intPDF4;
    }

    return weight;
  }

  // Recurse
  double w = mother->weightFirst(trial, as0, muR, newScale, asFSR, asISR,
               rndmPtr );

  // Do nothing for empty state
  if (state.size() < 3) return 0.0;

  // Find right scale
  double b = 1.;
  double asScale2 = newScale*newScale;
  int showerType = (mother->state[clusterIn.emittor].isFinal() ) ? 1 : -1;
  if (showerType == -1) {
    asScale2 += pow(mergingHooksPtr->pT0ISR(),2);
    b = 1.;
  }

  // Directly get argument of running alpha_s from shower plugin.
  if (mergingHooksPtr->useShowerPlugin() ){
    asScale2 = getShowerPluginScale(mother->state, clusterIn.emittor,
      clusterIn.emitted, clusterIn.recoiler, "scaleAS", asScale2);
    b = 1.;
  }

  // Find summand beta_0 / 2 * ln(muR^2/t_i) due to as expansion.
  double NF = 4.;
  double BETA0 = 11. - 2./3.* NF;
  // For fixed \alpha_s in matrix element
  w += as0 / (2.*M_PI) * 0.5 * BETA0 * log( (muR*muR) / (b*asScale2) );

  // Count emissions: New variant
  // Generate true average, not only one-point.
  bool fixpdf = true;
  bool fixas  = true;
  double nWeight1 = 0.;
  double nWeight2 = 0.;

  for(int i=0; i < NTRIAL; ++i) {
    // Get number of emissions
    vector<double> unresolvedEmissionTerm = countEmissions(trial, maxscale,
      newScale, 2, as0, asFSR, asISR, 3, fixpdf, fixas);
    nWeight1 += unresolvedEmissionTerm[1];
  }
  w += nWeight1/double(NTRIAL) + nWeight2/double(NTRIAL);

  // Calculate pdf ratios: Get both sides of event
  int inP = 3;
  int inM = 4;
  int sideP = (mother->state[inP].pz() > 0) ? 1 :-1;
  int sideM = (mother->state[inM].pz() > 0) ? 1 :-1;

  if ( mother->state[inP].colType() != 0 ) {
    // Find x value and flavour
    double x = getCurrentX(sideP);
    int flav = getCurrentFlav(sideP);
    // Find numerator scale
    double scaleNum = (children.empty()) ? hardFacScale(state) : maxscale;
    // Monte Carlo integrand.
    double intPDF4 = monteCarloPDFratios(flav, x, scaleNum, newScale,
                       mergingHooksPtr->muFinME(), as0, rndmPtr);
    w += intPDF4;

  }

  if ( mother->state[inM].colType() != 0 ) {
    // Find x value and flavour
    double x = getCurrentX(sideM);
    int flav = getCurrentFlav(sideM);
    // Find numerator scale
    double scaleNum = (children.empty()) ? hardFacScale(state) : maxscale;
    // Monte Carlo integrand.
    double intPDF4 = monteCarloPDFratios(flav, x, scaleNum, newScale,
                       mergingHooksPtr->muFinME(), as0, rndmPtr);
    w += intPDF4;

  }

  // Done
  return w;

}

//--------------------------------------------------------------------------

// Function to generate the O(\alpha_s)-term of the \alpha_s-ratios
// appearing in the CKKWL-weight.

double History::weightFirstAlphaS( double as0, double muR,
  AlphaStrong * asFSR, AlphaStrong * asISR ) {

  // Use correct scale
  double newScale = scale;
  // Done
  if ( !mother ) return 0.;
  // Recurse
  double w = mother->weightFirstAlphaS( as0, muR, asFSR, asISR );
  // Find right scale
  int showerType = (mother->state[clusterIn.emittor].isFinal() ) ? 1 : -1;
  double b = 1.;
  double asScale = pow2( newScale );
  if ( mergingHooksPtr->unorderedASscalePrescip() == 1 )
    asScale = pow2( clusterIn.pT() );
  if (showerType == -1) {
    asScale += pow2( mergingHooksPtr->pT0ISR() );
    b = 1.;
  }

  // Directly get argument of running alpha_s from shower plugin.
  if (mergingHooksPtr->useShowerPlugin() ) {
    asScale = getShowerPluginScale(mother->state, clusterIn.emittor,
      clusterIn.emitted, clusterIn.recoiler, "scaleAS", asScale);
    b = 1.;
  }

  // Find summand beta_0 / 2 * ln(muR^2/t_i) due to as expansion.
  double NF = 4.;
  double BETA0 = 11. - 2./3.* NF;
  // For fixed \alpha_s in matrix element
  w += as0 / (2.*M_PI) * 0.5 * BETA0 * log( (muR*muR) / (b*asScale) );

  // Done
  return w;

}

//--------------------------------------------------------------------------

// Function to generate the O(\alpha_s)-term of the PDF-ratios
// appearing in the CKKWL-weight.

double History::weightFirstPDFs( double as0, double maxscale, double pdfScale,
  Rndm* rndmPtr ) {

  // Use correct scale
  double newScale = scale;

  if ( !mother ) {

    double wt = 0.;

    // Calculate PDF first leg
    if (state[3].colType() != 0) {
      // Find x value and flavour
      double x        = 2.*state[3].e() / state[0].e();
      int flav        = state[3].id();
      // Find numerator/denominator scale
      double scaleNum = (children.empty()) ? hardFacScale(state) : maxscale;
      double scaleDen = mergingHooksPtr->muFinME();
      // Monte Carlo integrand.
      wt += monteCarloPDFratios(flav, x, scaleNum, scaleDen,
                          mergingHooksPtr->muFinME(), as0, rndmPtr);
    }
    // Calculate PDF ratio for second leg
    if (state[4].colType() != 0) {
      // Find x value and flavour
      double x        = 2.*state[4].e() / state[0].e();
      int flav        = state[4].id();
      // Find numerator/denominator scale
      double scaleNum = (children.empty()) ? hardFacScale(state) : maxscale;
      double scaleDen = mergingHooksPtr->muFinME();
      // Monte Carlo integrand.
      wt += monteCarloPDFratios(flav, x, scaleNum, scaleDen,
                         mergingHooksPtr->muFinME(), as0, rndmPtr);
    }

    // Done
    return wt;
  }

  // Remember new PDF scale n case true scale should be used for un-ordered
  // splittings.
  double newPDFscale = newScale;
  if (mergingHooksPtr->unorderedPDFscalePrescip() == 1)
    newPDFscale      = clusterIn.pT();

  // Recurse
  double w = mother->weightFirstPDFs( as0, newScale, newPDFscale, rndmPtr);

  // Calculate pdf ratios: Get both sides of event
  int inP   = 3;
  int inM   = 4;
  int sideP = (mother->state[inP].pz() > 0) ? 1 :-1;
  int sideM = (mother->state[inM].pz() > 0) ? 1 :-1;

  if ( mother->state[inP].colType() != 0 ) {
    // Find x value and flavour
    double x        = getCurrentX(sideP);
    int flav        = getCurrentFlav(sideP);
    // Find numerator / denominator scales
    double scaleNum = (children.empty())
                    ? hardFacScale(state)
                    : ( (mergingHooksPtr->unorderedPDFscalePrescip() == 1)
                      ? pdfScale : maxscale );
    double scaleDen = (mergingHooksPtr->unorderedPDFscalePrescip() == 1)
                    ? clusterIn.pT() : newScale;
    // Monte Carlo integrand.
    w += monteCarloPDFratios(flav, x, scaleNum, scaleDen,
                        mergingHooksPtr->muFinME(), as0, rndmPtr);
  }

  if ( mother->state[inM].colType() != 0 ) {
    // Find x value and flavour
    double x        = getCurrentX(sideM);
    int flav        = getCurrentFlav(sideM);
    // Find numerator / denominator scales
    double scaleNum = (children.empty())
                    ? hardFacScale(state)
                    : ( (mergingHooksPtr->unorderedPDFscalePrescip() == 1)
                      ? pdfScale : maxscale );
    double scaleDen = (mergingHooksPtr->unorderedPDFscalePrescip() == 1)
                    ? clusterIn.pT() : newScale;
    // Monte Carlo integrand.
    w += monteCarloPDFratios(flav, x, scaleNum, scaleDen,
                        mergingHooksPtr->muFinME(), as0, rndmPtr);
  }

  // Done
  return w;

}


//--------------------------------------------------------------------------

// Function to generate the O(\alpha_s)-term of the no-emission
// probabilities appearing in the CKKWL-weight.

double History::weightFirstEmissions(PartonLevel* trial, double as0,
  double maxscale, AlphaStrong * asFSR, AlphaStrong * asISR,
  bool fixpdf, bool fixas ) {

  // Use correct scale
  double newScale = scale;
  if ( !mother ) return 0.0;
  // Recurse
  double w = mother->weightFirstEmissions(trial, as0, newScale, asFSR, asISR,
                                          fixpdf, fixas );
  // Do nothing for empty state
  if (state.size() < 3) return 0.0;
  // Generate true average.
  double nWeight1 = 0.;
  double nWeight2 = 0.;
  for(int i=0; i < NTRIAL; ++i) {
    // Get number of emissions
    vector<double> unresolvedEmissionTerm = countEmissions(trial, maxscale,
      newScale, 2, as0, asFSR, asISR, 3, fixpdf, fixas);
    nWeight1 += unresolvedEmissionTerm[1];
  }

  w += nWeight1/double(NTRIAL) + nWeight2/double(NTRIAL);

  // Done
  return w;

}

//--------------------------------------------------------------------------

// Function to return the factorisation scale of the hard process in Pythia.

double History::hardFacScale(const Event& event) {
  // Declare output scale.
  double hardscale = 0.;
  // If scale should not be reset, done.
  if ( !mergingHooksPtr->resetHardQFac() ) return mergingHooksPtr->muF();
  // For pure QCD dijet events, calculate the hadronic cross section
  // of the hard process at the pT of the dijet system, rather than at fixed
  // arbitrary scale.
  if ( mergingHooksPtr->getProcessString().compare("pp>jj") == 0
    || mergingHooksPtr->getProcessString().compare("pp>aj") == 0
    || isQCD2to2(event)) {
    // Find the mT in the hard sub-process.
    vector <double> mT;
    for ( int i=0; i < event.size(); ++i)
      if ( event[i].isFinal() && event[i].colType() != 0 )
        mT.push_back( abs(event[i].mT2()) );
    if ( int(mT.size()) != 2 )
      hardscale = infoPtr->QFac();
    else
      hardscale = sqrt( min( mT[0], mT[1] ) );
  } else {
    hardscale = mergingHooksPtr->muF();
  }
  // Done
  return hardscale;
}

//--------------------------------------------------------------------------

// Function to return the factorisation scale of the hard process in Pythia.

double History::hardRenScale(const Event& event) {
  // Declare output scale.
  double hardscale = 0.;
  // If scale should not be reset, done.
  if ( !mergingHooksPtr->resetHardQRen() ) return mergingHooksPtr->muR();
  // For pure QCD dijet events, calculate the hadronic cross section
  // of the hard process at the pT of the dijet system, rather than at fixed
  // arbitrary scale.
  if ( mergingHooksPtr->getProcessString().compare("pp>jj") == 0
       || mergingHooksPtr->getProcessString().compare("pp>aj") == 0
       || isQCD2to2(event)) {
    // Find the mT in the hard sub-process.
    vector <double> mT;
    for ( int i=0; i < event.size(); ++i)
      if ( event[i].isFinal()
        && ( event[i].colType() != 0 || event[i].id() == 22 ) )
        mT.push_back( abs(event[i].mT()) );
    if ( int(mT.size()) != 2 )
      hardscale = infoPtr->QRen();
    else
      hardscale = sqrt( mT[0]*mT[1] );
  } else {
    hardscale = mergingHooksPtr->muR();
  }
  // Done
  return hardscale;
}

//--------------------------------------------------------------------------

// Perform a trial shower using the \a pythia object between
// maxscale down to this scale and return the corresponding Sudakov
// form factor.
// IN  trialShower : Shower object used as trial shower
//     double     : Maximum scale for trial shower branching
// OUT  0.0       : trial shower emission outside allowed pT range
//      1.0       : trial shower successful (any emission was below
//                  the minimal scale )

vector<double> History::doTrialShower( PartonLevel* trial, int type,
  double maxscaleIn, double minscaleIn ) {

  // Copy state to local process
  Event process        = state;
  // Set starting scale.
  double startingScale = maxscaleIn;
  // Careful when setting shower starting scale for pure QCD and prompt
  // photon case.
  if ( mergingHooksPtr->getNumberOfClusteringSteps(process) == 0
    && ( mergingHooksPtr->getProcessString().compare("pp>jj") == 0
         || mergingHooksPtr->getProcessString().compare("pp>aj") == 0
         || isQCD2to2(state) ) )
      startingScale = min( startingScale, hardFacScale(process) );

  int nWgts = mergingHooksPtr->nWgts;

  // Set output.
  bool doVeto          = false;
  bool canEnhanceTrial = trial->canEnhanceTrial();

  // Save shower weight vector before variation
  vector<double> showerWeightVecSave = infoPtr->
    weightContainerPtr->weightsSimpleShower.weightValues;
  // Set shower weights to 1.
  for (double &showerwt: infoPtr->weightContainerPtr
         ->weightsSimpleShower.weightValues)
    showerwt = 1.;
  // Get vector of shower weights, now just vector of 1. of correct length
  vector<double> wt( nWgts, 1.);

  while (true) {

    // Reset trialShower object
    trial->resetTrial();
    // Set shower weights to 1. for each enhanced emission
    if (canEnhanceTrial)
      for (double &showerwt: infoPtr->weightContainerPtr
             ->weightsSimpleShower.weightValues)
        showerwt = 1.;
    // Construct event to be showered
    Event event = Event();
    event.init("(hard process-modified)", particleDataPtr);
    event.clear();

    // Reset process scale so that shower starting scale is correctly set.
    process.scale(startingScale);
    doVeto = false;

    // Get pT before reclustering
    double minScale = (minscaleIn > 0.) ? minscaleIn : scale;

    // If the maximal scale and the minimal scale coincide (as would
    // be the case for the corrected scales of unordered histories),
    // do not generate Sudakov
    if (minScale >= startingScale) break;

    // Find z and pT values at which the current state was formed, to
    // ensure that the showers can order the next emission correctly in
    // rapidity, if required.
    // NOT CORRECTLY SET FOR HIGHEST MULTIPLICITY STATE!
    double z = ( mergingHooksPtr->getNumberOfClusteringSteps(state) == 0
               || !mother )
             ? 0.5
             : mother->getCurrentZ(clusterIn.emittor,clusterIn.recoiler,
                 clusterIn.emitted, clusterIn.flavRadBef);
    // Store z and pT values at which the current state was formed.
    infoPtr->zNowISR(z);
    infoPtr->pT2NowISR(pow(startingScale,2));
    infoPtr->hasHistory(true);

    // Setup weak shower settings.
    if (mergingHooksPtr->doWeakClustering()) setupSimpleWeakShower(0);

    // Make sure trial shower stops where it should
    mergingHooksPtr->setShowerStoppingScale(minScale);
    // Perform trial shower emission
    trial->next(process,event);
    // Get trial shower pT.
    double pTtrial   = trial->pTLastInShower();
    int typeTrial    = trial->typeLastInShower();

    // Clear parton systems.
    trial->resetTrial();

    // Get enhanced trial emission weight.
    double pTEnhanced = trial->getEnhancedTrialPT();
    double wtEnhanced = trial->getEnhancedTrialWeight();
    if ( canEnhanceTrial && pTEnhanced > 0.) pTtrial = pTEnhanced;

    // Get veto (merging) scale value
    double vetoScale  = (mother) ? 0. : mergingHooksPtr->tms();
    // Get merging scale in current event
    double tnow = mergingHooksPtr->tmsNow( event );

    // Done if evolution scale has fallen below minimum
    if ( pTtrial < minScale ) break;
    // Reset starting scale.
    startingScale = pTtrial;

    // Continue if this state is below the veto scale
    if ( tnow < vetoScale && vetoScale > 0. ) continue;

    // Retry if the trial emission was not allowed.
    if ( mergingHooksPtr->canVetoTrialEmission()
      && mergingHooksPtr->doVetoTrialEmission( process, event) ) continue;

    int iRecAft = event.size() - 1;
    int iEmt    = event.size() - 2;
    int iRadAft = event.size() - 3;
    if ( (event[iRecAft].status() != 52 && event[iRecAft].status() != -53) ||
         event[iEmt].status() != 51 || event[iRadAft].status() != 51)
      iRecAft = iEmt = iRadAft = -1;
    for (int i = event.size() - 1; i > 0; i--) {
      if      (iRadAft == -1 && event[i].status() == -41) iRadAft = i;
      else if (iEmt    == -1 && event[i].status() ==  43) iEmt    = i;
      else if (iRecAft == -1 && event[i].status() == -42) iRecAft = i;
      if (iRadAft != -1 && iEmt != -1 && iRecAft != -1) break;
    }

    // Only consider allowed emissions for veto:
    // Only allow MPI for MPI no-emission probability.
    if ( type == -1 && typeTrial != 1 ) continue;
    // Only allow ISR or FSR for radiative no-emission probability.
    if ( type ==  1 && !(typeTrial == 2 || typeTrial >= 3) ) continue;

    // Update enhanced trial shower weight. (1.-1./wtEnhanced) usual veto
    // factor, only variation factor applied in shower
    if (canEnhanceTrial && pTtrial > minScale) {
      vector<double> showerVar = infoPtr->weightContainerPtr->
        weightsSimpleShower.getMuRWeightVector();
      wt[0] *= (1.-1./wtEnhanced);
      for (int i = 1; i < nWgts; ++i) wt[i] *= (1. - showerVar[i]/wtEnhanced);
    }
    // Done with enhanced trial showers if weight is zero.
    if ( canEnhanceTrial && wt[0] == 0.) break;
    // Continue producing trial emissions in case of enhanced showers.
    if ( canEnhanceTrial && pTtrial > minScale) continue;

    // Continue if this state is below the veto scale
    // Veto event if trial pT was above the next nodal scale.
    if ( pTtrial > minScale ) doVeto = true;

    //// For last no-emission probability, veto event if the trial state
    //// is above the merging scale, i.e. in the matrix element region.
    //if ( !mother && tnow > vetoScale && vetoScale > 0. ) doVeto = true;

    // For 2 -> 2 pure QCD state, do not allow multiparton interactions
    // above the kinematical pT of the 2 -> 2 state.
    if ( type == -1
      && typeTrial == 1
      && mergingHooksPtr->getNumberOfClusteringSteps(process) == 0
      && ( mergingHooksPtr->getProcessString().compare("pp>jj") == 0
        || mergingHooksPtr->getProcessString().compare("pp>aj") == 0
           || isQCD2to2(state))
      && pTtrial > hardFacScale(process) ) {
      // Reset shower weights
      infoPtr->weightContainerPtr->weightsSimpleShower.weightValues =
        showerWeightVecSave;
      return vector<double>( nWgts, 0.0 );
    }

    // If pT of trial emission was in suitable range (trial shower
    // successful), return false
    if ( pTtrial < minScale ) doVeto = false;

    // Done
    break;
  }

  // Get combination of shower weights for muR variation in FSR and ISR
  vector<double> trialShowerWt =
    infoPtr->weightContainerPtr->weightsSimpleShower.getMuRWeightVector();

  // If not enhanced, apply veto to weights accumulated in shower
  if (!canEnhanceTrial) {
    wt[0] = trialShowerWt[0] * ((doVeto) ? 0. : 1.);
    for (int i = 1; i < nWgts; ++i) wt[i] = wt[0]*trialShowerWt[i];
  }
  // If MPI, no variation allowed (no-emission variations would bleed in from
  // shower without this catch)
  if (type == -1)
    for (size_t i = 1; i < wt.size(); ++i) wt[i] = wt[0];
  // Reset shower weights
  infoPtr->weightContainerPtr->weightsSimpleShower.weightValues =
    showerWeightVecSave;

  return wt;

}

//--------------------------------------------------------------------------

// Assume we have a vector of i elements containing indices into
// another vector with N elements. Update the indices so that all
// unique combinations (starting from 0,1,2,3, ...) are
// covered. Return false when all combinations have been ehausted.

bool History::updateind(vector<int> & ind, int i, int N) {
  if ( i < 0 ) return false;
  if ( ++ind[i] < N ) return true;
  if ( !updateind(ind, i - 1, N - 1) ) return false;
  ind[i] = ind[i - 1] + 1;
  return true;
}

//--------------------------------------------------------------------------

// Return the expansion of the no-emission probability up to the Nth
// term. Optionally calculate the the terms using fixed alphaS
// and/or PDF ratios.

vector<double> History::countEmissions(PartonLevel* trial, double maxscale,
                        double minscale, int showerType, double as0,
                        AlphaStrong * asFSR, AlphaStrong * asISR, int N = 1,
                        bool fixpdf = true, bool fixas = true) {

  if ( N < 0 ) return vector<double>();
  vector<double> result(N+1);
  result[0] = 1.0;
  if ( N < 1 ) return result;

  // Copy state to local process
  Event process = state;

  double startingScale   = maxscale;
  // Careful when setting shower starting scale for pure QCD and prompt
  // photon case.
  if ( mergingHooksPtr->getNumberOfClusteringSteps(process) == 0
    && ( mergingHooksPtr->getProcessString().compare("pp>jj") == 0
      || mergingHooksPtr->getProcessString().compare("pp>aj") == 0
         || isQCD2to2(state) ) )
      startingScale = min( startingScale, hardFacScale(process) );

  vector<double> wts;
  bool canEnhanceTrial = trial->canEnhanceTrial();

  // Save shower weight vector before variation
  vector<double> showerWeightVecSave = infoPtr->
    weightContainerPtr->weightsSimpleShower.weightValues;

  while ( true ) {
    // Reset trialShower object
    trial->resetTrial();
    // Set shower weights to 1.
    for (double &wt: infoPtr->weightContainerPtr
           ->weightsSimpleShower.weightValues) wt = 1.;
    // Construct event to be showered
    Event event = Event();
    event.init("(hard process-modified)", particleDataPtr);
    event.clear();

    // Reset process scale
    process.scale(startingScale);

    // If the maximal scale and the minimal scale coincide (as would
    // be the case for the corrected scales of unordered histories),
    // do not generate Sudakov
    if (minscale >= startingScale) return result;

    // Find z and pT values at which the current state was formed, to
    // ensure that the showers can order the next emission correctly in
    // rapidity, if required
    if ( mother ) {
      double z = ( mergingHooksPtr->getNumberOfClusteringSteps(state) == 0)
               ? 0.5
               : mother->getCurrentZ(clusterIn.emittor,clusterIn.recoiler,
                   clusterIn.emitted);
      // Store z and pT values at which the current state was formed
      infoPtr->zNowISR(z);
      infoPtr->pT2NowISR(pow(startingScale,2));
      infoPtr->hasHistory(true);
    }

    // Setup the weak shower information.
    if (mergingHooksPtr->doWeakClustering()) setupSimpleWeakShower(0);

    // Perform trial shower emission
    trial->next(process,event);

    // Get trial shower pT
    double pTtrial = trial->pTLastInShower();
    int typeTrial  = trial->typeLastInShower();

    // Restore weight vector, since variation higher order
    infoPtr->weightContainerPtr->weightsSimpleShower.weightValues
      = showerWeightVecSave;

    // Clear parton systems.
    trial->resetTrial();

    // Get enhanced trial emission weight.
    double pTEnhanced = trial->getEnhancedTrialPT();
    double wtEnhanced = trial->getEnhancedTrialWeight();
    if ( canEnhanceTrial && pTEnhanced > 0.) pTtrial = pTEnhanced;

    // Get veto (merging) scale value
    double vetoScale  = (mother) ? 0. : mergingHooksPtr->tms();
    // Get merging scale in current event
    double tnow = mergingHooksPtr->tmsNow( event );

    // Save scale of current state.
    startingScale   = pTtrial;
    // If the scale of the current state is below the minimal scale, exit.
    if ( pTtrial < minscale ) break;
    // If this state is below the merging scale, do not count emission.
    if ( tnow < vetoScale && vetoScale > 0. ) continue;
    // Retry if the trial emission was not allowed.
    if ( mergingHooksPtr->canVetoTrialEmission()
      && mergingHooksPtr->doVetoTrialEmission( process, event) ) continue;

    // Set weight of enhanced emission.
    double enhance = (canEnhanceTrial && pTtrial > minscale) ? wtEnhanced : 1.;

    // Check if a new emission should be generated, either because
    // the latest emission was not of the desired kind or if the
    // emission was above the minimal scale
    double alphaSinPS = as0;
    double pdfs = 1.0;

    double asScale2 = pTtrial*pTtrial;
    // Directly get argument of running alpha_s from shower plugin.
    if (mergingHooksPtr->useShowerPlugin() )
      asScale2 = getShowerPluginScale(mother->state, clusterIn.emittor,
        clusterIn.emitted, clusterIn.recoiler, "scaleAS", asScale2);

    // Initial state splittings.
    if ( (showerType == -1 || showerType == 2) && typeTrial == 2 ) {
      // Get weight to translate to alpha_s at fixed renormalisation scale.
      if ( fixas ) alphaSinPS = (*asISR).alphaS(asScale2);
      // Get weight to translate to PDFs at fixed factorisation scale.
      if ( fixpdf )
        pdfs = pdfFactor( event, typeTrial, pTtrial,
                          mergingHooksPtr->muFinME() );
    // Final state splittings.
    } else if ( (showerType == 1 || showerType == 2) && typeTrial >= 3 ) {
      // Get weight to translate to alpha_s at fixed renormalisation scale.
      if ( fixas ) alphaSinPS = (*asFSR).alphaS(asScale2);
      // Get weight to translate to PDFs at fixed factorisation scale. Needed
      // for final state splittings with initial state recoiler.
      if ( fixpdf )
        pdfs = pdfFactor( event, typeTrial, pTtrial,
                          mergingHooksPtr->muFinME() );
    }

    // Save weight correcting to emission generated with fixed scales.
    if ( typeTrial == 2 || typeTrial >= 3 )
      wts.push_back(as0/alphaSinPS * pdfs * 1./enhance);

  }

  for ( int n = 1; n <= min(N, int(wts.size())); ++n ) {
    vector<int> ind(N);
    for ( int i = 0; i < N; ++i ) ind[i] = i;
    do {
      double x = 1.0;
      for ( int j = 0; j < n; ++j ) x *= wts[ind[j]];
      result[n] += x;
    }  while ( updateind(ind, n - 1, wts.size()) );
    if ( n%2 ) result[n] *= -1.0;
  }

  // Done
  return result;
}

//--------------------------------------------------------------------------

// Function to integrate PDF ratios between two scales over x and t,
// where the PDFs are always evaluated at the lower t-integration limit

double History::monteCarloPDFratios(int flav, double x, double maxScale,
         double minScale, double pdfScale, double asME, Rndm* rndmPtr) {

  // Perform numerical integration for PDF ratios
  // Prefactor is as/2PI
  double factor = asME / (2.*M_PI);
  // Scale integration just produces a multiplicative logarithm
  factor *= log(maxScale/minScale);

  // For identical scales, done
  if (factor == 0.) return 0.;

  // Declare constants
  double CF = 4./3.;
  double CA = 3.;
  double NF = 4.;
  double TR = 1./2.;

  double integral = 0.;
  double RN = rndmPtr->flat();

  if (flav == 21) {
    double zTrial = pow(x,RN);
    integral  = -log(x) * zTrial *
                integrand(flav, x, pdfScale, zTrial);
    integral += 1./6.*(11.*CA - 4.*NF*TR)
              + 2.*CA*log(1.-x);
  } else {
    double zTrial = x + RN*(1. - x);
    integral  = (1.-x) *
                integrand(flav, x, pdfScale, zTrial);
    integral += 3./2.*CF
              + 2.*CF*log(1.-x);
  }

  // Done
  return (factor*integral);
}

/*--------------- METHODS USED FOR CONTRUCTION OF ALL HISTORIES --------- */

// Check if a ordered (and complete) path has been found in the
// initial node, in which case we will no longer be interested in
// any unordered paths.

bool History::onlyOrderedPaths() {
  if ( !mother || foundOrderedPath ) return foundOrderedPath;
  return  foundOrderedPath = mother->onlyOrderedPaths();
}

//--------------------------------------------------------------------------

// Check if a STRONGLY ordered (and complete) path has been found in the
// initial node, in which case we will no longer be interested in
// any unordered paths.

bool History::onlyStronglyOrderedPaths() {
  if ( !mother || foundStronglyOrderedPath ) return foundStronglyOrderedPath;
  return  foundStronglyOrderedPath = mother->onlyStronglyOrderedPaths();
}

//--------------------------------------------------------------------------

// Check if an allowed (according to user-criterion) path has been found in
// the initial node, in which case we will no longer be interested in
// any forbidden paths.

bool History::onlyAllowedPaths() {
  if ( !mother || foundAllowedPath ) return foundAllowedPath;
  return foundAllowedPath = mother->onlyAllowedPaths();
}

//--------------------------------------------------------------------------

// When a full path has been found, register it with the initial
// history node.
// IN  History : History to be registered as path
//     bool    : Specifying if clusterings so far were ordered
//     bool    : Specifying if path is complete down to 2->2 process
// OUT true if History object forms a plausible path (eg prob>0 ...)

bool History::registerPath(History & l, bool isOrdered,
       bool isStronglyOrdered, bool isAllowed, bool isComplete) {

  // We are not interested in improbable paths.
  if ( l.prob <= 0.0)
    return false;
  // We only register paths in the initial node.
  if ( mother ) return mother->registerPath(l, isOrdered,
                         isStronglyOrdered, isAllowed, isComplete);

  // Again, we are not interested in improbable paths.
  if ( sumpath == sumpath + l.prob )
    return false;
  if ( mergingHooksPtr->canCutOnRecState()
    && foundAllowedPath && !isAllowed )
    return false;
  if ( mergingHooksPtr->enforceStrongOrdering()
    && foundStronglyOrderedPath && !isStronglyOrdered )
    return false;
  if ( mergingHooksPtr->orderHistories()
    && foundOrderedPath && !isOrdered ) {
    // Prefer complete or allowed paths to ordered paths.
    if ( (!foundCompletePath && isComplete)
      || (!foundAllowedPath && isAllowed) ) ;
    else return false;
  }

  if ( foundCompletePath && !isComplete)
    return false;
  if ( !mergingHooksPtr->canCutOnRecState()
    && !mergingHooksPtr->allowCutOnRecState() )
    foundAllowedPath = true;

  if ( mergingHooksPtr->canCutOnRecState() && isAllowed && isComplete) {
    if ( !foundAllowedPath || !foundCompletePath ) {
      // If this is the first complete, allowed path, discard the
      // old, disallowed or incomplete ones.
      paths.clear();
      sumpath = 0.0;
    }
    foundAllowedPath = true;

  }

  if ( mergingHooksPtr->enforceStrongOrdering() && isStronglyOrdered
     && isComplete ) {
    if ( !foundStronglyOrderedPath || !foundCompletePath ) {
      // If this is the first complete, ordered path, discard the
      // old, non-ordered or incomplete ones.
      paths.clear();
      sumpath = 0.0;
    }
    foundStronglyOrderedPath = true;
    foundCompletePath = true;

  }

  if ( mergingHooksPtr->orderHistories() && isOrdered && isComplete ) {
    if ( !foundOrderedPath || !foundCompletePath ) {
      // If this is the first complete, ordered path, discard the
      // old, non-ordered or incomplete ones.
      paths.clear();
      sumpath = 0.0;
    }
    foundOrderedPath = true;
    foundCompletePath = true;

  }

  if ( isComplete ) {
    if ( !foundCompletePath ) {
      // If this is the first complete path, discard the old,
      // incomplete ones.
      paths.clear();
      sumpath = 0.0;
    }
    foundCompletePath = true;
  }

  // Remember, if this path is ordered, even if no ordering is required
  if ( isOrdered ) {
    foundOrderedPath = true;
  }

  // Calculate the probability for weak emissions in the path.
  double weakProb = 1.;
  if (mergingHooksPtr->doWeakClustering())
    weakProb = l.getWeakProb();

  // Index path by probability
  sumpath += l.prob * weakProb;
  paths[sumpath] = &l;

  updateProbMax(l.prob * weakProb, isComplete);

  return true;
}

//--------------------------------------------------------------------------

// For the history-defining state (and if necessary interfering
// states), find all possible clusterings.
// NO INPUT
// OUT vector of all (rad,rec,emt) systems

vector<Clustering> History::getAllQCDClusterings() {
  vector<Clustering> ret;
  // Initialise vectors to keep track of position of partons in the
  // history-defining state
  vector <int> posFinalPartn;
  vector <int> posInitPartn;
  vector <int> posFinalGluon;
  vector <int> posFinalQuark;
  vector <int> posFinalAntiq;
  vector <int> posInitGluon;
  vector <int> posInitQuark;
  vector <int> posInitAntiq;

  // Search event record for final state particles and store these in
  // quark, anti-quark and gluon vectors
  for ( int i=0; i < state.size(); ++i )
    if ( state[i].isFinal() && state[i].colType() !=0 ) {
      // Store final partons
      if ( state[i].id() == 21 ) posFinalGluon.push_back(i);
      else if ( state[i].idAbs() < 10 && state[i].id() > 0)
        posFinalQuark.push_back(i);
      else if ( state[i].idAbs() < 10 && state[i].id() < 0)
        posFinalAntiq.push_back(i);
    } else if (state[i].status() == -21 && state[i].colType() != 0 ) {
      // Store initial partons
      if ( state[i].id() == 21 ) posInitGluon.push_back(i);
      else if ( state[i].idAbs() < 10 && state[i].id() > 0)
        posInitQuark.push_back(i);
      else if ( state[i].idAbs() < 10 && state[i].id() < 0)
        posInitAntiq.push_back(i);
    }

  // Get all clusterings for input state
  vector<Clustering> systems;
  systems = getQCDClusterings(state);
  ret.insert(ret.end(), systems.begin(), systems.end());
  systems.resize(0);

  // If valid clusterings were found, return
  if ( !ret.empty() ) return ret;
  // If no clusterings have been found until now, try to find
  // clusterings of diagrams that interfere with the current one
  // (i.e. change the colours of the current event slightly and run
  //  search again)
  else if ( mergingHooksPtr->allowColourShuffling() ) {
    Event NewState = Event(state);
    // Start with changing final state quark colour
    for(int i = 0; i < int(posFinalQuark.size()); ++i) {
      // Never change the hard process candidates
      if ( mergingHooksPtr->hardProcess->matchesAnyOutgoing(posFinalQuark[i],
       NewState) )
        continue;
      int col = NewState[posFinalQuark[i]].col();
      for(int j = 0; j < int(posInitAntiq.size()); ++j) {
        // Now swap colours
        int acl = NewState[posInitAntiq[j]].acol();
        if ( col == acl ) continue;
        NewState[posFinalQuark[i]].col(acl);
        NewState[posInitAntiq[j]].acol(col);
        systems = getQCDClusterings(NewState);
        if (!systems.empty()) {
          state = NewState;
          NewState.clear();
          ret.insert(ret.end(), systems.begin(), systems.end());
          systems.resize(0);
          return ret;
        }
      }
    }
    // Now change final state antiquark anticolour
    for(int i = 0; i < int(posFinalAntiq.size()); ++i) {
      // Never change the hard process candidates
      if ( mergingHooksPtr->hardProcess->matchesAnyOutgoing(posFinalAntiq[i],
       NewState) )
        continue;
      int acl = NewState[posFinalAntiq[i]].acol();
      for(int j = 0; j < int(posInitQuark.size()); ++j) {
        // Now swap colours
        int col = NewState[posInitQuark[j]].col();
        if ( col == acl ) continue;
        NewState[posFinalAntiq[i]].acol(col);
        NewState[posInitQuark[j]].col(acl);
        systems = getQCDClusterings(NewState);
        if (!systems.empty()) {
          state = NewState;
          NewState.clear();
          ret.insert(ret.end(), systems.begin(), systems.end());
          systems.resize(0);
          return ret;
        }
      }
    }

  }

  // Done
  return ret;
}

//--------------------------------------------------------------------------

// For one given state, find all possible clusterings.
// IN  Event : state to be investigated
// OUT vector of all (rad,rec,emt) systems in the state

vector<Clustering> History::getQCDClusterings( const Event& event) {
  vector<Clustering> ret;

  // Initialise vectors to keep track of position of partons in the
  // input event
  vector <int> posFinalPartn;
  vector <int> posInitPartn;

  vector <int> posFinalGluon;
  vector <int> posFinalQuark;
  vector <int> posFinalAntiq;
  vector <int> posInitGluon;
  vector <int> posInitQuark;
  vector <int> posInitAntiq;

  // Search event record for final state particles and store these in
  // quark, anti-quark and gluon vectors
  for (int i=0; i < event.size(); ++i)
    if ( event[i].isFinal() && event[i].colType() !=0 ) {
      // Store final partons
      posFinalPartn.push_back(i);
      if ( event[i].id() == 21 ) posFinalGluon.push_back(i);
      else if ( event[i].idAbs() < 10 && event[i].id() > 0)
        posFinalQuark.push_back(i);
      else if ( event[i].idAbs() < 10 && event[i].id() < 0)
        posFinalAntiq.push_back(i);
    } else if ( event[i].status() == -21 && event[i].colType() != 0 ) {
      // Store initial partons
      posInitPartn.push_back(i);
      if ( event[i].id() == 21 ) posInitGluon.push_back(i);
      else if ( event[i].idAbs() < 10 && event[i].id() > 0)
        posInitQuark.push_back(i);
      else if ( event[i].idAbs() < 10 && event[i].id() < 0)
        posInitAntiq.push_back(i);
    }

  int nFiGluon = int(posFinalGluon.size());
  int nFiQuark = int(posFinalQuark.size());
  int nFiAntiq = int(posFinalAntiq.size());
  int nInGluon = int(posInitGluon.size());
  int nInQuark = int(posInitQuark.size());
  int nInAntiq = int(posInitAntiq.size());

  vector<Clustering> systems;

  // Find rad + emt + rec systems:
  // (1) Start from gluon and find all (rad,rec,emt=gluon) triples
  for (int i = 0; i < nFiGluon; ++i) {
    int EmtGluon = posFinalGluon[i];
    systems = findQCDTriple( EmtGluon, 2, event, posFinalPartn, posInitPartn);
    ret.insert(ret.end(), systems.begin(), systems.end());
    systems.resize(0);
  }

  // For more than one quark-antiquark pair in final state, check for
  // g -> qqbar splittings
  bool check_g2qq = true;
  if ( ( ( nInQuark + nInAntiq == 0 )
          && (nInGluon == 0)
          && (nFiQuark == 1) && (nFiAntiq == 1) )
    || ( ( nFiQuark + nFiAntiq == 0)
          && (nInQuark == 1) && (nInAntiq == 1) ) )
    check_g2qq = false;

  if ( check_g2qq ) {

    // (2) Start from quark and find all (rad,rec,emt=quark) triples
    //     ( when g -> q qbar occured )
    for( int i=0; i < nFiQuark; ++i) {
      int EmtQuark = posFinalQuark[i];
      systems = findQCDTriple( EmtQuark,1,event, posFinalPartn, posInitPartn);
      ret.insert(ret.end(), systems.begin(), systems.end());
      systems.resize(0);
    }

    // (3) Start from anti-quark and find all (rad,rec,emt=anti-quark)
    //     triples ( when g -> q qbar occured )
    for( int i=0; i < nFiAntiq; ++i) {
      int EmtAntiq = posFinalAntiq[i];
      systems = findQCDTriple( EmtAntiq,1,event, posFinalPartn, posInitPartn);
      ret.insert(ret.end(), systems.begin(), systems.end());
      systems.resize(0);
    }
  }

  return ret;
}

//--------------------------------------------------------------------------

// Function to attach (spin-dependent duplicates of) a clustering.

void History::attachClusterings (vector<Clustering>& clus, int iEmt, int iRad,
    int iRec, int iPartner, double pT, const Event& event) {

  if ( !mergingHooksPtr->doWeakClustering() ) {

    // Do nothing for kinematically forbidden state.
    if (pT <= 0.) return;

    // Get flavour of radiator before the splitting.
    int flavRadBef = getRadBeforeFlav(iRad, iEmt, event);
    clus.push_back( Clustering(iEmt, iRad, iRec, iPartner,
      pT, flavRadBef, 0, 0, 0, 9));

  } else {

  // Check if spins are already assigned.
  int radSpin   = event[iRad].intPol();
  int emtSpin   = event[iEmt].intPol();
  int recSpin   = event[iRec].intPol();
  bool hasRadSpin = (radSpin != 9);
  bool hasEmtSpin = (emtSpin != 9);
  bool hasRecSpin = (recSpin != 9);

  // Check if any of the partons are quarks.
  bool radQuark = event[iRad].idAbs()  < 10;
  bool emtQuark = event[iEmt].idAbs()  < 10;
  bool recQuark = event[iRec].idAbs() < 10;

  // Generate the vector of all spin structures
  vector < vector<int> > structs;
  structs.resize(0);
  for (int i = 0; i < 3; ++i){
    int sRad = (i==0) ? -1 : (i==1) ? 1 : 9;
    for (int j = 0; j < 3; ++j){
      int sEmt = (j==0) ? -1 : (j==1) ? 1 : 9;
      for (int k = 0; k < 3; ++k){
        int sRec = (k==0) ? -1 : (k==1) ? 1 : 9;
        vector <int> s;
        s.push_back(sRad); s.push_back(sEmt); s.push_back(sRec);
        structs.push_back(s);
      }
    }
  }

  vector < vector<int> > allStructs;
  for (int i = 0; i< int(structs.size()); ++i) {
    // Only pick allowed combinations if spin is already set.
    if (hasRadSpin && radQuark && structs[i][0] != radSpin) continue;
    if (hasEmtSpin && emtQuark && structs[i][1] != emtSpin) continue;
    if (hasRecSpin && recQuark && structs[i][2] != recSpin) continue;
    // Set +-1 for previously unset quark spins.
    if (!hasRadSpin && radQuark && structs[i][0] == 9) continue;
    if (!hasEmtSpin && emtQuark && structs[i][1] == 9) continue;
    if (!hasRecSpin && recQuark && structs[i][2] == 9) continue;
    // Leave spin 9 for gluons.
    if (!radQuark && structs[i][0] != radSpin) continue;
    if (!emtQuark && structs[i][1] != emtSpin) continue;
    if (!recQuark && structs[i][2] != recSpin) continue;
    // Ensure that the quarks in the g-> q qbar splitting have equal spin.
    if (radQuark &&  emtQuark && structs[i][0] != structs[i][1]) continue;
    // Store spin structure.
    allStructs.push_back(structs[i]);
  }

  // Get flavour of radiator before the splitting.
  int flavRadBef = getRadBeforeFlav(iRad, iEmt, event);
  // Push back all spin-dependent clusterings.
  for (int i = 0; i< int(allStructs.size()); ++i) {
    // Get spin of radiator before the splitting.
    int spinRadBef = getRadBeforeSpin(iRad, iEmt, allStructs[i][0],
                       allStructs[i][1], event);
    clus.push_back( Clustering(iEmt, iRad, iRec, iPartner, pT, flavRadBef,
      allStructs[i][0], allStructs[i][1], allStructs[i][2], spinRadBef) );
  }

  } // doWeakClustering

  return;

}

//--------------------------------------------------------------------------

// Function to construct (rad,rec,emt) triples from the event
// IN  int   : Position of Emitted in event record for which
//             dipoles should be constructed
//     int   : Colour topogy to be tested
//             1= g -> qqbar, causing 2 -> 2 dipole splitting
//             2= q(bar) -> q(bar) g && g -> gg,
//              causing a 2 -> 3 dipole splitting
//     Event : event record to be checked for ptential partners
// OUT vector of all allowed radiator+recoiler+emitted triples

vector<Clustering> History::findQCDTriple (int EmtTagIn, int colTopIn,
                      const Event& event,
                      vector<int> posFinalPartn,
                      vector <int> posInitPartn ) {

  // Copy input parton tag
  int EmtTag = EmtTagIn;
  // Copy input colour topology tag
  // (1: g --> qqbar splitting present, 2:rest)
  int colTop = colTopIn;

  // Initialise FinalSize
  int finalSize = int(posFinalPartn.size());
  int initSize = int(posInitPartn.size());
  int size = initSize + finalSize;

  vector<Clustering> clus;

  // Search final partons to find partons colour-connected to
  // event[EmtTag], choose radiator, then choose recoiler
  for ( int a = 0; a < size; ++a ) {
    int i    = (a < finalSize)? a : (a - finalSize) ;
    int iRad = (a < finalSize)? posFinalPartn[i] : posInitPartn[i];

    if ( event[iRad].col() == event[EmtTag].col()
      && event[iRad].acol() == event[EmtTag].acol() )
      continue;

    if (iRad != EmtTag ) {
      int pTdef = event[iRad].isFinal() ? 1 : -1;
      int sign = (a < finalSize)? 1 : -1 ;

      // First colour topology: g --> qqbar. Here, emt & rad should
      // have same flavour (causes problems for gamma->qqbar).
      if (colTop == 1) {

        if ( event[iRad].id() == -sign*event[EmtTag].id() ) {
          int col = -1;
          int acl = -1;

          if (event[iRad].isFinal() ) {
            if (event[iRad].id() < 0) {
              col = event[EmtTag].col();
              acl = 0;
            } else {
              acl = event[EmtTag].acol();
              col = 0;
            }
          } else {
            if (event[iRad].id() < 0) {
              acl = event[EmtTag].acol();
              col = 0;
            } else {
              col = event[EmtTag].col();
              acl = 0;
            }
          }

          // Recoiler
          int iRec     = 0;
          // Colour partner
          int iPartner = 0;

          if (col > 0) {
            // Find recoiler by colour
            iRec = FindCol(col,iRad,EmtTag,event,1,true);
            // In initial state splitting has final state colour partner,
            // Save both partner and recoiler
            if ( (sign < 0) && (event[iRec].isFinal()) ) {
              // Save colour recoiler
              iPartner = iRec;
              // Reset kinematic recoiler to initial state parton
              for(int l = 0; l < int(posInitPartn.size()); ++l)
                if (posInitPartn[l] != iRad) iRec = posInitPartn[l];
            // For final state splittings, colour partner and recoiler are
            // identical
            } else {
              iPartner = iRec;
            }
            if ( iRec != 0 && iPartner != 0
             && allowedClustering( iRad, EmtTag, iRec, iPartner, event) ) {
               attachClusterings (clus, EmtTag, iRad, iRec, iPartner,
                   pTLund(event, iRad, EmtTag, iRec, pTdef), event);
              continue;
            }

            // Find recoiler by colour
            iRec = FindCol(col,iRad,EmtTag,event,2,true);
            // In initial state splitting has final state colour partner,
            // Save both partner and recoiler
            if ( (sign < 0) && (event[iRec].isFinal()) ) {
              // Save colour recoiler
              iPartner = iRec;
              // Reset kinematic recoiler to initial state parton
              for(int l = 0; l < int(posInitPartn.size()); ++l)
                if (posInitPartn[l] != iRad) iRec = posInitPartn[l];
            // For final state splittings, colour partner and recoiler are
            // identical
            } else {
              iPartner = iRec;
            }
            if ( iRec != 0 && iPartner != 0
             && allowedClustering( iRad, EmtTag, iRec, iPartner, event) ) {
                attachClusterings (clus, EmtTag, iRad, iRec, iPartner,
                   pTLund(event, iRad, EmtTag, iRec, pTdef), event);
              continue;
            }
          }


          if (acl > 0) {

            // Find recoiler by colour
            iRec = FindCol(acl,iRad,EmtTag,event,1,true);
            // In initial state splitting has final state colour partner,
            // Save both partner and recoiler
            if ( (sign < 0) && (event[iRec].isFinal()) ) {
              // Save colour recoiler
              iPartner = iRec;
              // Reset kinematic recoiler to initial state parton
              for(int l = 0; l < int(posInitPartn.size()); ++l)
                if (posInitPartn[l] != iRad) iRec = posInitPartn[l];
            // For final state splittings, colour partner and recoiler are
            // identical
            } else {
              iPartner = iRec;
            }
            if ( iRec != 0 && iPartner != 0
             && allowedClustering( iRad, EmtTag, iRec, iPartner, event) ) {
                attachClusterings (clus, EmtTag, iRad, iRec, iPartner,
                   pTLund(event, iRad, EmtTag, iRec, pTdef), event);
              continue;
            }

            // Find recoiler by colour
            iRec = FindCol(acl,iRad,EmtTag,event,2,true);
            // In initial state splitting has final state colour partner,
            // Save both partner and recoiler
            if ( (sign < 0) && (event[iRec].isFinal()) ) {
              // Save colour recoiler
              iPartner = iRec;
              // Reset kinematic recoiler to initial state parton
              for(int l = 0; l < int(posInitPartn.size()); ++l)
                if (posInitPartn[l] != iRad) iRec = posInitPartn[l];
            // For final state splittings, colour partner and recoiler are
            // identical
            } else {
              iPartner = iRec;
            }
            if ( iRec != 0 && iPartner != 0
             && allowedClustering( iRad, EmtTag, iRec, iPartner, event) ) {
                attachClusterings (clus, EmtTag, iRad, iRec, iPartner,
                   pTLund(event, iRad, EmtTag, iRec, pTdef), event);
              continue;
            }
          }
        // Initial gluon splitting
        } else if ( event[iRad].id() == 21
                  &&(  event[iRad].col() == event[EmtTag].col()
                    || event[iRad].acol() == event[EmtTag].acol() )) {
          // For an initial state radiator, always set recoiler
          // to the other initial state parton (recoil is taken
          // by full remaining system, so this is just a
          // labelling for such a process)
          int RecInit  = 0;
          for(int l = 0; l < int(posInitPartn.size()); ++l)
            if (posInitPartn[l] != iRad) RecInit = posInitPartn[l];

          // Find the colour connected partner
          // Find colour index of radiator before splitting
          int col = getRadBeforeCol(iRad, EmtTag, event);
          int acl = getRadBeforeAcol(iRad, EmtTag, event);

          // Find the correct partner: If a colour line has split,
          // the partner is connected to the radiator before the splitting
          // by a colour line (same reasoning for anticolour). The colour
          // that split is the colour appearing twice in the
          // radiator + emitted pair.
          // Thus, if we remove a colour index with the clustering,
          // we should look for a colour partner, else look for
          // an anticolour partner
          int colRemove = (event[iRad].col() == event[EmtTag].col())
                  ? event[iRad].col() : event[iRad].acol();

          int iPartner = 0;
          if (colRemove > 0 && col > 0 && col != colRemove)
            iPartner = FindCol(col,iRad,EmtTag,event,1,true)
                     + FindCol(col,iRad,EmtTag,event,2,true);
          else if (colRemove > 0 && acl > 0 && acl != colRemove)
            iPartner = FindCol(acl,iRad,EmtTag,event,1,true)
                     + FindCol(acl,iRad,EmtTag,event,2,true);

          if ( allowedClustering( iRad, EmtTag, RecInit, iPartner, event ) ) {
               attachClusterings (clus, EmtTag, iRad, RecInit, iPartner,
                   pTLund(event, iRad, EmtTag, RecInit, pTdef), event);
              continue;
          }
        }

      // Second colour topology: Gluon emission

      } else {
        if ( (event[iRad].col() == event[EmtTag].acol())
           || (event[iRad].acol() == event[EmtTag].col())
           || (event[iRad].col() == event[EmtTag].col())
           || (event[iRad].acol() == event[EmtTag].acol()) ) {
          // For the rest, choose recoiler to have a common colour
          // tag with radiator, while not being the "Emitted"

          int col = -1;
          int acl = -1;

          if (event[iRad].isFinal() ) {

            if ( event[iRad].id() < 0) {
              acl = event[EmtTag].acol();
              col = event[iRad].col();
            } else if ( event[iRad].id() > 0 && event[iRad].id() < 10) {
              col = event[EmtTag].col();
              acl = event[iRad].acol();
            } else {
              col = event[EmtTag].col();
              acl = event[EmtTag].acol();
            }

            int iRec = 0;
            if (col > 0) {
              iRec = FindCol(col,iRad,EmtTag,event,1,true);
              if ( (sign < 0) && (event[iRec].isFinal()) ) iRec = 0;
              if (iRec != 0
               && allowedClustering( iRad, EmtTag, iRec, iRec, event) ) {
                  attachClusterings (clus, EmtTag, iRad, iRec, iRec,
                     pTLund(event, iRad, EmtTag, iRec, pTdef), event);
                continue;
              }

              iRec = FindCol(col,iRad,EmtTag,event,2,true);
              if ( (sign < 0) && (event[iRec].isFinal()) ) iRec = 0;
              if (iRec != 0
               && allowedClustering( iRad, EmtTag, iRec, iRec, event) ) {
                  attachClusterings (clus, EmtTag, iRad, iRec, iRec,
                   pTLund(event, iRad, EmtTag, iRec, pTdef), event);
                continue;
              }
            }

            if (acl > 0) {
              iRec = FindCol(acl,iRad,EmtTag,event,1,true);
              if ( (sign < 0) && (event[iRec].isFinal()) ) iRec = 0;
              if (iRec != 0
               && allowedClustering( iRad, EmtTag, iRec, iRec, event) ) {
                  attachClusterings (clus, EmtTag, iRad, iRec, iRec,
                   pTLund(event, iRad, EmtTag, iRec, pTdef), event);
                continue;
              }

              iRec = FindCol(acl,iRad,EmtTag,event,2,true);
              if ( (sign < 0) && (event[iRec].isFinal()) ) iRec = 0;
              if (iRec != 0
               && allowedClustering( iRad, EmtTag, iRec, iRec, event) ) {
                  attachClusterings (clus, EmtTag, iRad, iRec, iRec,
                   pTLund(event, iRad, EmtTag, iRec, pTdef), event);
                continue;
              }
            }

          } else {

            // For an initial state radiator, always set recoiler
            // to the other initial state parton (recoil is taken

            // by full remaining system, so this is just a
            // labelling for such a process)
            int RecInit = 0;
            int iPartner = 0;
            for(int l = 0; l < int(posInitPartn.size()); ++l)
              if (posInitPartn[l] != iRad) RecInit = posInitPartn[l];

            // Find the colour connected partner
            // Find colour index of radiator before splitting
            col = getRadBeforeCol(iRad, EmtTag, event);
            acl = getRadBeforeAcol(iRad, EmtTag, event);

            // Find the correct partner: If a colour line has split,
            // the partner is connected to the radiator before the splitting
            // by a colour line (same reasoning for anticolour). The colour
            // that split is the colour appearing twice in the
            // radiator + emitted pair.
            // Thus, if we remove a colour index with the clustering,
            // we should look for a colour partner, else look for
            // an anticolour partner
            int colRemove = (event[iRad].col() == event[EmtTag].col())
                    ? event[iRad].col() : 0;
            iPartner = (colRemove > 0)
                     ?   FindCol(col,iRad,EmtTag,event,1,true)
                       + FindCol(col,iRad,EmtTag,event,2,true)
                     :   FindCol(acl,iRad,EmtTag,event,1,true)
                       + FindCol(acl,iRad,EmtTag,event,2,true);

            if ( allowedClustering( iRad, EmtTag, RecInit, iPartner, event)) {
                 attachClusterings (clus, EmtTag, iRad, RecInit, iPartner,
                   pTLund(event, iRad, EmtTag, RecInit, pTdef), event);
              continue;
            }
          }
        }
      }
    }
  }

  // Done
  return clus;
}

//--------------------------------------------------------------------------

// For the history-defining state (and if necessary interfering
// states), find all possible clusterings.
// NO INPUT
// OUT vector of all (rad,rec,emt) systems

vector<Clustering> History::getAllEWClusterings() {
  vector<Clustering> ret;

  // Get all clusterings for input state
  vector<Clustering> systems;
  systems = getEWClusterings(state);
  ret.insert(ret.end(), systems.begin(), systems.end());
  // Done
  return ret;
}

//--------------------------------------------------------------------------

// For one given state, find all possible clusterings.
// IN  Event : state to be investigated
// OUT vector of all (rad,rec,emt) systems in the state

vector<Clustering> History::getEWClusterings( const Event& event) {
  vector<Clustering> ret;

  // Initialise vectors to keep track of position of partons in the
  // input event
  vector <int> posFinalPartn;
  vector <int> posInitPartn;
  vector <int> posFinalW;
  vector <int> posFinalZ;

  // Search event record for final state particles and store these in
  // quark, anti-quark and gluon vectors
  for ( int i=3; i < event.size(); ++i )
    if ( event[i].isFinal() ) {
      // Store final partons
      posFinalPartn.push_back(i);
    } else {
      // Store initial partons
      posInitPartn.push_back(i);
    }
  // Search event record for final W.
  for ( int i=0; i < event.size(); ++i )
    if ( event[i].isFinal() && event[i].idAbs() == 24 )
      posFinalW.push_back( i );

 // Search event record for final Z.
  for ( int i=0; i < event.size(); ++i )
    if ( event[i].isFinal() && event[i].idAbs() == 23 )
      posFinalZ.push_back( i );


  vector<Clustering> systems;
  // Find rad + emt + rec systems:
  // (1) Start from W boson and find all (rad,rec,emt=W) triples
  for ( int i = 0; i <  int(posFinalW.size()); ++i ) {
    int emtW = posFinalW[i];
    systems = findEWTripleW( emtW, event, posFinalPartn, posInitPartn);
    ret.insert(ret.end(), systems.begin(), systems.end());
    systems.resize(0);
  }
  // Find rad + emt + rec systems:
  // (1) Start from Z boson and find all (rad,rec,emt=W) triples
  for ( int i = 0; i <  int(posFinalZ.size()); ++i ) {
    int emtZ = posFinalZ[i];

    systems = findEWTripleZ( emtZ, event, posFinalPartn, posInitPartn);
    ret.insert(ret.end(), systems.begin(), systems.end());
    systems.resize(0);
  }

  return ret;
}

//--------------------------------------------------------------------------

// Function to construct (rad,rec,emt) triples from the event
// IN  int   : Position of Emitted in event record for which
//             dipoles should be constructed
//     int   : Colour topogy to be tested
//             1= g -> qqbar, causing 2 -> 2 dipole splitting
//             2= q(bar) -> q(bar) g && g -> gg,
//              causing a 2 -> 3 dipole splitting
//     Event : event record to be checked for ptential partners
// OUT vector of all allowed radiator+recoiler+emitted triples

vector<Clustering> History::findEWTripleW ( int emtTagIn, const Event& event,
                     vector<int> posFinalPartn, vector<int> posInitPartn ) {
  // Copy input parton tag
  int emtTag = emtTagIn;
  int flavEmt = event[emtTag].id();

  // Copy input colour topology tag
  // (1: g --> qqbar splitting present, 2:rest)

  // Initialise FinalSize
  int finalSize = int(posFinalPartn.size());
  int initSize  = int(posInitPartn.size());

  // Store flavour count to check if the new flavour configuration is valid.
  vector<int> flavCounts(30,0);

  for ( int a = 0; a < finalSize; ++a ) {
    if (event[posFinalPartn[a]].idAbs() < 20) {
      int sign = 1;
      if (event[posFinalPartn[a]].id() < 0)
        sign = -1;
      flavCounts[event[posFinalPartn[a]].idAbs()] += sign;
    }
    if (event[posFinalPartn[a]].idAbs() == 24)
      flavCounts[24]++;
  }

  for ( int a = 0; a < initSize; ++a ) {
    if (event[posInitPartn[a]].idAbs() < 20) {
      int sign = 1;
      if (event[posInitPartn[a]].id() < 0)
        sign = -1;
      flavCounts[event[posInitPartn[a]].idAbs()] -= sign;
    }
  }

  vector<Clustering> clus;

  // Search final partons to find partons colour-connected to
  // event[EmtTag], choose radiator, then choose recoiler
  for ( int a = 0; a < finalSize; ++a ) {

    int iRad = posFinalPartn[a];
    if (iRad != emtTag) {

      // Spin information.
      int spinRad = event[iRad].intPol();
      if (spinRad == -1 || spinRad == 9 || spinRad == 0) {

        int pTdef = 1;
        // Find recoiler by flavour.
        int flavRad = event[iRad].id();
        // Only allow quark and leptons to be radiators.
        if (event[iRad].isQuark() || event[iRad].isLepton()) {

          // Check if the W+- matches that of the quark/lepton.
          int flavExp = (flavRad > 0) ? 24 : -24;
          if (abs(flavRad) % 2 == 0) flavExp = -flavExp;
          if (flavExp == flavEmt) {

            // Find possible flavours that the W can change the quark to.
            vector<int> flavRadBefs = posFlavCKM(flavRad);

            // Change to anti particles if radiator is an anti particle.
            if (flavRad < 0)
              for (int i = 0;i < int(flavRadBefs.size()); ++i)
                flavRadBefs[i] = - flavRadBefs[i];

            // Loop through final partons and try to find matching flavours.
            for ( int i = 0; i < finalSize; ++i ) {
              int iRec = posFinalPartn[i];

              // Check for particle overlaps.
              if ( iRec != iRad && iRec != emtTag ) {

                for (int j = 0;j <  int(flavRadBefs.size()); ++j) {
                  // Check new flavour structure. If multiple Ws
                  // are still present, do not check flavour yet.
                  if (flavCounts[24] <= 1 && !checkFlavour(flavCounts,
                      flavRad, flavRadBefs[j], 1))
                    continue;

                  clus.push_back( Clustering(emtTag, iRad, iRec, iRec,
                    pTLund(event, iRad, emtTag, iRec, pTdef, flavRadBefs[j]),
                    flavRadBefs[j], -1 ) );
                }
              }
            }
          }
        }
      }
    }
  }

  // Search for initial shower histories.
  for (int a = 0;a < int(posInitPartn.size()); ++a) {
    int iRad = posInitPartn[a];
    int flavRad = event[iRad].id();
    // Only allow quarks and leptons to radiate weak bosons.
    if (event[iRad].isQuark() || event[iRad].isLepton()) {

      // Spin information.
      int spinRad = event[iRad].intPol();
      if (spinRad == -1 || spinRad == 9 || spinRad == 0) {

        // Check if the W+- matches that of the quark/lepton.
        int flavExp = (flavRad > 0) ? 24 : -24;
        if (abs(flavRad) % 2 == 1) flavExp = -flavExp;
        if (flavExp == flavEmt) {
          // Find possible flavours that the W cam change the quark to.
          vector<int> flavRadBefs = posFlavCKM(flavRad);

          // Change to anti particles if radiator is an anti particle.
          if (flavRad < 0)
            for (int i = 0;i < int(flavRadBefs.size()); ++i)
              flavRadBefs[i] = - flavRadBefs[i];

          // Loop through final partons and try to find matching flavours.
          for ( int i = 0; i < int(posInitPartn.size()); ++i ) {
            int iRec = posInitPartn[i];

            // Check for particle overlaps.
            if ( i != a && iRec != emtTag) {
              for (int j = 0;j <  int(flavRadBefs.size()); ++j) {

                // Check new flavour structure.
                // If multiple Ws are still present, do not check flavour yet.
                if (flavCounts[24] <= 1 && !checkFlavour(flavCounts,
                  flavRad, flavRadBefs[j], -1))
                  continue;
                clus.push_back( Clustering(emtTag, iRad, iRec, iRec,
                  pTLund(event, iRad, emtTag, iRec, -1, flavRadBefs[j]),
                  flavRadBefs[j], -1 ) );
              }
            }
          }
        }
      }
    }
  }

  // Done
  return clus;
}

//--------------------------------------------------------------------------

// Function to construct (rad,rec,emt) triples from the event
// IN  int   : Position of Emitted in event record for which
//             dipoles should be constructed
//     int   : Colour topogy to be tested
//             1= g -> qqbar, causing 2 -> 2 dipole splitting
//             2= q(bar) -> q(bar) g && g -> gg,
//              causing a 2 -> 3 dipole splitting
//     Event : event record to be checked for ptential partners
// OUT vector of all allowed radiator+recoiler+emitted triples

vector<Clustering> History::findEWTripleZ ( int emtTagIn, const Event& event,
                     vector<int> posFinalPartn, vector<int> posInitPartn ) {
  // Copy input parton tag
  int emtTag = emtTagIn;

  // Copy input colour topology tag
  // (1: g --> qqbar splitting present, 2:rest)

  // Initialise FinalSize
  int finalSize = int(posFinalPartn.size());
  int initSize  = int(posInitPartn.size());

  // Store flavour count to check if the new flavour configuration is valid.
  vector<int> flavCounts(30,0);

  for ( int a = 0; a < finalSize; ++a ) {
    if (event[posFinalPartn[a]].idAbs() < 20) {
      int sign = 1;
      if (event[posFinalPartn[a]].id() < 0)
        sign = -1;
      flavCounts[event[posFinalPartn[a]].idAbs()] += sign;
    }
    if (event[posFinalPartn[a]].idAbs() == 24)
      flavCounts[24]++;
  }

  for ( int a = 0; a < initSize; ++a ) {
    if (event[posInitPartn[a]].idAbs() < 20) {
      int sign = 1;
      if (event[posInitPartn[a]].id() < 0)
        sign = -1;
      flavCounts[event[posInitPartn[a]].idAbs()] -= sign;
    }
  }

  vector<Clustering> clus;
  // Add Z reclusterings.

  // Search final partons to find partons colour-connected to
  // event[EmtTag], choose radiator, then choose recoiler
  for ( int a = 0; a < finalSize; ++a ) {

    int iRad = posFinalPartn[a];
    if (iRad != emtTag) {
      int pTdef = 1;
      // Find recoiler by flavour.
      int flavRad = event[iRad].id();

      // Only allow quark and leptons to be radiators.
      if (event[iRad].isQuark() || event[iRad].isLepton())
      // Loop through final partons and try to find matching flavours.
      for ( int i = 0; i < finalSize; ++i ) {
        int iRec = posFinalPartn[i];

        // Check for particle overlaps.
        if ( iRec != iRad && iRec != emtTag ) {
          // Check new flavour structure.
          // If multiple Ws are still present, do not check flavour yet.
          if (flavCounts[24] <= 1 && !checkFlavour(flavCounts,
              flavRad, flavRad, 1))
            continue;

          clus.push_back( Clustering(emtTag, iRad, iRec, iRec,
            pTLund(event, iRad, emtTag, iRec, pTdef, flavRad),
            flavRad, -1 ) );
        }
      }
    }
  }

  // Search for initial shower histories.
  for (int a = 0;a < int(posInitPartn.size()); ++a) {
    int iRad = posInitPartn[a];
    int flavRad = event[iRad].id();
    // Only allow quarks and leptons to radiate weak bosons.
    if (event[iRad].isQuark() || event[iRad].isLepton()) {

      // Loop through initial partons and try to find matching flavours.
      for ( int i = 0; i < int(posInitPartn.size()); ++i ) {
        int iRec = posInitPartn[i];

        // Check for particle overlaps.
        if ( i != a && iRec != emtTag) {
          // Check new flavour structure.
          // If multiple Ws are still present, do not check flavour yet.
          if (flavCounts[24] <= 1 && !checkFlavour(flavCounts,
             flavRad, flavRad, -1))
            continue;
          clus.push_back( Clustering(emtTag, iRad, iRec, iRec,
            pTLund(event, iRad, emtTag, iRec, -1, flavRad),
            flavRad, -1 ) );
        }
      }
    }
  }

  // Done
  return clus;
}

//--------------------------------------------------------------------------

// For the history-defining state (and if necessary interfering
// states), find all possible clusterings.
// NO INPUT
// OUT vector of all (rad,rec,emt) systems

vector<Clustering> History::getAllSQCDClusterings() {
  vector<Clustering> ret;

  // Get all clusterings for input state
  vector<Clustering> systems;
  systems = getSQCDClusterings(state);
  ret.insert(ret.end(), systems.begin(), systems.end());
  // Done
  return ret;
}

//--------------------------------------------------------------------------

// For one given state, find all possible clusterings.
// IN  Event : state to be investigated
// OUT vector of all (rad,rec,emt) systems in the state

vector<Clustering> History::getSQCDClusterings( const Event& event) {
  vector<Clustering> ret;

  // Initialise vectors to keep track of position of partons in the
  // input event
  vector <int> posFinalPartn;
  vector <int> posInitPartn;

  vector <int> posFinalGluon;
  vector <int> posFinalQuark;
  vector <int> posFinalAntiq;
  vector <int> posInitGluon;
  vector <int> posInitQuark;
  vector <int> posInitAntiq;

  // Search event record for final state particles and store these in
  // quark, anti-quark and gluon vectors
  for (int i=0; i < event.size(); ++i)
    if ( event[i].isFinal() && event[i].colType() !=0 ) {
      // Store final partons
      posFinalPartn.push_back(i);
      if ( event[i].id() == 21 || event[i].id() == 1000021)
        posFinalGluon.push_back(i);
      else if ( (event[i].idAbs() < 10 && event[i].id() > 0)
             || (event[i].idAbs() < 1000010 && event[i].idAbs() > 1000000
             && event[i].id() > 0)
             || (event[i].idAbs() < 2000010 && event[i].idAbs() > 2000000
             && event[i].id() > 0))
        posFinalQuark.push_back(i);
      else if ( (event[i].idAbs() < 10 && event[i].id() < 0)
             || (event[i].idAbs() < 1000010 && event[i].idAbs() > 1000000
             && event[i].id() < 0)
             || (event[i].idAbs() < 2000010 && event[i].idAbs() > 2000000
             && event[i].id() < 0))
        posFinalAntiq.push_back(i);
    } else if ( event[i].status() == -21 && event[i].colType() != 0 ) {
      // Store initial partons
      posInitPartn.push_back(i);
      if ( event[i].id() == 21 || event[i].id() == 1000021)
        posInitGluon.push_back(i);
      else if ( (event[i].idAbs() < 10 && event[i].id() > 0)
             || (event[i].idAbs() < 1000010 && event[i].idAbs() > 1000000
             && event[i].id() > 0)
             || (event[i].idAbs() < 2000010 && event[i].idAbs() > 2000000
             && event[i].id() > 0))
        posInitQuark.push_back(i);
      else if ( (event[i].idAbs() < 10 && event[i].id() < 0)
             || (event[i].idAbs() < 1000010 && event[i].idAbs() > 1000000
             && event[i].id() < 0)
             || (event[i].idAbs() < 2000010 && event[i].idAbs() > 2000000
             && event[i].id() < 0))
        posInitAntiq.push_back(i);
    }

  int nFiGluon = int(posFinalGluon.size());
  int nFiQuark = int(posFinalQuark.size());
  int nFiAntiq = int(posFinalAntiq.size());
  int nInGluon = int(posInitGluon.size());
  int nInQuark = int(posInitQuark.size());
  int nInAntiq = int(posInitAntiq.size());
  vector<Clustering> systems;

  // Find rad + emt + rec systems:
  // (1) Start from gluon and find all (rad,rec,emt=gluon) triples
  for (int i = 0; i < nFiGluon; ++i) {
    int EmtGluon = posFinalGluon[i];
    systems = findSQCDTriple( EmtGluon, 2, event, posFinalPartn, posInitPartn);
    ret.insert(ret.end(), systems.begin(), systems.end());
    systems.resize(0);
  }

  // For more than one quark-antiquark pair in final state, check for
  // g -> qqbar splittings
  bool check_g2qq = true;
  if ( ( ( nInQuark + nInAntiq == 0 )
          && (nInGluon == 0)
          && (nFiQuark == 1) && (nFiAntiq == 1) )
    || ( ( nFiQuark + nFiAntiq == 0)
          && (nInQuark == 1) && (nInAntiq == 1) ) )
    check_g2qq = false;

  if ( check_g2qq ) {

    // (2) Start from quark and find all (rad,rec,emt=quark) triples
    //     ( when g -> q qbar occured )
    for( int i=0; i < nFiQuark; ++i) {
      int EmtQuark = posFinalQuark[i];
      systems = findSQCDTriple( EmtQuark,1,event, posFinalPartn, posInitPartn);
      ret.insert(ret.end(), systems.begin(), systems.end());
      systems.resize(0);
    }

    // (3) Start from anti-quark and find all (rad,rec,emt=anti-quark)
    //     triples ( when g -> q qbar occured )
    for( int i=0; i < nFiAntiq; ++i) {
      int EmtAntiq = posFinalAntiq[i];
      systems = findSQCDTriple( EmtAntiq,1,event, posFinalPartn, posInitPartn);
      ret.insert(ret.end(), systems.begin(), systems.end());
      systems.resize(0);
    }

  }

  return ret;
}

//--------------------------------------------------------------------------

// Function to construct (rad,rec,emt) triples from the event
// IN  int   : Position of Emitted in event record for which
//             dipoles should be constructed
//     int   : Colour topogy to be tested
//             1= g -> qqbar, causing 2 -> 2 dipole splitting
//             2= q(bar) -> q(bar) g && g -> gg,
//              causing a 2 -> 3 dipole splitting
//     Event : event record to be checked for ptential partners
// OUT vector of all allowed radiator+recoiler+emitted triples

vector<Clustering> History::findSQCDTriple (int EmtTagIn, int colTopIn,
                      const Event& event,
                      vector<int> posFinalPartn,
                      vector <int> posInitPartn ) {

  // Copy input parton tag
  int EmtTag = EmtTagIn;
  // Copy input colour topology tag
  // (1: g --> qqbar splitting present, 2:rest)
  int colTop = colTopIn;

  // PDG numbering offset for squarks
  int offsetL = 1000000;
  int offsetR = 2000000;

  // Initialise FinalSize
  int finalSize = int(posFinalPartn.size());
  int initSize = int(posInitPartn.size());
  int size = initSize + finalSize;

  vector<Clustering> clus;

  // Search final partons to find partons colour-connected to
  // event[EmtTag], choose radiator, then choose recoiler
  for ( int a = 0; a < size; ++a ) {
    int i    = (a < finalSize)? a : (a - finalSize) ;
    int iRad = (a < finalSize)? posFinalPartn[i] : posInitPartn[i];

    if ( event[iRad].col() == event[EmtTag].col()
      && event[iRad].acol() == event[EmtTag].acol() )
      continue;

    // Save radiator flavour.
    int radID = event[iRad].id();
    // Remember if radiator is BSM.
    bool isSQCDrad = (abs(radID) > offsetL);
    // Remember if emitted is BSM.
    bool isSQCDemt = (event[EmtTag].idAbs() > offsetL );

    if (iRad != EmtTag ) {
      int pTdef = event[iRad].isFinal() ? 1 : -1;
      int sign = (a < finalSize)? 1 : -1 ;

      // Disalllow clusterings resulting in an initial state sQCD parton!
      int radBefID = getRadBeforeFlav(iRad,EmtTag,event);
      if ( pTdef == -1 && abs(radBefID) > offsetL ) continue;

      // First colour topology: g --> qqbar. Here, emt & rad should
      // have same flavour (causes problems for gamma->qqbar).
      if (colTop == 1) {

        int radSign = (event[iRad].id() < 0) ? -1 : 1;
        int emtSign = (event[EmtTag].id() < 0) ? -1 : 1;

        // Final gluino splitting.
        bool finalSplitting = false;
        if ( abs(radID) < 10
          && radSign*(abs(radID)+offsetL) == -sign*event[EmtTag].id() )
          finalSplitting = true;
        if ( abs(radID) < 10
          && radSign*(abs(radID)+offsetR) == -sign*event[EmtTag].id() )
          finalSplitting = true;
        if ( abs(radID) > offsetL && abs(radID) < offsetL+10
          && radID == -sign*emtSign*( event[EmtTag].idAbs() + offsetL) )
          finalSplitting = true;
        if ( abs(radID) > offsetR && abs(radID) < offsetR+10
          && radID == -sign*emtSign*( event[EmtTag].idAbs() + offsetR) )
          finalSplitting = true;

        // Initial gluon splitting.
        bool initialSplitting = false;
        if ( radID == 21 && ( ( event[EmtTag].idAbs() > offsetL
                             && event[EmtTag].idAbs() < offsetL+10)
                           || ( event[EmtTag].idAbs() > offsetR
                             && event[EmtTag].idAbs() < offsetR+10) )
          && ( event[iRad].col() == event[EmtTag].col()
            || event[iRad].acol() == event[EmtTag].acol() ) )
          initialSplitting = true;

        if ( finalSplitting ) {

          int col = -1;
          int acl = -1;
          if ( radID < 0 && event[iRad].colType() == -1) {
            acl = event[EmtTag].acol();
            col = event[iRad].acol();
          } else if ( event[iRad].colType() == 1 ) {
            col = event[EmtTag].col();
            acl = event[iRad].col();
          }

          // Recoiler
          int iRec     = 0;
          // Colour partner
          int iPartner = 0;

          if (col > 0) {
            // Find recoiler by colour
            iRec = FindCol(col,iRad,EmtTag,event,1,true);
            // In initial state splitting has final state colour partner,
            // Save both partner and recoiler
            if ( (sign < 0) && (event[iRec].isFinal()) ) {
              // Save colour recoiler
              iPartner = iRec;
              // Reset kinematic recoiler to initial state parton
              for(int l = 0; l < int(posInitPartn.size()); ++l)
                if (posInitPartn[l] != iRad) iRec = posInitPartn[l];
            // For final state splittings, colour partner and recoiler are
            // identical
            } else {
              iPartner = iRec;
            }

            // Not interested in pure QCD triples here.
            if ( !isSQCDrad && !isSQCDemt
              && (event[iRec].idAbs() < 10 || event[iRec].id() == 21) )
              iRec = 0;

            if ( iRec != 0 && iPartner != 0
             && allowedClustering( iRad, EmtTag, iRec, iPartner, event) ) {
                attachClusterings (clus, EmtTag, iRad, iRec, iPartner,
                   pTLund(event, iRad, EmtTag, iRec, pTdef), event);
              continue;
            }

            // Find recoiler by colour
            iRec = FindCol(col,iRad,EmtTag,event,2,true);
            // In initial state splitting has final state colour partner,
            // Save both partner and recoiler
            if ( (sign < 0) && (event[iRec].isFinal()) ) {
              // Save colour recoiler
              iPartner = iRec;
              // Reset kinematic recoiler to initial state parton
              for(int l = 0; l < int(posInitPartn.size()); ++l)
                if (posInitPartn[l] != iRad) iRec = posInitPartn[l];
            // For final state splittings, colour partner and recoiler are
            // identical
            } else {
              iPartner = iRec;
            }

            // Not interested in pure QCD triples here.
            if ( !isSQCDrad && !isSQCDemt
              && (event[iRec].idAbs() < 10 || event[iRec].id() == 21) )
              iRec = 0;

            if ( iRec != 0 && iPartner != 0
             && allowedClustering( iRad, EmtTag, iRec, iPartner, event) ) {
                attachClusterings (clus, EmtTag, iRad, iRec, iPartner,
                   pTLund(event, iRad, EmtTag, iRec, pTdef), event);
              continue;
            }
          }

          if (acl > 0) {

            // Find recoiler by colour
            iRec = FindCol(acl,iRad,EmtTag,event,1,true);
            // In initial state splitting has final state colour partner,
            // Save both partner and recoiler
            if ( (sign < 0) && (event[iRec].isFinal()) ) {
              // Save colour recoiler
              iPartner = iRec;
              // Reset kinematic recoiler to initial state parton
              for(int l = 0; l < int(posInitPartn.size()); ++l)
                if (posInitPartn[l] != iRad) iRec = posInitPartn[l];
            // For final state splittings, colour partner and recoiler are
            // identical
            } else {
              iPartner = iRec;
            }

            // Not interested in pure QCD triples here.
            if ( !isSQCDrad && !isSQCDemt
              && (event[iRec].idAbs() < 10 || event[iRec].id() == 21) )
              iRec = 0;

            if ( iRec != 0 && iPartner != 0
             && allowedClustering( iRad, EmtTag, iRec, iPartner, event) ) {
                attachClusterings (clus, EmtTag, iRad, iRec, iPartner,
                   pTLund(event, iRad, EmtTag, iRec, pTdef), event);
              continue;
            }

            // Find recoiler by colour
            iRec = FindCol(acl,iRad,EmtTag,event,2,true);
            // In initial state splitting has final state colour partner,
            // Save both partner and recoiler
            if ( (sign < 0) && (event[iRec].isFinal()) ) {
              // Save colour recoiler
              iPartner = iRec;
              // Reset kinematic recoiler to initial state parton
              for(int l = 0; l < int(posInitPartn.size()); ++l)
                if (posInitPartn[l] != iRad) iRec = posInitPartn[l];
            // For final state splittings, colour partner and recoiler are
            // identical
            } else {
              iPartner = iRec;
            }

            // Not interested in pure QCD triples here.
            if ( !isSQCDrad && !isSQCDemt
              && (event[iRec].idAbs() < 10 || event[iRec].id() == 21) )
              iRec = 0;

            if ( iRec != 0 && iPartner != 0
             && allowedClustering( iRad, EmtTag, iRec, iPartner, event) ) {
                attachClusterings (clus, EmtTag, iRad, iRec, iPartner,
                   pTLund(event, iRad, EmtTag, iRec, pTdef), event);
              continue;
            }
          }
        // Initial gluon splitting
        } else if ( initialSplitting ) {

          // SM splittings already taken care of in findQCDTriple.
          if ( !isSQCDrad && !isSQCDemt ) continue;

          // For an initial state radiator, always set recoiler
          // to the other initial state parton (recoil is taken
          // by full remaining system, so this is just a
          // labelling for such a process)
          int RecInit  = 0;
          for(int l = 0; l < int(posInitPartn.size()); ++l)
            if (posInitPartn[l] != iRad) RecInit = posInitPartn[l];

          // Find the colour connected partner
          // Find colour index of radiator before splitting
          int col = getRadBeforeCol(iRad, EmtTag, event);
          int acl = getRadBeforeAcol(iRad, EmtTag, event);

          // Find the correct partner: If a colour line has split,
          // the partner is connected to the radiator before the splitting
          // by a colour line (same reasoning for anticolour). The colour
          // that split is the colour appearing twice in the
          // radiator + emitted pair.
          // Thus, if we remove a colour index with the clustering,
          // we should look for a colour partner, else look for
          // an anticolour partner
          int colRemove = (event[iRad].col() == event[EmtTag].col())
                  ? event[iRad].col() : 0;

          int iPartner = 0;
          if (colRemove > 0 && col > 0)
            iPartner = FindCol(col,iRad,EmtTag,event,1,true)
                     + FindCol(col,iRad,EmtTag,event,2,true);
          else if (colRemove > 0 && acl > 0)
            iPartner = FindCol(acl,iRad,EmtTag,event,1,true)
                     + FindCol(acl,iRad,EmtTag,event,2,true);

          if ( allowedClustering( iRad, EmtTag, RecInit, iPartner, event ) ) {
               attachClusterings (clus, EmtTag, iRad, RecInit, iPartner,
                   pTLund(event, iRad, EmtTag, RecInit, pTdef), event);
              continue;
          }
        }

      // Second colour topology: Gluino emission

      } else {

        if ( (event[iRad].col() == event[EmtTag].acol())
           || (event[iRad].acol() == event[EmtTag].col())
           || (event[iRad].col() == event[EmtTag].col())
           || (event[iRad].acol() == event[EmtTag].acol()) ) {
          // For the rest, choose recoiler to have a common colour
          // tag with radiator, while not being the "Emitted"

          int col = -1;
          int acl = -1;

          if (event[iRad].isFinal() ) {

            if ( radID < 0 && event[iRad].colType() == -1) {
              acl = event[EmtTag].acol();
              col = event[iRad].col();
            } else if ( radID > 0 && event[iRad].colType() == 1 ) {
              col = event[EmtTag].col();
              acl = event[iRad].acol();
            } else {
              col = event[iRad].col();
              acl = event[iRad].acol();
            }

            int iRec = 0;
            if (col > 0) {
              iRec = FindCol(col,iRad,EmtTag,event,1,true);
              if ( (sign < 0) && (event[iRec].isFinal()) ) iRec = 0;
              // Not interested in pure QCD triples here.
              if ( !isSQCDrad && !isSQCDemt
                && (event[iRec].idAbs() < 10 || event[iRec].id() == 21) )
                iRec = 0;
              if (iRec != 0
               && allowedClustering( iRad, EmtTag, iRec, iRec, event) ) {
                  attachClusterings (clus, EmtTag, iRad, iRec, iRec,
                    pTLund(event, iRad, EmtTag, iRec, pTdef), event);
                continue;
              }

              iRec = FindCol(col,iRad,EmtTag,event,2,true);
              if ( (sign < 0) && (event[iRec].isFinal()) ) iRec = 0;
              // Not interested in pure QCD triples here.
              if ( !isSQCDrad && !isSQCDemt
                && (event[iRec].idAbs() < 10 || event[iRec].id() == 21) )
                iRec = 0;
              if (iRec != 0
               && allowedClustering( iRad, EmtTag, iRec, iRec, event) ) {
                  attachClusterings (clus, EmtTag, iRad, iRec, iRec,
                    pTLund(event, iRad, EmtTag, iRec, pTdef), event);
                continue;
              }
            }

            if (acl > 0) {
              iRec = FindCol(acl,iRad,EmtTag,event,1,true);
              if ( (sign < 0) && (event[iRec].isFinal()) ) iRec = 0;
              // Not interested in pure QCD triples here.
              if ( !isSQCDrad && !isSQCDemt
                && (event[iRec].idAbs() < 10 || event[iRec].id() == 21) )
                iRec = 0;
              if (iRec != 0
               && allowedClustering( iRad, EmtTag, iRec, iRec, event) ) {
                  attachClusterings (clus, EmtTag, iRad, iRec, iRec,
                    pTLund(event, iRad, EmtTag, iRec, pTdef), event);
                continue;
              }

              iRec = FindCol(acl,iRad,EmtTag,event,2,true);
              if ( (sign < 0) && (event[iRec].isFinal()) ) iRec = 0;
              // Not interested in pure QCD triples here.
              if ( !isSQCDrad && !isSQCDemt
                && (event[iRec].idAbs() < 10 || event[iRec].id() == 21) )
                iRec = 0;
              if (iRec != 0
               && allowedClustering( iRad, EmtTag, iRec, iRec, event) ) {
                  attachClusterings (clus, EmtTag, iRad, iRec, iRec,
                    pTLund(event, iRad, EmtTag, iRec, pTdef), event);
                continue;
              }
            }

          } else {

            // SM splittings already taken care of in findQCDTriple. Since
            // initial state splittings will not know if the true
            // colour-connected recoiler is a SM particle, any ISR splitting
            // of a SM particle will be included by findQCDTriple. To not
            // include the same splitting twice, continue for SM ISR radiator
            if ( !isSQCDrad || !isSQCDemt ) continue;

            // For an initial state radiator, always set recoiler
            // to the other initial state parton (recoil is taken
            // by full remaining system, so this is just a
            // labelling for such a process)
            int RecInit = 0;
            int iPartner = 0;
            for(int l = 0; l < int(posInitPartn.size()); ++l)
              if (posInitPartn[l] != iRad) RecInit = posInitPartn[l];

            // Find the colour connected partner
            // Find colour index of radiator before splitting
            col = getRadBeforeCol(iRad, EmtTag, event);
            acl = getRadBeforeAcol(iRad, EmtTag, event);

            // Find the correct partner: If a colour line has split,
            // the partner is connected to the radiator before the splitting
            // by a colour line (same reasoning for anticolour). The colour
            // that split is the colour appearing twice in the
            // radiator + emitted pair.
            // Thus, if we remove a colour index with the clustering,
            // we should look for a colour partner, else look for
            // an anticolour partner
            int colRemove = (event[iRad].col() == event[EmtTag].col())
                    ? event[iRad].col() : 0;
            iPartner = (colRemove > 0)
                     ?   FindCol(col,iRad,EmtTag,event,1,true)
                       + FindCol(col,iRad,EmtTag,event,2,true)
                     :   FindCol(acl,iRad,EmtTag,event,1,true)
                       + FindCol(acl,iRad,EmtTag,event,2,true);

            if ( allowedClustering( iRad, EmtTag, RecInit, iPartner, event)) {
              attachClusterings (clus, EmtTag, iRad, RecInit, iPartner,
                   pTLund(event, iRad, EmtTag, RecInit, pTdef), event);
              continue;
            }
          }
        }
      }
    }
  }

  // Done
  return clus;

}

//--------------------------------------------------------------------------

// Calculate and return the probability of a clustering.
// IN  Clustering : rad,rec,emt - System for which the splitting
//                  probability should be calcuated
// OUT splitting probability

double History::getProb(const Clustering & SystemIn) {

  // Disregard probabilities (and other kinematical information) when
  // calling History from within aMC@NLO.
  if (mergingHooksPtr->doRuntimeAMCATNLOInterface()) return 1.;

  // Get local copies of input system
  int Rad = SystemIn.emittor;
  int Rec = SystemIn.recoiler;
  int Emt = SystemIn.emitted;

  // Initialise shower probability
  double showerProb = 0.0;

  // If the splitting resulted in disallowed evolution variable,
  // disallow the splitting
  if (SystemIn.pT() <= 0.) return 0.;

  // Initialise all combinatorical factors
  double CF = 4./3.;
  double CA = 3.;
  // Flavour is known when reclustring, thus n_f=1
  double TR = 1./2.;

  // Split up in FSR and ISR
  bool isFSR = (state[Rad].isFinal() && state[Rec].isFinal());
  bool isFSRinREC = (state[Rad].isFinal() && !state[Rec].isFinal());
  bool isISR = !state[Rad].isFinal();

  // Check if external splitting probability should be used.
  if ( mergingHooksPtr->useShowerPlugin() ) {
    int iPartner = (isISR && SystemIn.partner > 0) ? SystemIn.partner : Rec;

    double pr = 0.;
    bool isFSR2 = showers->timesPtr->isTimelike(state, Rad, Emt, iPartner, "");
    if (isFSR2) {
      string name = showers->timesPtr->getSplittingName( state, Rad, Emt,
                    iPartner).front();
      pr          = showers->timesPtr->getSplittingProb( state, Rad, Emt,
                    iPartner, name);
    } else {
      string name = showers->spacePtr->getSplittingName(state, Rad, Emt,
                    iPartner).front();
      pr          = showers->spacePtr->getSplittingProb(state, Rad, Emt,
                    iPartner, name);
    }
    return abs(pr);
  }

  // Check if this is the clustering 2->3 to 2->2.
  // If so, use weight for joined evolution
  int nFinal = 0;
  for(int i=0; i < state.size(); ++i)
    if (state[i].isFinal()) nFinal++;
  bool isLast = (nFinal == (mergingHooksPtr->hardProcess->nQuarksOut()
                           +mergingHooksPtr->hardProcess->nLeptonOut()+1));

  // Do not calculate splitting functions for electroweak emissions
  bool isElectroWeak = (state[Emt].idAbs() == 23 || state[Emt].idAbs() == 24);

  if (isISR) {
    // Find incoming particles
    int inP = 0;
    int inM = 0;
    for(int i=0;i< int(state.size()); ++i) {
      if (state[i].mother1() == 1) inP = i;
      if (state[i].mother1() == 2) inM = i;
    }
    // Construct dipole mass, eCM and sHat = x1*x2*s
    Vec4   sum     = state[Rad].p() + state[Rec].p() - state[Emt].p();
    double m2Dip = sum.m2Calc();
    double sHat = (state[inM].p() + state[inP].p()).m2Calc();
    // Energy fraction z=E_q1/E_qi in branch q(i)q(2) -> q(1)g(3)q(2)
    double z1 = m2Dip / sHat;
    // Virtuality of the splittings
    Vec4 Q1( state[Rad].p() - state[Emt].p() );
    Vec4 Q2( state[Rec].p() - state[Emt].p() );
    // Q^2 for emission off radiator line
    double Q1sq = -Q1.m2Calc();
    // pT^2 for emission off radiator line
    double pT1sq = pow2(pTLund(state, Rad, Emt, Rec, -1, SystemIn.flavRadBef));
    // Remember if massive particles involved: Mass corrections for
    // to g->QQ and Q->Qg splittings
    bool g2QQmassive = mergingHooksPtr->includeMassive()
        && state[Rad].id() == 21
        && ( (state[Emt].idAbs() >= 4 && state[Emt].idAbs() < 7)
          || (state[Emt].idAbs() > 1000000 && state[Emt].idAbs() < 1000010 )
          || (state[Emt].idAbs() > 2000000 && state[Emt].idAbs() < 2000010 ));
    bool Q2Qgmassive = mergingHooksPtr->includeMassive()
        && state[Emt].id() == 21
        && ( (state[Rad].idAbs() >= 4 && state[Rad].idAbs() < 7)
          || (state[Rad].idAbs() > 1000000 && state[Rad].idAbs() < 1000010 )
          || (state[Rad].idAbs() > 2000000 && state[Rad].idAbs() < 2000010 ));
    bool isMassive = mergingHooksPtr->includeMassive()
                    && ( g2QQmassive || Q2Qgmassive
                      || state[Emt].id() == 1000021);
    double m2Emt0 = state[Emt].p().m2Calc();
    double m2Rad0 = pow(particleDataPtr->m0(state[Rad].id()),2);

    // Correction of virtuality for massive splittings
    if ( g2QQmassive)      Q1sq += m2Emt0;
    else if (Q2Qgmassive)  Q1sq += m2Rad0;

    // pT0 dependence!!!
    double pT0sq = pow(mergingHooksPtr->pT0ISR(),2);
    double Q2sq = -Q2.m2Calc();

    // Correction of virtuality of other splitting
    bool g2QQmassiveRec = mergingHooksPtr->includeMassive()
        && state[Rec].id() == 21
        && ( state[Emt].idAbs() >= 4 && state[Emt].idAbs() < 7);
    bool Q2QgmassiveRec = mergingHooksPtr->includeMassive()
        && state[Emt].id() == 21
        && ( state[Rec].idAbs() >= 4 && state[Rec].idAbs() < 7);
    double m2Rec0 = pow(particleDataPtr->m0(state[Rec].id()),2);
    if ( g2QQmassiveRec)      Q2sq += m2Emt0;
    else if (Q2QgmassiveRec)  Q2sq += m2Rec0;

    bool hasJoinedEvol = (state[Emt].id() == 21
                       || state[Rad].id() == state[Rec].id());

    // Initialise normalization factor multiplying the splitting
    // function numerator
    double fac = 1.;
    if ( mergingHooksPtr->pickByFull() || mergingHooksPtr->pickBySumPT()) {
      double facJoined  = ( Q2sq + pT0sq/(1.-z1) )
                        * 1./(Q1sq*Q2sq + pT0sq*sHat + pow(pT0sq/(1.-z1),2));
      double facSingle = mergingHooksPtr->nonJoinedNorm()*1./( pT1sq + pT0sq);

      fac = (hasJoinedEvol && isLast) ? facJoined : facSingle;

    } else if (mergingHooksPtr->pickByPoPT2()) {
      fac = 1./(pT1sq + pT0sq);
    } else {
      loggerPtr->ERROR_MSG(
        "scheme for calculating shower splitting probability is undefined");
    }

    // Calculate shower splitting probability:
    // Splitting functions*normalization*ME reweighting factors

    if ( isElectroWeak ) {

      // For electroweak splittings, the probabilities depend on the
      // full shower history, and can hence not be calculated correctly
      // here. Thus, use dummy value and "dress" with full probabilities
      // later, once the path is known.
      showerProb = 1.;

    // Calculate branching probability for q -> q g
    } else if ( state[Emt].id() == 21 && state[Rad].id() != 21) {
      // Find splitting kernel
      double num = CF*(1. + pow(z1,2)) / (1.-z1);
      if (isMassive) num -= CF * z1 * (1.-z1) * (m2Rad0/pT1sq);

      // Find ME reweighting factor
      double meReweighting = 1.;
      // Find the number of final state coloured particles, apart
      // from those coming from the hard process
      int nCol = 0;
      for(int i=0; i < state.size(); ++i)
        if (state[i].isFinal() && state[i].colType() != 0
          && !mergingHooksPtr->hardProcess->matchesAnyOutgoing(i,state) )
          nCol++;
      // For first splitting of single vector boson production,
      // apply ME corrections
      if (nCol == 1
       && int(mergingHooksPtr->hardProcess->hardIntermediate.size()) == 1) {
        double sH = m2Dip / z1;
        double tH = -Q1sq;
        double uH = Q1sq - m2Dip * (1. - z1) / z1;
        double misMatch = (uH*tH - (uH + tH)*pT0sq/(1.-z1)
                          + pow(pT0sq/(1.-z1),2) ) / (uH*tH);
        meReweighting *= (tH*tH + uH*uH + 2. * m2Dip * sH)
                       / (sH*sH + m2Dip*m2Dip);
        meReweighting *= misMatch;
      }
      // Multiply factors
      showerProb = num*fac*meReweighting;

    // Calculate branching probability for g -> g g
    } else if ( state[Emt].id() == 21 && state[Rad].id() == 21) {
      // Calculate splitting kernel
      double num = 2.*CA*pow2(1. - z1*(1.-z1)) / (z1*(1.-z1));

      // Include ME reweighting for higgs!!
      // Find ME reweighting factor
      double meReweighting = 1.;
      // Find the number of final state coloured particles, apart
      // from those coming from the hard process
      int nCol = 0;
      for(int i=0; i < state.size(); ++i)
        if (state[i].isFinal() && state[i].colType() != 0
          && !mergingHooksPtr->hardProcess->matchesAnyOutgoing(i,state) )
          nCol++;
      // For first splitting of single vector boson production,
      // apply ME corrections
      if ( nCol == 1
       && mergingHooksPtr->getProcessString().compare("pp>h") == 0
       && int(mergingHooksPtr->hardProcess->hardIntermediate.size()) == 1 ) {
        double sH = m2Dip / z1;
        double tH = -Q1sq;
        double uH = Q1sq - m2Dip * (1. - z1) / z1;
        meReweighting *= 0.5
                       * (pow4(sH) + pow4(tH) + pow4(uH) + pow4(m2Dip))
                       / pow2(sH*sH - m2Dip * (sH - m2Dip));
      }

      // Multiply factors
      showerProb = num*fac*meReweighting;

    // Calculate branching probability for q -> g q
    } else if ( state[Emt].id() != 21 && state[Rad].id() != 21 ) {
      // Calculate splitting kernel
      double num = CF*(1. + pow2(1.-z1)) / z1;

      // Include ME reweighting for higgs!!
      // Find ME reweighting factor
      double meReweighting = 1.;
      // Find the number of final state coloured particles, apart
      // from those coming from the hard process
      int nCol = 0;
      for ( int i=0; i < state.size(); ++i )
        if ( state[i].isFinal() && state[i].colType() != 0
          && !mergingHooksPtr->hardProcess->matchesAnyOutgoing(i,state) )
          nCol++;
      // For first splitting of single vector boson production,
      // apply ME corrections
      if (nCol == 1
       && mergingHooksPtr->getProcessString().compare("pp>h") == 0
       && int(mergingHooksPtr->hardProcess->hardIntermediate.size()) == 1) {
        double sH = m2Dip / z1;
        double uH = Q1sq - m2Dip * (1. - z1) / z1;
        meReweighting *= (sH*sH + uH*uH)
                       / (sH*sH + pow2(sH -m2Dip));
      }

      // Multiply factors
      showerProb = num*fac*meReweighting;

    // Calculate branching probability for g -> q qbar
    } else if ( state[Emt].id() != 21 && state[Rad].id() == 21 ) {

      // Calculate splitting kernel
      double num = TR * ( pow(z1,2) + pow(1.-z1,2) );
      if (isMassive) num += TR * 2.*z1*(1.-z1)*(m2Emt0/pT1sq);
      // Calculate ME reweighting factor
      double meReweighting = 1.;
      // Find the number of final state coloured particles, apart
      // from those coming from the hard process
      int nCol = 0;
      for ( int i=0; i < state.size(); ++i )
        if ( state[i].isFinal() && state[i].colType() != 0
         && !mergingHooksPtr->hardProcess->matchesAnyOutgoing(i,state) )
          nCol++;
      // For first splitting of single vector boson production,
      // apply ME corrections
      if (nCol == 1
        && int(mergingHooksPtr->hardProcess->hardIntermediate.size()) == 1) {
        double sH = m2Dip / z1;
        double tH = -Q1sq;
        double uH = Q1sq - m2Dip * (1. - z1) / z1;
        swap( tH, uH);
        double misMatch = ( uH - pT0sq/(1.-z1) ) / uH;
        double me = (sH*sH + uH*uH + 2. * m2Dip * tH)
                  / (pow2(sH - m2Dip) + m2Dip*m2Dip);
        // Weight with me/overestimate
        meReweighting *= me;
        meReweighting *= misMatch;
      }
      // Multiply factors
      showerProb = num*fac*meReweighting;

    // Print error if no kernel calculated
    } else {
      loggerPtr->ERROR_MSG("splitting kernel undefined in ISR in clustering");
    }

    // If corrected pT below zero in ISR, put probability to zero
    double m2Sister = pow(state[Emt].m(),2);
    double pT2corr = (Q1sq - z1*(m2Dip + Q1sq)*(Q1sq + m2Sister)/m2Dip);
    if (pT2corr < 0.) showerProb  = 0.0;

    // If creating heavy quark by Q -> gQ then next need g -> Q + Qbar.
    // So minimum total mass2 is 4 * m2Sister, but use more to be safe.
    if ( state[Emt].id() == state[Rad].id()
       && ( state[Rad].idAbs() == 4 || state[Rad].idAbs() == 5 )) {
      double m2QQsister =  2.*4.*m2Sister;
      double pT2QQcorr = Q1sq - z1*(m2Dip + Q1sq)*(Q1sq + m2QQsister)
                       / m2Dip;
      if (pT2QQcorr < 0.0) showerProb = 0.0;
    }

    // Check cuts on momentum fraction.
    double zMaxAbs = 1.;
    double zMinAbs = 2. * state[Rad].e() / state[0].e() * z1;
    double pT2minNow = pow2(mergingHooksPtr->pTminISRSave);
    zMaxAbs   = 1. - 0.5 * (pT2minNow / m2Dip) *
      ( sqrt( 1. + 4. * m2Dip / pT2minNow ) - 1. );
    zMaxAbs          = min(1.,zMaxAbs);

    // Massive z limit.
    int radBefID = getRadBeforeFlav(Rad, Emt, state);
    if ( abs(radBefID) == 4 || abs(radBefID) == 5 ) {
      double m2Massive   = pow2(particleDataPtr->m0(radBefID));
      double mRatio      = sqrt( m2Massive / m2Dip );
      double zMaxMassive = (1. -  mRatio) / ( 1. +  mRatio * (1. -  mRatio) );
      zMaxAbs            = min(zMaxAbs, zMaxMassive);
    }

    if (z1 < zMinAbs || z1 > zMaxAbs) showerProb = 0.0;

    if (mergingHooksPtr->includeRedundant()) {
      // Initialise the spacelike shower alpha_S
      AlphaStrong* asISR = mergingHooksPtr->AlphaS_ISR();
      double as = (*asISR).alphaS(pT1sq + pT0sq) / (2.*M_PI);
      // Multiply with alpha_S
      showerProb *= as;
    }

  // Done for ISR case, begin FSR case

  }  else if (isFSR || isFSRinREC) {

    // Construct dipole mass
    int recSign  = (state[Rec].isFinal()) ? 1 : -1;
    Vec4   sum   = state[Rad].p() + recSign*state[Rec].p() + state[Emt].p();
    double m2Dip = abs(sum.m2Calc());

    // Virtuality of the splittings
    Vec4 Q1( state[Rad].p() + state[Emt].p() );
    Vec4 Q2( state[Rec].p() + state[Emt].p() );

    // Get z value.
    double z1 = getCurrentZ( Rad, Rec, Emt, SystemIn.flavRadBef);

    // Q^2 for emission off radiator line
    double Q1sq = Q1.m2Calc();
    // pT^2 for emission off radiator line
    double pT1sq = pow(SystemIn.pT(),2);
    // Q^2 for emission off recoiler line
    double Q2sq = Q2.m2Calc();

    // Remember if radiator or recoiler is massive.
    bool isMassiveRad = ( state[Rad].idAbs() >= 4
                       && state[Rad].id() != 21 );
    bool isMassiveRec = ( state[Rec].idAbs() >= 4
                       && state[Rec].id() != 21 );

    // Correction of virtuality for massive splittings.
    double m2Rad0 = pow(particleDataPtr->m0(state[Rad].id()),2);
    double m2Rec0 = pow(particleDataPtr->m0(state[Rec].id()),2);
    if ( mergingHooksPtr->includeMassive() && isMassiveRad ) Q1sq -= m2Rad0;
    if ( mergingHooksPtr->includeMassive() && isMassiveRec ) Q2sq -= m2Rec0;

    // Initialise normalization factor multiplying the splitting
    // function numerator
    double fac = 1.;
    if ( mergingHooksPtr->pickByFull() || mergingHooksPtr->pickBySumPT()) {
      double facJoined = (1.-z1)/Q1sq * m2Dip/( Q1sq + Q2sq );
      double facSingle = mergingHooksPtr->fsrInRecNorm() * 1./ pT1sq;
      fac = (!isFSRinREC && isLast) ? facJoined : facSingle;

    } else if (mergingHooksPtr->pickByPoPT2()) {
      fac = 1. / pT1sq;
    } else {
      loggerPtr->ERROR_MSG(
        "scheme for calculating shower splitting probability is undefined");
    }
    // Calculate shower splitting probability:
    // Splitting functions*normalization*ME reweighting factors

    if ( isElectroWeak ) {

      // For electroweak splittings, the probabilities depend on the
      // full shower history, and can hence not be calculated correctly
      // here. Thus, use dummy value and "dress" with full probabilities
      // later, once the path is known.
      showerProb = 1.;

    // Calculate branching probability for g -> g_1 g_2
    } else if ( state[Emt].id() == 21 && state[Rad].colType() == 2) {

      // Calculate splitting kernel
      double num = 0.5* CA * (1. + pow3(z1)) / (1.-z1);
      // Multiply factors
      showerProb = num*fac;

    // Calculate branching probability for q -> q g with quark recoiler
    } else if ( state[Emt].id() == 21
             && state[Rad].colType() != 2 && state[Rec].colType() != 2) {
      // For a qqbar dipole in FSR, ME corrections exist and the
      // splitting function "z-weight" is set to 1.0 (only for 2->2 ??)
      double num = CF * 2./(1.-z1);
      // Find the number of final state coloured particles, apart
      // from those coming from the hard process
      int nCol = 0;
        for(int i=0; i < state.size(); ++i)
          if (state[i].isFinal() && state[i].colType() != 0
          && !mergingHooksPtr->hardProcess->matchesAnyOutgoing(i,state) )
            nCol++;
      // Calculate splitting kernel
      if ( nCol > 3
        || int(mergingHooksPtr->hardProcess->hardIntermediate.size()) > 1)
        num = CF * (1. + pow2(z1)) /(1.-z1);
      // Calculate ME reweighting factor
      double meReweighting = 1.;
      // Correct if this is the process created by the first
      // FSR splitting of a 2->2 process
      if ( nCol == 3
        && int(mergingHooksPtr->hardProcess->hardIntermediate.size()) == 1 ) {
        // Construct 2->3 variables for FSR
        double x1 = 2. * (sum * state[Rad].p()) / m2Dip;
        double x2 = 2. * (sum * state[Rec].p()) / m2Dip;
        double prop1  = max(1e-12, 1. - x1);
        double prop2  = max(1e-12, 1. - x2);
        double x3     = max(1e-12, 2. - x1 - x2);
        // Calculate the ME reweighting factor
        double ShowerRate1       = 2./( x3 * prop2 );
        double meDividingFactor1 = prop1 / x3;
        double me                = (pow(x1,2) + pow(x2,2))/(prop1*prop2);
        meReweighting = meDividingFactor1 * me / ShowerRate1;
      }
      // Multiply factors
      showerProb = num*fac*meReweighting;

    // Calculate branching probability for q -> q g with gluon recoiler
    } else if ( state[Emt].id() == 21 && state[Rad].colType() != 2
      && state[Rec].colType() == 2 ) {
      // For qg /qbarg dipoles, the splitting function is
      // calculated and not weighted by a ME correction factor
      // Shower splitting function
      double num = CF * (1. + pow2(z1)) / (1.-z1);
      showerProb = num*fac;

    // Calculate branching probability for g -> q qbar
    } else if ( state[Emt].id() != 21 ) {
      // Get flavour of quark / antiquark
      int flavour = state[Emt].id();
      // Get correct masses for the quarks
      // (needed to calculate splitting function?)
      double mFlavour = particleDataPtr->m0(flavour);
      // Get mass of quark/antiquark pair
      double mDipole = m(state[Rad].p(), state[Emt].p());
      // Factor determining if gluon decay was allowed
      double beta = sqrtpos( 1. - 4.*pow2(mFlavour)/pow2(mDipole) );
      // Shower splitting function
      double num = 0.5*TR * ( z1*z1 + (1.-z1)*(1.-z1) );
      if (beta <= 0.) beta = 0.;

      showerProb = num*fac*beta;

    // Print error if no kernel calculated
    } else {
      loggerPtr->ERROR_MSG("splitting kernel undefined in FSR clustering");
    }

    if (mergingHooksPtr->includeRedundant()) {
      // Initialise the spacelike shower alpha_S
      AlphaStrong* asFSR = mergingHooksPtr->AlphaS_FSR();
      double as = (*asFSR).alphaS(pT1sq) / (2.*M_PI);
      // Multiply with alpha_S
      showerProb *= as;
    }

    double m2DipCorr  = pow2(sqrt(m2Dip) - sqrt(m2Rec0)) - m2Rad0;
    double zMin       = 0.5 - sqrtpos( 0.25 - pT1sq / m2DipCorr );
    double m2         = m2Rad0 + 2. * state[Rad].p()*state[Emt].p();
    bool keepMassive  = (z1 > zMin && z1 < 1. - zMin
      && m2 * m2Dip < z1 * (1. - z1) * pow2(m2Dip + m2 - m2Rec0) );
    // No emission probability outside disallowed z range.
    if (!keepMassive) showerProb *= 0.0;

    // Done for FSR
  } else {
    loggerPtr->ERROR_MSG("radiation could not be interpreted as FSR or ISR");
  }

  if (mergingHooksPtr->doWeakClustering()) {

    // Every time we assign spin, equivalent QCD histories are counted twice,
    // due to distingushing between quark spins.
    // To remove this overcounting, multiply by QCD probabilities by 1/2,
    // for each quark spin that has been assigned.
    double factor = 1.;
    if (state[Rad].idAbs()  < 10 && state[Rad].intPol() == 9
      && SystemIn.spinRad != 9) factor *= 0.5;
    if (state[Emt].idAbs()  < 10 && state[Emt].intPol() == 9
      && SystemIn.spinEmt != 9) factor *= 0.5;
    if (state[Rec].idAbs()  < 10 && state[Rec].intPol() == 9
      && SystemIn.spinRec != 9) factor *= 0.5;
    if ( state[Emt].colType() != 0 ) {
      showerProb *= factor;
    }

    // The g -> q qbar splitting leads to two histories, not four.
    // The previous clustering steps overcounted the number of histories to be
    // four, leading to a too small probability of a path by 1/2. Correct!
    if ( state[Emt].idAbs() < 10 && state[Rad].colType() != 0) {
      showerProb *= 2.0;
    }

  }

  // Done
  return showerProb;

}

//--------------------------------------------------------------------------

// Set up the beams (fill the beam particles with the correct
// current incoming particles) to allow calculation of splitting
// probability.
// For interleaved evolution, set assignments dividing PDFs into
// sea and valence content. This assignment is, until a history path
// is chosen and a first trial shower performed, not fully correct
// (since content is chosen form too high x and too low scale). The
// assignment used for reweighting will be corrected after trial
// showering

void History::setupBeams() {

  // Do nothing for empty event, possible if sequence of
  // clusterings was ill-advised in that it results in
  // colour-disconnected states
  if (state.size() < 4) return;
  // Do nothing for e+e- beams
  if ( state[3].colType() == 0 ) return;
  if ( state[4].colType() == 0 ) return;

  // Incoming partons to hard process are stored in slots 3 and 4.
  int inS = 0;
  int inP = 0;
  int inM = 0;
  for(int i=0;i< int(state.size()); ++i) {
    if (state[i].mother1() == 1) inP = i;
    if (state[i].mother1() == 2) inM = i;
  }

  // Save some info before clearing beams
  // Mothers of incoming partons companion code
  int motherPcompRes = -1;
  int motherMcompRes = -1;

  bool sameFlavP = false;
  bool sameFlavM = false;

  if (mother) {
    int inMotherP = 0;
    int inMotherM = 0;
    for(int i=0;i< int(mother->state.size()); ++i) {
      if (mother->state[i].mother1() == 1) inMotherP = i;
      if (mother->state[i].mother1() == 2) inMotherM = i;
    }
    sameFlavP = (state[inP].id() == mother->state[inMotherP].id());
    sameFlavM = (state[inM].id() == mother->state[inMotherM].id());

    motherPcompRes = (sameFlavP) ? beamA[0].companion() : -2;
    motherMcompRes = (sameFlavM) ? beamB[0].companion() : -2;
  }

  // Append the current incoming particles to the beam
  beamA.clear();
  beamB.clear();

  // Get energy of incoming particles
  double Ep = 2. * state[inP].e();
  double Em = 2. * state[inM].e();

  // If incoming partons are massive then recalculate to put them massless.
  if (state[inP].m() != 0. || state[inM].m() != 0.) {
    Ep = state[inP].pPos() + state[inM].pPos();
    Em = state[inP].pNeg() + state[inM].pNeg();
  }

  // Add incoming hard-scattering partons to list in beam remnants.
  double x1 = Ep / state[inS].m();
  beamA.append( inP, state[inP].id(), x1);
  double x2 = Em / state[inS].m();
  beamB.append( inM, state[inM].id(), x2);

  // Scale. For ME multiplicity history, put scale to mu_F
  // (since sea/valence quark content is chosen from this scale)
  double scalePDF = (mother) ? scale : infoPtr->QFac();
  // Find whether incoming partons are valence or sea. Store.
  // Can I do better, e.g. by setting the scale to the hard process
  // scale (= M_W) or by replacing one of the x values by some x/z??
  beamA.xfISR( 0, state[inP].id(), x1, scalePDF*scalePDF);
  if (!mother) {
    beamA.pickValSeaComp();
  }  else {
    beamA[0].companion(motherPcompRes);
  }
  beamB.xfISR( 0, state[inM].id(), x2, scalePDF*scalePDF);
  if (!mother) {
    beamB.pickValSeaComp();
  } else {
    beamB[0].companion(motherMcompRes);
  }

}

//--------------------------------------------------------------------------

// Calculate the PDF ratio used in the argument of the no-emission
// probability

double History::pdfForSudakov() {

  // Do nothing for e+e- beams
  if ( state[3].colType() == 0 ) return 1.0;
  if ( state[4].colType() == 0 ) return 1.0;

  // Check if splittings was ISR or FSR
  bool FSR = (   mother->state[clusterIn.emittor].isFinal()
             && mother->state[clusterIn.recoiler].isFinal());
  bool FSRinRec = (   mother->state[clusterIn.emittor].isFinal()
                  && !mother->state[clusterIn.recoiler].isFinal());

  // Done for pure FSR
  if (FSR) return 1.0;

  int iInMother = (FSRinRec)? clusterIn.recoiler : clusterIn.emittor;
  //  Find side of event that was reclustered
  int side = ( mother->state[iInMother].pz() > 0 ) ? 1 : -1;

  int inP = 0;
  int inM = 0;
  for(int i=0;i< int(state.size()); ++i) {
    if (state[i].mother1() == 1) inP = i;
    if (state[i].mother1() == 2) inM = i;
  }

  // Save mother id
  int idMother = mother->state[iInMother].id();
  // Find daughter position and id
  int iDau = (side == 1) ? inP : inM;
  int idDaughter = state[iDau].id();
  // Get mother x value
  double xMother = 2. * mother->state[iInMother].e() / mother->state[0].e();
  // Get daughter x value of daughter
  double xDaughter = 2.*state[iDau].e() / state[0].e(); // x1 before isr

  // Calculate pdf ratio
  double ratio = getPDFratio(side, true, false, idMother, xMother, scale,
                   idDaughter, xDaughter, scale);

  // For FSR with incoming recoiler, maximally return 1.0, as
  // is done in Pythia::TimeShower.
  // For ISR, return ratio
  return ( (FSRinRec)? min(1.,ratio) : ratio);
}

//--------------------------------------------------------------------------

// Calculate the hard process matrix element to include in the selection
// probability.

double History::hardProcessME( const Event& event ) {

  // Calculate prob for Drell-Yan process.
  if (isEW2to1(event)) {

    // qqbar -> W.
    if (event[5].idAbs() == 24) {
      int idIn1  = event[3].id();
      int idIn2  = event[4].id();
      double mW = particleDataPtr->m0(24);
      double gW = particleDataPtr->mWidth(24) / mW;
      double sH = (event[3].p()+event[4].p()).m2Calc();

      double thetaWRat = 1. / (12. * coupSMPtr->sin2thetaW());
      double ckmW = coupSMPtr->V2CKMid(abs(idIn1), abs(idIn2));

      double bwW = 12. * M_PI / ( pow2(sH - pow2(mW)) + pow2(sH * gW) );
      double preFac = thetaWRat * sqrt(sH) * particleDataPtr->mWidth(24);
      return ckmW * preFac * bwW;
    }
    // qqbar -> Z. No interference with gamma included.
    else if (event[5].idAbs() == 23) {
      double mZ = particleDataPtr->m0(23);
      double gZ = particleDataPtr->mWidth(23) / mZ;
      double sH = (event[3].p()+event[4].p()).m2Calc();
      int idInit = event[3].idAbs();
      double thetaZRat = (pow2(coupSMPtr->rf(idInit))
        + pow2(coupSMPtr->lf(idInit))) /
        (24. * coupSMPtr->sin2thetaW() * coupSMPtr->cos2thetaW());
      double bwW = 12. * M_PI / ( pow2(sH - pow2(mZ)) + pow2(sH * gZ) );
      double preFac = thetaZRat * sqrt(sH) * particleDataPtr->mWidth(23);
      return preFac * bwW;
    }
    else {
      loggerPtr->WARNING_MSG(
        "only Z/W are supported as 2->1 processes. Skipping history");
      return 0;
    }
  }
  // 2 to 2 process, assume QCD.
    else if (isQCD2to2(event)) {
    int idIn1  = event[3].id();
    int idIn2  = event[4].id();
    int idOut1 = event[5].id();
    int idOut2 = event[6].id();

    double sH = (event[3].p()+event[4].p()).m2Calc();
    double tH = (event[3].p()-event[5].p()).m2Calc();
    double uH = (event[3].p()-event[6].p()).m2Calc();

    // Verify that it is QCD.
    bool isQCD = true;
    if (!(abs(idIn1) < 10 || abs(idIn1) == 21) ) isQCD = false;
    if (!(abs(idIn2) < 10 || abs(idIn2) == 21) ) isQCD = false;
    if (!(abs(idOut1) < 10 || abs(idOut1) == 21) ) isQCD = false;
    if (!(abs(idOut2) < 10 || abs(idOut2) == 21) ) isQCD = false;

    // Overall phase-space constant (dsigma/dcos(theta)).
    double cor = M_PI / (9. * pow2(sH));

    // If it is QCD calculate cross section.
    if (isQCD) {
      // Find out which 2->2 process it is.

      // incoming gluon pair.
      if (abs(idIn1) == 21 && abs(idIn2) == 21) {
        if (abs(idOut1) == 21 && abs(idOut2) == 21)
          return cor * simpleWeakShowerMEs.getMEgg2gg(sH, tH, uH);
        else return cor * simpleWeakShowerMEs.getMEgg2qqbar(sH, tH, uH);

      // Incoming single gluon
      } else if (abs(idIn1) == 21 || abs(idIn2) == 21) {
        if (idIn1 != idOut1) swap(uH, tH);
        return cor * simpleWeakShowerMEs.getMEqg2qg(sH, tH, uH);
      }

      // Incoming quarks
      else {
        if (abs(idOut1) == 21 && abs(idOut2) == 21)
          return cor * simpleWeakShowerMEs.getMEqqbar2gg(sH, tH, uH);
        if (idIn1 == -idIn2) {
          if (abs(idIn1) == abs(idOut1)) {
            if (idIn1 != idOut1) swap(uH, tH);
            return cor * simpleWeakShowerMEs.getMEqqbar2qqbar(sH,tH,uH,true);
          }
          else {
            return cor * simpleWeakShowerMEs.getMEqqbar2qqbar(sH,tH,uH,false);
          }
        }
        else if (idIn1 == idIn2)
          return cor * simpleWeakShowerMEs.getMEqq2qq(sH, tH, uH, true);
        else {
          if (idIn1 == idOut1) swap(uH,tH);
          return cor * simpleWeakShowerMEs.getMEqq2qq(sH, tH, uH, false);
        }
      }
    }
  }


  // Get hard process.
  string process = mergingHooksPtr->getProcessString();
  double result = 1.;

  if ( process.compare("pp>e+ve") == 0
    || process.compare("pp>e-ve~") == 0
    || process.compare("pp>LEPTONS,NEUTRINOS") == 0 ) {
    // Do nothing for incomplete process.
    int nFinal = 0;
    for ( int i=0; i < int(event.size()); ++i )
      if ( event[i].isFinal() ) nFinal++;
    if ( nFinal != 2 ) return 1.;
    // Get W-boson mass and width.
    double mW = particleDataPtr->m0(24);
    double gW = particleDataPtr->mWidth(24) / mW;
    // Get incoming particles.
    int inP = (event[3].pz() > 0) ? 3 : 4;
    int inM = (event[3].pz() > 0) ? 4 : 3;
    // Get outgoing particles.
    int outP = 0;
    for ( int i=0; i < int(event.size()); ++i ) {
      if ( event[i].isFinal() && event[i].px() > 0 ) outP = i;
    }
    // Get Mandelstam variables.
    double sH = (event[inP].p() + event[inM].p()).m2Calc();
    double tH = (event[inP].p() - event[outP].p()).m2Calc();
    double uH = - sH - tH;

    // Return kinematic part of matrix element.
    result = ( 1. + (tH - uH)/sH ) / ( pow2(sH - mW*mW) + pow2(sH*gW) );
  } else
    result = mergingHooksPtr->hardProcessME(event);

  return result;

}

//--------------------------------------------------------------------------

// Perform the clustering of the current state and return the
// clustered state.
// IN Clustering : rad,rec,emt triple to be clustered to two partons
// OUT clustered state

Event History::cluster( Clustering & inSystem ) {

  // Initialise tags of particles to be changed
  int Rad = inSystem.emittor;
  int Rec = inSystem.recoiler;
  int Emt = inSystem.emitted;
  // Initialise eCM,mHat
  double eCM = state[0].e();
  // Flags for type of radiation
  int radType = state[Rad].isFinal() ? 1 : -1;
  int recType = state[Rec].isFinal() ? 1 : -1;

  // Construct the clustered event
  Event NewEvent = Event();
  NewEvent.init("(hard process-modified)", particleDataPtr);
  NewEvent.clear();
  map<int,int> iPosMothTmp, iPosMoth;

  // Check if external clustering should be used.
  if ( mergingHooksPtr->useShowerPlugin() ) {
    int iPartner = (radType == -1 && inSystem.partner > 0)
                 ? inSystem.partner : Rec;
    bool isFSR = showers->timesPtr->isTimelike(state, Rad, Emt, iPartner, "");
    if (isFSR) {
      string name = showers->timesPtr->getSplittingName(state,Rad,Emt,
                    iPartner).front();
      return        showers->timesPtr->clustered(state,Rad,Emt,iPartner,name);
    } else {
      string name = showers->spacePtr->getSplittingName(state,Rad,Emt,
                    iPartner).front();
      return        showers->spacePtr->clustered(state,Rad,Emt,iPartner,name);
    }
  }

  // Copy all unchanged particles to NewEvent
  for (int i = 0; i < state.size(); ++i) {
    if ( i == Rad || i == Rec || i == Emt ) continue;
    int iNext = NewEvent.append( state[i] );
    iPosMothTmp[iNext] = i;
  }

  // Copy all the junctions one by one
  for (int i = 0; i < state.sizeJunction(); ++i)
    NewEvent.appendJunction( state.getJunction(i) );
  // Find an appropriate scale for the hard process
  double mu = choseHardScale(state);
  // Initialise scales for new event
  NewEvent.saveSize();
  NewEvent.saveJunctionSize();
  NewEvent.scale(mu);
  NewEvent.scaleSecond(mu);

  // Set properties of radiator/recoiler after the clustering
  // Recoiler properties will be unchanged
  Particle RecBefore = Particle( state[Rec] );
  RecBefore.setEvtPtr(&NewEvent);
  RecBefore.daughters(0,0);
  RecBefore.pol(inSystem.spinRec);
  // Find flavour of radiator before splitting
  int radID = inSystem.flavRadBef;
  if (radID == 0) radID = getRadBeforeFlav(Rad, Emt, state);
  int recID = state[Rec].id();
  Particle RadBefore = Particle( state[Rad] );
  RadBefore.setEvtPtr(&NewEvent);
  RadBefore.id(radID);
  RadBefore.pol(inSystem.spinRadBef);
  RadBefore.daughters(0,0);
  // Put dummy values for colours
  RadBefore.cols(RecBefore.acol(),RecBefore.col());

  // Reset status if the reclustered radiator is a resonance.
  if ( particleDataPtr->isResonance(radID) && radType == 1)
    RadBefore.status(state[Rad].status());

  // Put mass for radiator and recoiler
  double radMass = particleDataPtr->m0(radID);
  double recMass = particleDataPtr->m0(recID);
  if (radType == 1 ) RadBefore.m(radMass);
  else RadBefore.m(0.0);
  if (recType == 1 ) RecBefore.m(recMass);
  else RecBefore.m(0.0);

  // Construct momenta and  colours of clustered particles
  // ISR/FSR splittings are treated differently
  if ( radType + recType == 2 && state[Emt].idAbs() != 23 &&
       state[Emt].idAbs() != 24) {
    // Clustering of final(rad)/final(rec) dipole splitting
    // Get eCM of (rad,rec,emt) triple
    Vec4   sum     = state[Rad].p() + state[Rec].p() + state[Emt].p();
    double eCMME   = sum.mCalc();

    // Define radiator and recoiler back-to-back in the dipole
    // rest frame [=(state[rad]+state[emt])+state[rec] rest frame]
    Vec4 Rad4mom;
    Vec4 Rec4mom;
    double mDsq   = pow2(eCMME);
    // If possible, keep the invariant mass of the radiator.
    double mRsq   = (radID == state[Rad].id() )
                  ? abs(state[Rad].p().m2Calc())
                  : pow2(particleDataPtr->m0(radID));
    double mSsq   = abs(state[Rec].p().m2Calc());
    double a = 0.5*sqrt(mDsq);
    double b = 0.25*(mRsq - mSsq) / a;
    double c = sqrt(pow2(a) + pow2(b) - 2.*a*b - mSsq);

    Rad4mom.p( 0., 0., c, a+b);
    Rec4mom.p( 0., 0.,-c, a-b);

    // Find boost from Rad4mom+Rec4mom rest frame to event cm frame
    Vec4 old1 = Vec4(state[Rad].p() + state[Emt].p());
    Vec4 old2 = Vec4(state[Rec].p());
    RotBstMatrix fromCM;
    fromCM.fromCMframe(old1, old2);
    // Transform momenta
    Rad4mom.rotbst(fromCM);
    Rec4mom.rotbst(fromCM);

    RadBefore.p(Rad4mom);
    RecBefore.p(Rec4mom);
    RadBefore.m(sqrt(mRsq));
    RecBefore.m(sqrt(mSsq));

  } else if ( radType + recType == 2 && (state[Emt].idAbs() == 23 ||
              state[Emt].idAbs() == 24) ) {
    // Clustering of final(rad)/final(rec) dipole splitting
    // Get eCM of (rad,rec,emt) triple
    Vec4   sum     = state[Rad].p() + state[Rec].p() + state[Emt].p();
    double eCMME   = sum.mCalc();

    // Define radiator and recoiler back-to-back in the dipole
    // rest frame [=(state[rad]+state[emt])+state[rec] rest frame]
    Vec4 Rad4mom;
    Vec4 Rec4mom;
    double mDsq   = pow2(eCMME);
    // If possible, keep the invariant mass of the radiator.
    double mRsq   = (radID == state[Rad].id() )
                  ? abs(state[Rad].p().m2Calc())
                  : pow2(particleDataPtr->m0(radID));
    double mSsq   = abs(state[Rec].p().m2Calc());
    double a = 0.5*sqrt(mDsq);
    double b = 0.25*(mRsq - mSsq) / a;
    double c = sqrt(pow2(a) + pow2(b) - 2.*a*b - mSsq);

    Rad4mom.p( 0., 0., c, a+b);
    Rec4mom.p( 0., 0.,-c, a-b);

    // Find boost from Rad4mom+Rec4mom rest frame to event cm frame
    Vec4 old1 = Vec4(state[Rad].p() + state[Emt].p());
    Vec4 old2 = Vec4(state[Rec].p());
    RotBstMatrix fromCM;
    fromCM.fromCMframe(old1, old2);
    // Transform momenta
    Rad4mom.rotbst(fromCM);
    Rec4mom.rotbst(fromCM);

    RadBefore.p(Rad4mom);
    RecBefore.p(Rec4mom);
    RadBefore.m(sqrt(mRsq));
    RecBefore.m(sqrt(mSsq));

  } else if ( radType + recType == 0 ) {

    // Clustering of final(rad)/initial(rec) dipole splitting
    // Get eCM of (rad,rec,emt) triple
    Vec4   sum     = state[Rad].p() + state[Rec].p() + state[Emt].p();
    double eCMME   = sum.mCalc();
    // Define radiator and recoiler back-to-back in the dipole
    // rest frame [=(state[rad]+state[emt])+state[rec] rest frame]
    Vec4 Rad4mom;
    Vec4 Rec4mom;
    double mDsq   = pow2(eCMME);
    // If possible, keep the invariant mass of the radiator.
    double mRsq   = (radID == state[Rad].id() )
                  ? abs(state[Rad].p().m2Calc())
                  : pow2(particleDataPtr->m0(radID));
    double mSsq   = abs(state[Rec].p().m2Calc());
    double a = 0.5*sqrt(mDsq);
    double b = 0.25*(mRsq - mSsq) / a;
    double c = sqrt(pow2(a) + pow2(b) - 2.*a*b - mSsq);

    Rad4mom.p( 0., 0., c, a+b);
    Rec4mom.p( 0., 0.,-c, a-b);

    // Find boost from Rad4mom+Rec4mom rest frame to event cm frame
    Vec4 old1 = Vec4(state[Rad].p() + state[Emt].p());
    Vec4 old2 = Vec4(state[Rec].p());
    RotBstMatrix fromCM;
    fromCM.fromCMframe(old1, old2);
    // Transform momenta
    Rad4mom.rotbst(fromCM);
    Rec4mom.rotbst(fromCM);

    // Rescale recoiler momentum
    Rec4mom = 2.*state[Rec].p() - Rec4mom;

    // Ensure that recoiler is massless to
    // very good accuracy.
    if ( abs(Rec4mom.mCalc()) > 1e-7 ) {
      double pzSign = (Rec4mom.pz() > 0.) ? 1. : -1.;
      double eRec   = Rec4mom.e();
      Rec4mom.p(0., 0., pzSign*eRec, eRec);
    }

    RadBefore.p(Rad4mom);
    RecBefore.p(Rec4mom);
    RadBefore.m(sqrt(mRsq));

    // Set mass of initial recoiler to zero
    RecBefore.m( 0.0 );

  } else {

    // Clustering of initial(rad)/initial(rec) dipole splitting
    // We want to cluster: Meaning doing the inverse of a process
    //            ( pDaughter + pRecoiler -> pOut )
    //        ==> ( pMother + pPartner -> pOut' + pSister )
    // produced by an initial state splitting. The matrix element
    // provides us with pMother, pPartner, pSister and pOut'
    Vec4 pMother( state[Rad].p() );
    Vec4 pSister( state[Emt].p() );
    Vec4 pPartner( state[Rec].p() );
    Vec4 pDaughterBef( 0.,0.,0.,0. );
    Vec4 pRecoilerBef( 0.,0.,0.,0. );
    Vec4 pDaughter( 0.,0.,0.,0. );
    Vec4 pRecoiler( 0.,0.,0.,0. );

    // Find side that radiates event (mother moving in sign * p_z direction).
    int sign = (state[Rad].pz() > 0.) ? 1 : -1;

    // Find rotation by phi that would have been done for a
    // splitting daughter -> mother + sister
    double phi = pSister.phi();
    // Find rotation with -phi
    RotBstMatrix rot_by_mphi;
    rot_by_mphi.rot(0.,-phi);
    // Find rotation with +phi
    RotBstMatrix rot_by_pphi;
    rot_by_pphi.rot(0.,phi);

    // Get mother and partner x values
    // x1 after isr
    double x1 = 2. * pMother.e() / eCM;
    // x2 after isr
    double x2 = 2. * pPartner.e() / eCM;

    // Find z of the splitting
    Vec4 qDip( pMother - pSister);
    Vec4 qAfter(pMother + pPartner);
    Vec4 qBefore(qDip + pPartner);
    double z = qBefore.m2Calc() / qAfter.m2Calc();

    // Calculate e_CM^2 before the splitting.
    double x1New = z*x1; // x1 before isr
    double x2New = x2;   // x2 before isr
    double sHat = x1New*x2New*eCM*eCM;

    // Construct daughter and recoiler momenta before the splitting.
    // (Note: For final result, only needs to be boosted into
    //        frame with unchanged "recoiler" momentum)
    pDaughterBef.p( 0., 0.,  sign*0.5*sqrt(sHat), 0.5*sqrt(sHat));
    pRecoilerBef.p( 0., 0., -sign*0.5*sqrt(sHat), 0.5*sqrt(sHat));

    // Rotate momenta defined in the lab frame by phi
    pMother.rotbst( rot_by_mphi );
    pSister.rotbst( rot_by_mphi );
    pPartner.rotbst( rot_by_mphi );
    for(int i=3; i< NewEvent.size(); ++i)
      NewEvent[i].rotbst( rot_by_mphi );

    // Find boost from lab frame to rest frame of
    // off-shell daughter + on-shell recoiler dipole
    pDaughter.p( pMother - pSister);
    pRecoiler.p( pPartner );
    RotBstMatrix from_CM_to_DRoff;
    if (sign == 1)
      from_CM_to_DRoff.toCMframe(pDaughter, pRecoiler);
    else
      from_CM_to_DRoff.toCMframe(pRecoiler, pDaughter);

    // Rotate and boost all momenta to rest frame of off-shell daughter +
    // on-shell recoiler dipole
    pMother.rotbst( from_CM_to_DRoff );
    pPartner.rotbst( from_CM_to_DRoff );
    pSister.rotbst( from_CM_to_DRoff );
    for(int i=3; i< NewEvent.size(); ++i)
      NewEvent[i].rotbst( from_CM_to_DRoff );

    // Find longitudinal boost from on-shell daughter + on-shell recoiler
    // dipole rest frame to the frame in which the recoiler momentum (x-value)
    // does not change in the splitting process.
    RotBstMatrix from_DR_to_CM;
    from_DR_to_CM.bst( 0., 0., sign*( x1New - x2New ) / ( x1New + x2New ) );

    // Boost all momenta into the "unchanged recoiler" frame, thereby
    // correcting for momentum mismatch by transferring the recoil to all
    // final state particles.
    pDaughterBef.rotbst( from_DR_to_CM );
    pRecoilerBef.rotbst( from_DR_to_CM );
    for(int i=3; i< NewEvent.size(); ++i)
      NewEvent[i].rotbst( from_DR_to_CM );

    // Transform outgoing momenta
    for(int i=3; i< NewEvent.size(); ++i)
      NewEvent[i].rotbst( rot_by_pphi );

    // Ensure that radiator and recoiler are massless to
    // very good accuracy.
    if ( abs(pRecoilerBef.mCalc()) > 1e-7 ) {
      double pzSign = (pRecoilerBef.pz() > 0.) ? 1. : -1.;
      double eRec   = pRecoilerBef.e();
      pRecoilerBef.p(0., 0., pzSign*eRec, eRec);
    }
    if ( abs(pDaughterBef.mCalc()) > 1e-7 ) {
      double pzSign = (pDaughterBef.pz() > 0.) ? 1. : -1.;
      double eDau   = pDaughterBef.e();
      pDaughterBef.p(0., 0., pzSign*eDau, eDau);
    }
    // Transform pMother and outgoing momenta
    // Set momenta of particles to be attached to new event record
    RecBefore.p( pRecoilerBef );
    RadBefore.p( pDaughterBef );
    if (RecBefore.pz() > 0.) RecBefore.mother1(1);
    else RecBefore.mother1(2);
    if (RadBefore.pz() > 0.) RadBefore.mother1(1);
    else RadBefore.mother1(2);

  }

  // Put some dummy production scales for RecBefore, RadBefore
  RecBefore.scale(mu);
  RadBefore.scale(mu);

  // Append new recoiler and find new radiator colour
  NewEvent.append(RecBefore);

  // Assign the correct colour to re-clustered radiator.
  // Keep old radiator colours for electroweak emission.
  int emtID = state[Emt].id();
  if ( emtID == 22 || emtID == 23 || abs(emtID) == 24 )
    RadBefore.cols( state[Rad].col(), state[Rad].acol() );
  // For QCD, carefully construct colour.
  else if ( !connectRadiator( RadBefore, radType, RecBefore, recType,
               NewEvent ) ) {
    // Could happen if previous clustering produced several colour
    // singlett subsystems in the event
    NewEvent.reset();
    return NewEvent;
  }

  // Build the clustered event
  Event outState = Event();
  outState.init("(hard process-modified)", particleDataPtr);
  outState.clear();

  // Copy system and incoming beam particles to outState
  for (int i = 0; i < 3; ++i) {
    int iNext = outState.append( NewEvent[i] );
    iPosMoth[iNext] = iPosMothTmp[i];
  }
  // Copy all the junctions one by one
  for (int i = 0; i < state.sizeJunction(); ++i)
    outState.appendJunction( state.getJunction(i) );
  // Initialise scales for new event
  outState.saveSize();
  outState.saveJunctionSize();
  outState.scale(mu);
  outState.scaleSecond(mu);
  bool radAppended = false;
  bool recAppended = false;
  // Save position of radiator and recoiler in new event record.
  int radPos = 0, recPos = 0;

  // Append first incoming particle
  if ( RecBefore.mother1() == 1) {
    recPos = outState.append( RecBefore );
    iPosMoth[recPos] = Rec;
    recAppended = true;
  } else if ( RadBefore.mother1() == 1 ) {
    radPos = outState.append( RadBefore );
    iPosMoth[radPos] = Rad;
    radAppended = true;
  } else {
    // Find second incoming in input event
    int in1 = 0;
    for(int i=0; i < int(state.size()); ++i)
      if (state[i].mother1() == 1) in1 =i;
    int iNext = outState.append( state[in1] );
    iPosMoth[iNext] = in1;
  }
  // Append second incoming particle
  if ( RecBefore.mother1() == 2) {
    recPos = outState.append( RecBefore );
    iPosMoth[recPos] = Rec;
    recAppended = true;
  } else if ( RadBefore.mother1() == 2 ) {
    radPos = outState.append( RadBefore );
    iPosMoth[radPos] = Rad;
    radAppended = true;
  } else {
    // Find second incoming in input event
    int in2 = 0;
    for(int i=0; i < int(state.size()); ++i)
      if (state[i].mother1() == 2) in2 =i;
    int iNext = outState.append( state[in2] );
    iPosMoth[iNext] = in2;
  }

  // Append new recoiler if not done already
  if (!recAppended && !RecBefore.isFinal()) {
    recAppended = true;
    recPos = outState.append( RecBefore);
    iPosMoth[recPos] = Rec;
  }
  // Append new radiator if not done already
  if (!radAppended && !RadBefore.isFinal()) {
    radAppended = true;
    radPos = outState.append( RadBefore);
    iPosMoth[radPos] = Rad;
  }

  // Append intermediate particle
  // (careful not to append reclustered recoiler).
  for (int i = 0; i < int(NewEvent.size()-1); ++i) {
    if (NewEvent[i].status() == -22) {
      int iNext = outState.append( NewEvent[i] );
      iPosMoth[iNext] = iPosMothTmp[i];
    }
  }
  // Append final state particles, resonances first.
  for (int i = 0; i < int(NewEvent.size()-1); ++i) {
    if (NewEvent[i].status() == 22) {
      int iNext = outState.append( NewEvent[i] );
      iPosMoth[iNext] = iPosMothTmp[i];
    }
  }
  // Then start appending partons.
  if (!radAppended && RadBefore.statusAbs() == 22) {
    radPos = outState.append(RadBefore);
    iPosMoth[radPos] = Rad;
  }
  if (!recAppended) {
    recPos = outState.append(RecBefore);
    iPosMoth[recPos] = Rec;
  }
  if (!radAppended && RadBefore.statusAbs() != 22) {
    radPos = outState.append(RadBefore);
    iPosMoth[radPos] = Rad;
  }
  // Then partons (not reclustered recoiler).
  for (int i = 0; i < int(NewEvent.size()-1); ++i) {
    if ( NewEvent[i].status()  != 22
      && NewEvent[i].colType() != 0
      && NewEvent[i].isFinal()) {
      int iNext = outState.append( NewEvent[i] );
      iPosMoth[iNext] = iPosMothTmp[i];
    }
  }
  // Then the rest.
  for (int i = 0; i < int(NewEvent.size()-1); ++i) {
    if ( NewEvent[i].status() != 22
      && NewEvent[i].colType() == 0
      && NewEvent[i].isFinal()) {
      int iNext = outState.append( NewEvent[i] );
      iPosMoth[iNext] = iPosMothTmp[i];
    }
  }

  // Find intermediate and respective daughters
  vector<int> posIntermediate;
  vector<int> posDaughter1;
  vector<int> posDaughter2;
  for(int i=0; i < int(outState.size()); ++i)
    if (outState[i].status() == -22) {
      posIntermediate.push_back(i);
      int d1 = outState[i].daughter1();
      int d2 = outState[i].daughter2();
      // Find daughters in output state
      int daughter1 = FindParticle( state[d1], outState);
      int daughter2 = FindParticle( state[d2], outState);

      // Careful if resonance daughters have been reclustered.
      if      (daughter1 < 0 && (d1==Rad || d1 == Emt)) daughter1 = radPos;
      else if (daughter1 < 0 && d1==Rec)                daughter1 = recPos;
      if      (daughter2 < 0 && (d2==Rad || d2 == Emt)) daughter2 = radPos;
      else if (daughter2 < 0 && d2==Rec)                daughter2 = recPos;

      // If both daughters found, done.
      // Else put first final particle as first daughter
      // and last final particle as second daughter.
      if (daughter1 > 0)
        posDaughter1.push_back( daughter1);
      else {
        daughter1 = 0;
        while(!outState[daughter1].isFinal() ) daughter1++;
        posDaughter1.push_back( daughter1);
      }
      if (daughter2 > 0)
        posDaughter2.push_back( daughter2);
      else {
        daughter2 = outState.size()-1;
        while(!outState[daughter2].isFinal() ) daughter2--;
        posDaughter2.push_back( daughter2);
      }
    }
  // Set daughters and mothers
  for(int i=0; i < int(posIntermediate.size()); ++i) {
    outState[posIntermediate[i]].daughters(posDaughter1[i],posDaughter2[i]);
    outState[posDaughter1[i]].mother1(posIntermediate[i]);
    outState[posDaughter2[i]].mother1(posIntermediate[i]);
  }

  // Find range of final state partons
  int minParFinal = int(outState.size());
  int maxParFinal = 0;
  for(int i=0; i < int(outState.size()); ++i)
    if (outState[i].mother1() == 3 && outState[i].mother2() == 4) {
      minParFinal = min(i,minParFinal);
      maxParFinal = max(i,maxParFinal);
    }

  if (minParFinal == maxParFinal) maxParFinal = 0;
  outState[3].daughters(minParFinal,maxParFinal);
  outState[4].daughters(minParFinal,maxParFinal);

  // Update event properties
  outState.saveSize();
  outState.saveJunctionSize();

  // Store radiator and recoiler positions.
  inSystem.recBef = recPos;
  inSystem.radBef = radPos;

  // Almost there...
  // If an intermediate coloured parton exists which was directly
  // colour connected to the radiator before the splitting, and the
  // radiator before and after the splitting had only one colour, problems
  // will arise since the colour of the radiator will be changed, whereas
  // the intermediate parton still has the old colour. In effect, this
  // means that when setting up a event for trial showering, one colour will
  // be free.
  // Hence, check for an intermediate coloured triplet resonance has been
  // colour-connected to the "old" radiator.
  // Find resonance
  int iColRes = 0;
  if ( radType == -1 && state[Rad].colType() == 1) {
      // Find resonance connected to initial colour
      for(int i=0; i < int(state.size()); ++i)
        if ( i != Rad && i != Emt && i != Rec
          && state[i].status() == -22
          && state[i].col() == state[Rad].col() )
          iColRes = i;
  } else if ( radType == -1 && state[Rad].colType() == -1) {
      // Find resonance connected to initial anticolour
      for(int i=0; i < int(state.size()); ++i)
        if ( i != Rad && i != Emt && i != Rec
          && state[i].status() == -22
          && state[i].acol() == state[Rad].acol() )
          iColRes = i;
  } else if ( radType == 1 && state[Rad].colType() == 1) {
      // Find resonance connected to final state colour
      for(int i=0; i < int(state.size()); ++i)
        if ( i != Rad && i != Emt && i != Rec
          && state[i].status() == -22
          && state[i].col() == state[Rad].col() )
          iColRes = i;
  } else if ( radType == 1 && state[Rad].colType() == -1) {
      // Find resonance connected to final state anticolour
      for(int i=0; i < int(state.size()); ++i)
        if ( i != Rad && i != Emt && i != Rec
          && state[i].status() == -22
          && state[i].acol() == state[Rad].acol() )
          iColRes = i;
  }

  if (iColRes > 0) {
    // Now find this resonance in the reclustered state
    int iColResNow = FindParticle( state[iColRes], outState);

    // Find reclustered radiator colours
    int radCol = outState[radPos].col();
    int radAcl = outState[radPos].acol();
    // Find resonance radiator colours
    int resCol = outState[iColResNow].col();
    int resAcl = outState[iColResNow].acol();
    // Check if any of the reclustered radiators colours match the resonance
    bool matchesRes =  (radCol > 0
                          && ( radCol == resCol || radCol == resAcl))
                    || (radAcl > 0
                          && ( radAcl == resCol || radAcl == resAcl));

    // If a resonance has been found, but no colours match, change
    // the colour of the resonance
    if (!matchesRes && iColResNow > 0) {
      if ( radType == -1 && outState[radPos].colType() == 1)
        outState[iColResNow].col(radCol);
      else if ( radType ==-1 && outState[radPos].colType() ==-1)
        outState[iColResNow].acol(radAcl);
      else if ( radType == 1 && outState[radPos].colType() == 1)
        outState[iColResNow].col(radCol);
      else if ( radType == 1 && outState[radPos].colType() ==-1)
        outState[iColResNow].acol(radAcl);
    }


    // If a resonance has been found, but no colours match, and the position
    // of the resonance in the event record has been changed, update the
    // radiator mother
    if (!matchesRes && iColResNow > 0 && iColRes != iColResNow)
      outState[radPos].mother1(iColResNow);

  }

  // Store 1-to-1 map between particles in clustered and unclustered state.
  inSystem.iPosInMother = iPosMoth;

  // If event is not constructed properly, return false
  if ( !validEvent(outState) ) {
    // Set momenta of particles to be attached to new event record
    outState.reset();
    return outState;
  }

  // Remember position of reclustered radiator in state
  iReclusteredNew = radPos;

  // Done
  return outState;
}

//--------------------------------------------------------------------------

// Function to get the flavour of the radiator before the splitting
// for clustering
// IN int  : Flavour of the radiator after the splitting
//    int  : Flavour of the emitted after the splitting
// OUT int : Flavour of the radiator before the splitting

int History::getRadBeforeFlav(const int RadAfter, const int EmtAfter,
      const Event& event) {

  int type = event[RadAfter].isFinal() ? 1 :-1;
  int emtID  = event[EmtAfter].id();
  int radID  = event[RadAfter].id();
  int emtCOL = event[EmtAfter].col();
  int radCOL = event[RadAfter].col();
  int emtACL = event[EmtAfter].acol();
  int radACL = event[RadAfter].acol();

  bool colConnected = ((type == 1) && ( (emtCOL !=0 && (emtCOL ==radACL))
                                     || (emtACL !=0 && (emtACL ==radCOL)) ))
                    ||((type ==-1) && ( (emtCOL !=0 && (emtCOL ==radCOL))
                                     || (emtACL !=0 && (emtACL ==radACL)) ));
  // QCD splittings
  // Gluon radiation
  if ( emtID == 21 )
    return radID;
  // Final state gluon splitting
  if ( type == 1 && emtID == -radID && !colConnected )
    return 21;
  // Initial state s-channel gluon splitting
  if ( type ==-1 && radID == 21 )
    return -emtID;
  // Initial state t-channel gluon splitting
  if ( type ==-1 && !colConnected
    && radID != 21 && abs(emtID) < 10 && abs(radID) < 10)
    return 21;

  // SQCD splittings
  int radSign = (radID < 0) ? -1 : 1;
  int offsetL = 1000000;
  int offsetR = 2000000;
  // Gluino radiation
  if ( emtID == 1000021 ) {
    // Gluino radiation combined with quark yields squark.
    if (abs(radID) < 10 ) {
      int offset = offsetL;
      // Check if righthanded squark present. If so, make the reclustered
      // squark match. Works for squark pair production + gluino emission.
      for (int i=0; i < int(event.size()); ++i)
        if ( event[i].isFinal()
          && event[i].idAbs() < offsetR+10 && event[i].idAbs() > offsetR)
          offset = offsetR;
      return radSign*(abs(radID)+offset);
    }
    // Gluino radiation combined with squark yields quark.
    if (abs(radID) > offsetL && abs(radID) < offsetL+10 )
      return radSign*(abs(radID)-offsetL);
    if (abs(radID) > offsetR && abs(radID) < offsetR+10 )
      return radSign*(abs(radID)-offsetR);
    // Gluino radiation off gluon yields gluino.
    if (radID == 21 ) return emtID;
  }

  int emtSign = (emtID < 0) ? -1 : 1;
  // Get PDG numbering offsets.
  int emtOffset = 0;
  if ( abs(emtID) > offsetL && abs(emtID) < offsetL+10 )
    emtOffset = offsetL;
  if ( abs(emtID) > offsetR && abs(emtID) < offsetR+10 )
    emtOffset = offsetR;
  int radOffset = 0;
  if ( abs(radID) > offsetL && abs(radID) < offsetL+10 )
    radOffset = offsetL;
  if ( abs(radID) > offsetR && abs(radID) < offsetR+10 )
    radOffset = offsetR;

  // Final state gluino splitting
  if ( type == 1 && !colConnected ) {
    // Emitted squark, radiating quark.
    if ( emtOffset > 0 && radOffset == 0
      && emtSign*(abs(emtID) - emtOffset) == -radID )
      return 1000021;
    // Emitted quark, radiating squark.
    if ( emtOffset == 0 && radOffset > 0
      && emtID == -radSign*(abs(radID) - radOffset) )
      return 1000021;
  }

  // Initial state s-channel gluino splitting
  if ( type ==-1 && radID == 1000021 ) {
    // Quark entering underlying hard process.
    if ( emtOffset > 0 ) return -emtSign*(abs(emtID) - emtOffset);
    // Squark entering underlying hard process.
    else return -emtSign*(abs(emtID) + emtOffset);
  }

  // Initial state t-channel gluino splitting.
  if ( type ==-1
    && ( (abs(emtID) > offsetL && abs(emtID) < offsetL+10)
      || (abs(emtID) > offsetR && abs(emtID) < offsetR+10))
    && ( (abs(radID) > offsetL && abs(radID) < offsetL+10)
      || (abs(radID) > offsetR && abs(radID) < offsetR+10))
    && emtSign*(abs(emtID)+emtOffset) == radSign*(abs(radID) - radOffset)
    && !colConnected ) {
    return 1000021;
  }

  // Electroweak splittings splittings
  // Photon / Z radiation: Calculate invariant mass of system
  double m2final = (event[RadAfter].p()+ event[EmtAfter].p()).m2Calc();

  if ( emtID == 22 || emtID == 23 ) return radID;
  // Final state Photon splitting
  if ( type == 1 && emtID == -radID && colConnected && sqrt(m2final) <= 10. )
    return 22;
  // Final state Photon splitting
  if ( type == 1 && emtID == -radID && colConnected && sqrt(m2final)  > 10. )
    return 23;
  // Initial state s-channel photon/ Z splitting
  if ( type ==-1 && (radID == 22 || radID == 23) )
    return -emtID;
  // Initial state t-channel photon / Z splitting: Always bookkeep as photon
  if ( type ==-1 && abs(emtID) < 10 && abs(radID) < 10 && colConnected )
    return 22;

  // W+ radiation
  // Final state W+ splitting
  if ( emtID == 24 && radID < 0 ) return radID + 1;
  if ( emtID == 24 && radID > 0 ) return radID + 1;

  // W- radiation
  // Final state W- splitting
  if ( emtID ==-24 && radID < 0 ) return radID - 1;
  if ( emtID ==-24 && radID > 0 ) return radID - 1;

  // Done.
  return 0;

}

//--------------------------------------------------------------------------

// Function to get the spin of the radiator before the splitting
// IN int  : Spin of the radiator after the splitting
//    int  : Spin of the emitted after the splitting
// OUT int : Spin of the radiator before the splitting

int History::getRadBeforeSpin(const int radAfter, const int emtAfter,
      const int spinRadAfter, const int spinEmtAfter,
      const Event& event) {

  // Get flavour before the splitting.
  int radBeforeFlav = getRadBeforeFlav(radAfter, emtAfter, event);

  // Gluon in final state g-> q qbar
  if ( event[radAfter].isFinal()
    && event[radAfter].id() == -event[emtAfter].id())
    return (spinRadAfter == 9) ? spinEmtAfter : spinRadAfter;

  // Quark in final state q -> q g
  if ( event[radAfter].isFinal() && abs(radBeforeFlav) < 10
    && event[radAfter].idAbs() < 10)
    // Special oddity: Gluon does not change spin.
    return spinRadAfter;

  // Quark in final state q -> g q
  if ( event[radAfter].isFinal() && abs(radBeforeFlav) < 10
    && event[emtAfter].idAbs() < 10)
    // Special oddity: Gluon does not change spin.
    return spinEmtAfter;

  // Gluon in final state g -> g g
  if ( event[radAfter].isFinal() && radBeforeFlav == 21
    && event[radAfter].id() == 21)
    // Special oddity: Gluon does not change spin.
    return (spinRadAfter == 9) ? spinEmtAfter : spinRadAfter;

  // Gluon in initial state g-> q qbar
  if ( !event[radAfter].isFinal()
    && radBeforeFlav == -event[emtAfter].id())
    return (spinRadAfter == 9) ? spinEmtAfter : spinRadAfter;

  // Quark in initial state q -> q g
  if ( !event[radAfter].isFinal() && abs(radBeforeFlav) < 10
    && event[radAfter].idAbs() < 10)
    // Special oddity: Gluon does not change spin.
    return spinRadAfter;

  // Gluon in initial state q -> g q
  if ( !event[radAfter].isFinal() && radBeforeFlav == 21
    && event[emtAfter].idAbs() < 10)
    // Special oddity: Gluon does not change spin.
    return spinEmtAfter;

  // Done. Return default value.
  return 9;

}

//--------------------------------------------------------------------------

// Function to properly colour-connect the radiator to the rest of
// the event, as needed during clustering
// IN  Particle& : Particle to be connected
//     Particle  : Recoiler forming a dipole with Radiator
//     Event     : event to which Radiator shall be appended
// OUT true               : Radiator could be connected to the event
//     false              : Radiator could not be connected to the
//                          event or the resulting event was
//                          non-valid

bool History::connectRadiator( Particle& Radiator, const int RadType,
                      const Particle& Recoiler, const int RecType,
                      const Event& event ) {

  // Start filling radiator colour indices with dummy values
  Radiator.cols( -1, -1 );

  // Radiator should always be colour-connected to recoiler.
  // Three cases (rad = Anti-Quark, Quark, Gluon) to be considered
  if ( Radiator.colType() == -1 ) {
    // For final state antiquark radiator, the anticolour is fixed
    // by the final / initial state recoiler colour / anticolour
    if ( RadType + RecType == 2 )
      Radiator.cols( 0, Recoiler.col());
    else if ( RadType + RecType == 0 )
      Radiator.cols( 0, Recoiler.acol());
    // For initial state antiquark radiator, the anticolour is fixed
    // by the colour of the emitted gluon (which will be the
    // leftover anticolour of a final state particle or the leftover
    // colour of an initial state particle ( = the recoiler))
    else {
      // Set colour of antiquark radiator to zero
      Radiator.col( 0 );
      for (int i = 0; i < event.size(); ++i) {
        int col = event[i].col();
        int acl = event[i].acol();

        if ( event[i].isFinal()) {
          // Search for leftover anticolour in final / initial state
          if ( acl > 0 && FindCol(acl,i,0,event,1,true) == 0
              && FindCol(acl,i,0,event,2,true) == 0 )
            Radiator.acol(event[i].acol());
        } else {
          // Search for leftover colour in initial / final state
          if ( col > 0 && FindCol(col,i,0,event,1,true) == 0
              && FindCol(col,i,0,event,2,true) == 0 )
            Radiator.acol(event[i].col());
        }
      } // end loop over particles in event record
    }

  } else if ( Radiator.colType() == 1 ) {
    // For final state quark radiator, the colour is fixed
    // by the final / initial state recoiler anticolour / colour
    if ( RadType + RecType == 2 )
      Radiator.cols( Recoiler.acol(), 0);

    else if ( RadType + RecType == 0 )
      Radiator.cols( Recoiler.col(), 0);
    // For initial state quark radiator, the colour is fixed
    // by the anticolour of the emitted gluon (which will be the
    // leftover colour of a final state particle or the leftover
    // anticolour of an initial state particle ( = the recoiler))

    else {
      // Set anticolour of quark radiator to zero
      Radiator.acol( 0 );
      for (int i = 0; i < event.size(); ++i) {
        int col = event[i].col();
        int acl = event[i].acol();

        if ( event[i].isFinal()) {
          // Search for leftover colour in final / initial state
          if ( col > 0 && FindCol(col,i,0,event,1,true) == 0
              && FindCol(col,i,0,event,2,true) == 0)
            Radiator.col(event[i].col());
        } else {
          // Search for leftover anticolour in initial / final state
          if ( acl > 0 && FindCol(acl,i,0,event,1,true) == 0
              && FindCol(acl,i,0,event,2,true) == 0)
            Radiator.col(event[i].acol());
        }
      } // end loop over particles in event record

    } // end distinction between fsr / fsr+initial recoiler / isr

  } else if ( Radiator.colType() == 2 ) {
    // For a gluon radiator, one (anticolour) colour index is defined
    // by the recoiler colour (anticolour).
    // The remaining index is chosen to match the free index in the
    // event
    // Search for leftover colour (anticolour) in the final state
    for (int i = 0; i < event.size(); ++i) {
      int col = event[i].col();
      int acl = event[i].acol();
      int iEx = i;

      if ( event[i].isFinal()) {
        if ( col > 0 && FindCol(col,iEx,0,event,1,true) == 0
          && FindCol(col,iEx,0,event,2,true) == 0) {
          if (Radiator.status() < 0 ) Radiator.col(event[i].col());
          else Radiator.acol(event[i].col());
        }
        if ( acl > 0 && FindCol(acl,iEx,0,event,2,true) == 0
          && FindCol(acl,iEx,0,event,1,true) == 0 ) {
          if (Radiator.status() < 0 )  Radiator.acol(event[i].acol());
          else Radiator.col(event[i].acol());
        }
      } else {
        if ( col > 0 && FindCol(col,iEx,0,event,1,true) == 0
          && FindCol(col,iEx,0,event,2,true) == 0) {
          if (Radiator.status() < 0 ) Radiator.acol(event[i].col());
          else Radiator.col(event[i].col());
        }
        if ( acl > 0 && (FindCol(acl,iEx,0,event,2,true) == 0
          && FindCol(acl,iEx,0,event,1,true) == 0)) {
          if (Radiator.status() < 0 ) Radiator.col(event[i].acol());
          else Radiator.acol(event[i].acol());
        }
      }
    } // end loop over particles in event record
  } // end cases of different radiator colour type

  // If either colour or anticolour has not been set, return false
  if (Radiator.col() < 0 || Radiator.acol() < 0) return false;
  // Done
  return true;
}

//--------------------------------------------------------------------------

// Function to find a colour (anticolour) index in the input event
// IN  int col       : Colour tag to be investigated
//     int iExclude1 : Identifier of first particle to be excluded
//                     from search
//     int iExclude2 : Identifier of second particle to be excluded
//                     from  search
//     Event event   : event to be searched for colour tag
//     int type      : Tag to define if col should be counted as
//                      colour (type = 1) [->find anti-colour index
//                                         contracted with col]
//                      anticolour (type = 2) [->find colour index
//                                         contracted with col]
// OUT int           : Position of particle in event record
//                     contraced with col [0 if col is free tag]

int History::FindCol(int col, int iExclude1, int iExclude2,
            const Event& event, int type, bool isHardIn) {

  bool isHard = isHardIn;
  int index = 0;

  if (isHard) {
    // Search event record for matching colour & anticolour
    for(int n = 0; n < event.size(); ++n) {
      if ( n != iExclude1 && n != iExclude2
        && event[n].colType() != 0
        &&(   event[n].status() > 0          // Check outgoing
           || event[n].status() == -21) ) {  // Check incoming
         if ( event[n].acol() == col ) {
          index = -n;
          break;
        }
        if ( event[n].col()  == col ) {
          index =  n;
          break;
        }
      }
    }
  } else {

    // Search event record for matching colour & anticolour
    for(int n = 0; n < event.size(); ++n) {
      if (  n != iExclude1 && n != iExclude2
        && event[n].colType() != 0
        &&(   event[n].status() == 43        // Check outgoing from ISR
           || event[n].status() == 51        // Check outgoing from FSR
           || event[n].status() == -41       // first initial
           || event[n].status() == -42) ) {  // second initial
        if ( event[n].acol() == col ) {
          index = -n;
          break;
        }
        if ( event[n].col()  == col ) {
          index =  n;
          break;
        }
      }
    }
  }
  // if no matching colour / anticolour has been found, return false
  if ( type == 1 && index < 0) return abs(index);
  if ( type == 2 && index > 0) return abs(index);

  return 0;
}

//--------------------------------------------------------------------------

// Function to in the input event find a particle with quantum
// numbers matching those of the input particle
// IN  Particle : Particle to be searched for
//     Event    : Event to be searched in
// OUT int      : > 0 : Position of matching particle in event
//                < 0 : No match in event

int History::FindParticle( const Particle& particle, const Event& event,
  bool checkStatus ) {

  int index = -1;

  for ( int i = int(event.size()) - 1; i > 0; --i )
    if ( event[i].id()         == particle.id()
      && event[i].colType()    == particle.colType()
      && event[i].chargeType() == particle.chargeType()
      && event[i].col()        == particle.col()
      && event[i].acol()       == particle.acol()
      && event[i].charge()     == particle.charge() ) {
      index = i;
      break;
    }

  if (index >= 0 && checkStatus && event[index].status() != particle.status())
    index = -1;

  return index;

}

//--------------------------------------------------------------------------

// Function to get the colour of the radiator before the splitting
// for clustering
// IN  int   : Position of the radiator after the splitting, in the event
//     int   : Position of the emitted after the splitting, in the event
//     Event : Reference event
// OUT int   : Colour of the radiator before the splitting

int History::getRadBeforeCol(const int rad, const int emt,
      const Event& event) {

  // Save type of splitting
  int type = (event[rad].isFinal()) ? 1 :-1;
  // Get flavour of radiator after potential clustering
  int radBeforeFlav = getRadBeforeFlav(rad,emt,event);
  // Get colours of the radiator before the potential clustering
  int radBeforeCol = -1;
  // Get reconstructed gluon colours
  if (radBeforeFlav == 21) {

    // Start with quark emissions in FSR
    if (type == 1 && event[emt].id() != 21) {
      radBeforeCol = (event[rad].col()  > 0)
                   ? event[rad].col() : event[emt].col();
    // Quark emissions in ISR
    } else if (type == -1 && event[emt].id() != 21) {
      radBeforeCol = (event[rad].col()  > 0)
                   ? event[rad].col() : event[emt].acol();
    //Gluon emissions in FSR
    } else if (type == 1 && event[emt].id() == 21) {
      // If emitted is a gluon, remove the repeated index, and take
      // the remaining indices as colour and anticolour
      int colRemove = (event[rad].col() == event[emt].acol())
                    ? event[rad].col() : event[rad].acol();
      radBeforeCol  = (event[rad].col()  == colRemove)
                    ? event[emt].col() : event[rad].col();
    //Gluon emissions in ISR
    } else if (type == -1 && event[emt].id() == 21) {
      // If emitted is a gluon, remove the repeated index, and take
      // the remaining indices as colour and anticolour
      int colRemove = (event[rad].col() == event[emt].col())
                    ? event[rad].col() : event[rad].acol();
      radBeforeCol  = (event[rad].col()  == colRemove)
                    ? event[emt].acol() : event[rad].col();
    }

  // Get reconstructed quark colours
  } else if (radBeforeFlav > 0) {

    // Quark emission in FSR
    if (type == 1 && event[emt].id() != 21) {
      // If radiating is a quark, remove the repeated index, and take
      // the remaining indices as colour and anticolour
      int colRemove = (event[rad].col() == event[emt].acol())
                    ? event[rad].acol() : 0;
      radBeforeCol  = (event[rad].col()  == colRemove)
                    ? event[emt].col() : event[rad].col();
    //Gluon emissions in FSR
    } else if (type == 1 && event[emt].id() == 21) {
      // If emitted is a gluon, remove the repeated index, and take
      // the remaining indices as colour and anticolour
      int colRemove = (event[rad].col() == event[emt].acol())
                    ? event[rad].col() : 0;
      radBeforeCol  = (event[rad].col()  == colRemove)
                    ? event[emt].col() : event[rad].col();
    //Quark emissions in ISR
    } else if (type == -1 && event[emt].id() != 21) {
      // If emitted is a quark, remove the repeated index, and take
      // the remaining indices as colour and anticolour
      int colRemove = (event[rad].col() == event[emt].col())
                    ? event[rad].col() : 0;
      radBeforeCol  = (event[rad].col()  == colRemove)
                    ? event[emt].acol() : event[rad].col();
    //Gluon emissions in ISR
    } else if (type == -1 && event[emt].id() == 21) {
      // If emitted is a gluon, remove the repeated index, and take
      // the remaining indices as colour and anticolour
      int colRemove = (event[rad].col() == event[emt].col())
                    ? event[rad].col() : 0;
      radBeforeCol  = (event[rad].col()  == colRemove)
                    ? event[emt].acol() : event[rad].col();
    }
  // Other particles are assumed uncoloured
  } else {
    radBeforeCol = 0;
  }

  return radBeforeCol;

}

//--------------------------------------------------------------------------

// Function to get the anticolour of the radiator before the splitting
// for clustering
// IN  int   : Position of the radiator after the splitting, in the event
//     int   : Position of the emitted after the splitting, in the event
//     Event : Reference event
// OUT int   : Anticolour of the radiator before the splitting

int History::getRadBeforeAcol(const int rad, const int emt,
      const Event& event) {

  // Save type of splitting
  int type = (event[rad].isFinal()) ? 1 :-1;
  // Get flavour of radiator after potential clustering

  int radBeforeFlav = getRadBeforeFlav(rad,emt,event);
  // Get colours of the radiator before the potential clustering
  int radBeforeAcl = -1;
  // Get reconstructed gluon colours
  if (radBeforeFlav == 21) {

    // Start with quark emissions in FSR
    if (type == 1 && event[emt].id() != 21) {
      radBeforeAcl = (event[rad].acol() > 0)
                   ? event[rad].acol() : event[emt].acol();
    // Quark emissions in ISR
    } else if (type == -1 && event[emt].id() != 21) {
      radBeforeAcl = (event[rad].acol() > 0)
                   ? event[rad].acol() : event[emt].col();
    //Gluon emissions in FSR
    } else if (type == 1 && event[emt].id() == 21) {
      // If emitted is a gluon, remove the repeated index, and take
      // the remaining indices as colour and anticolour
      int colRemove = (event[rad].col() == event[emt].acol())
                    ? event[rad].col() : event[rad].acol();
      radBeforeAcl  = (event[rad].acol() == colRemove)
                    ? event[emt].acol() : event[rad].acol();
    //Gluon emissions in ISR
    } else if (type == -1 && event[emt].id() == 21) {
      // If emitted is a gluon, remove the repeated index, and take
      // the remaining indices as colour and anticolour
      int colRemove = (event[rad].col() == event[emt].col())
                    ? event[rad].col() : event[rad].acol();
      radBeforeAcl  = (event[rad].acol() == colRemove)
                    ? event[emt].col() : event[rad].acol();
    }

  // Get reconstructed anti-quark colours
  } else if (radBeforeFlav < 0) {

    // Antiquark emission in FSR
    if (type == 1 && event[emt].id() != 21) {
      // If radiating is a antiquark, remove the repeated index, and take
      // the remaining indices as colour and anticolour
      int colRemove = (event[rad].col() == event[emt].acol())
                    ? event[rad].acol() : 0;
      radBeforeAcl  = (event[rad].acol()  == colRemove)
                    ? event[emt].acol() : event[rad].acol();
    //Gluon emissions in FSR
    } else if (type == 1 && event[emt].id() == 21) {
      // If emitted is a gluon, remove the repeated index, and take
      // the remaining indices as colour and anticolour
      int colRemove = (event[rad].acol() == event[emt].col())
                    ? event[rad].acol() : 0;
      radBeforeAcl  = (event[rad].acol()  == colRemove)
                    ? event[emt].acol() : event[rad].acol();
    //Antiquark emissions in ISR
    } else if (type == -1 && event[emt].id() != 21) {
      // If emitted is an antiquark, remove the repeated index, and take
      // the remaining indices as colour and anticolour
      int colRemove = (event[rad].acol() == event[emt].acol())
                    ? event[rad].acol() : 0;
      radBeforeAcl  = (event[rad].acol()  == colRemove)
                    ? event[emt].col() : event[rad].acol();
    //Gluon emissions in ISR
    } else if (type == -1 && event[emt].id() == 21) {
      // If emitted is a gluon, remove the repeated index, and take
      // the remaining indices as colour and anticolour
      int colRemove = (event[rad].acol() == event[emt].acol())
                    ? event[rad].acol() : 0;
      radBeforeAcl  = (event[rad].acol()  == colRemove)
                    ? event[emt].col() : event[rad].acol();
    }
  // Other particles are considered uncoloured
  } else {
    radBeforeAcl = 0;
  }

  return radBeforeAcl;

}

//--------------------------------------------------------------------------

  // Function to get the parton connected to in by a colour line
  // IN  int   : Position of parton for which partner should be found
  //     Event : Reference event
  // OUT int   : If a colour line connects the "in" parton with another
  //             parton, return the Position of the partner, else return 0

int History::getColPartner(const int in, const Event& event) {

  if (event[in].col() == 0) return 0;

  int partner = 0;
  // Try to find anticolour index first
  partner = FindCol(event[in].col(),in,0,event,1,true);
  // If no anticolour index has been found, try colour
  if (partner == 0)
   partner = FindCol(event[in].col(),in,0,event,2,true);

  return partner;

}

//--------------------------------------------------------------------------


  // Function to get the parton connected to in by an anticolour line
  // IN  int   : Position of parton for which partner should be found
  //     Event : Reference event
  // OUT int   : If an anticolour line connects the "in" parton with another
  //             parton, return the Position of the partner, else return 0

int History::getAcolPartner(const int in, const Event& event) {

  if (event[in].acol() == 0) return 0;

  int partner = 0;
  // Try to find colour index first
  partner = FindCol(event[in].acol(),in,0,event,2,true);
  // If no colour index has been found, try anticolour
  if (partner == 0)
   partner = FindCol(event[in].acol(),in,0,event,1,true);

  return partner;

}

//--------------------------------------------------------------------------

// Function to get the list of partons connected to the particle
// formed by reclusterinf emt and rad by colour and anticolour lines
// IN  int          : Position of radiator in the clustering
// IN  int          : Position of emitted in the clustering
//     Event        : Reference event
// OUT vector<int>  : List of positions of all partons that are connected
//                    to the parton that will be formed
//                    by clustering emt and rad.

vector<int> History::getReclusteredPartners(const int rad, const int emt,
  const Event& event) {

  // Save type
  int type = event[rad].isFinal() ? 1 : -1;
  // Get reclustered colours
  int radBeforeCol = getRadBeforeCol(rad, emt, event);
  int radBeforeAcl = getRadBeforeAcol(rad, emt, event);
  // Declare output
  vector<int> partners;


  // Start with FSR clusterings
  if (type == 1) {

    for(int i=0; i < int(event.size()); ++i) {
      // Check all initial state partons
      if ( i != emt && i != rad
        && event[i].status() == -21
        && event[i].col() > 0
        && event[i].col() == radBeforeCol)
          partners.push_back(i);
      // Check all final state partons
      if ( i != emt && i != rad
        && event[i].isFinal()
        && event[i].acol() > 0
        && event[i].acol() == radBeforeCol)
          partners.push_back(i);
      // Check all initial state partons
      if ( i != emt && i != rad
        && event[i].status() == -21
        && event[i].acol() > 0
        && event[i].acol() == radBeforeAcl)
          partners.push_back(i);
      // Check all final state partons
      if ( i != emt && i != rad
        && event[i].isFinal()
        && event[i].col() > 0
        && event[i].col() == radBeforeAcl)
          partners.push_back(i);
    }
  // Start with ISR clusterings
  } else {

    for(int i=0; i < int(event.size()); ++i) {
      // Check all initial state partons
      if ( i != emt && i != rad
        && event[i].status() == -21
        && event[i].acol() > 0
        && event[i].acol() == radBeforeCol)
          partners.push_back(i);
      // Check all final state partons
      if ( i != emt && i != rad
        && event[i].isFinal()
        && event[i].col() > 0
        && event[i].col() == radBeforeCol)
          partners.push_back(i);
      // Check all initial state partons
      if ( i != emt && i != rad
        && event[i].status() == -21
        && event[i].col() > 0
        && event[i].col() == radBeforeAcl)
          partners.push_back(i);
      // Check all final state partons
      if ( i != emt && i != rad
        && event[i].isFinal()
        && event[i].acol() > 0
        && event[i].acol() == radBeforeAcl)
          partners.push_back(i);
    }

  }
  // Done
  return partners;
}

//--------------------------------------------------------------------------

// Function to extract a chain of colour-connected partons in
// the event
// IN     int          : Type of parton from which to start extracting a
//                       parton chain. If the starting point is a quark
//                       i.e. flavType = 1, a chain of partons that are
//                       consecutively connected by colour-lines will be
//                       extracted. If the starting point is an antiquark
//                       i.e. flavType =-1, a chain of partons that are
//                       consecutively connected by anticolour-lines
//                       will be extracted.
// IN      int         : Position of the parton from which a
//                       colour-connected chain should be derived
// IN      Event       : Refernence event
// IN/OUT  vector<int> : Partons that should be excluded from the search.
// OUT     vector<int> : Positions of partons along the chain
// OUT     bool        : Found singlet / did not find singlet

bool History::getColSinglet( const int flavType, const int iParton,
  const Event& event, vector<int>& exclude, vector<int>& colSinglet) {

  // If no possible flavour to start from has been found
  if (iParton < 0) return false;

  // If no further partner has been found in a previous iteration,
  // and the whole final state has been excluded, we're done
  if (iParton == 0) {

    // Count number of final state partons
    int nFinal = 0;
    for(int i=0; i < int(event.size()); ++i)
      if ( event[i].isFinal() && event[i].colType() != 0)
        nFinal++;

    // Get number of initial state partons in the list of
    // excluded partons
    int nExclude = int(exclude.size());
    int nInitExclude = 0;
    if (!event[exclude[2]].isFinal())
      nInitExclude++;
    if (!event[exclude[3]].isFinal())
      nInitExclude++;

    // If the whole final state has been considered, return
    if (nFinal == nExclude - nInitExclude)
      return true;
    else
      return false;

  }

  // Declare colour partner
  int colP = 0;
  // Save the colour partner
  colSinglet.push_back(iParton);
  // Remove the partner from the list
  exclude.push_back(iParton);
  // When starting out from a quark line, follow the colour lines
  if (flavType == 1)
    colP = getColPartner(iParton,event);
  // When starting out from an antiquark line, follow the anticolour lines
  else
    colP = getAcolPartner(iParton,event);

  // Do not count excluded partons twice
  for(int i = 0; i < int(exclude.size()); ++i)
    if (colP == exclude[i])
      return true;

  // Recurse
  return getColSinglet(flavType,colP,event,exclude,colSinglet);

}

//--------------------------------------------------------------------------

// Function to check that a set of partons forms a colour singlet
// IN  Event       : Reference event
// IN  vector<int> : Positions of the partons in the set
// OUT bool        : Is a colour singlet / is not

bool History::isColSinglet( const Event& event,
  vector<int> system ) {

  // Check if system forms a colour singlet
  for(int i=0; i < int(system.size()); ++i ) {
    // Match quark and gluon colours
    if ( system[i] > 0
      && (event[system[i]].colType() == 1
       || event[system[i]].colType() == 2) ) {
      for(int j=0; j < int(system.size()); ++j)
        // If flavour matches, remove both partons and continue
        if ( system[j] > 0
          && event[system[i]].col() == event[system[j]].acol()) {
          // Remove index and break
          system[i] = 0;
          system[j] = 0;
          break;
        }
    }
    // Match antiquark and gluon anticolours
    if ( system[i] > 0
      && (event[system[i]].colType() == -1
       || event[system[i]].colType() == 2) ) {
      for(int j=0; j < int(system.size()); ++j)
        // If flavour matches, remove both partons and continue
        if ( system[j] > 0
          && event[system[i]].acol() == event[system[j]].col()) {
          // Remove index and break
          system[i] = 0;
          system[j] = 0;
          break;
        }
    }

  }

  // The system is a colour singlet if for all colours,
  // an anticolour was found
  bool isColSing = true;
  for(int i=0; i < int(system.size()); ++i)
    if ( system[i] != 0 )
      isColSing = false;

  // Return
  return isColSing;


}

//--------------------------------------------------------------------------

// Function to check that a set of partons forms a flavour singlet
// IN  Event       : Reference event
// IN  vector<int> : Positions of the partons in the set
// IN  int         : Flavour of all the quarks in the set, if
//                   all quarks in a set should have a fixed flavour
// OUT bool        : Is a flavour singlet / is not

bool History::isFlavSinglet( const Event& event,
  vector<int> system, int flav) {

  // If a decoupled colour singlet has been found, check if this is also
  // a flavour singlet
  // Check that each quark matches an antiquark
  for(int i=0; i < int(system.size()); ++i)
    if ( system[i] > 0 ) {
      for(int j=0; j < int(system.size()); ++j) {
        // If flavour of outgoing partons matches,
        // remove both partons and continue.
        // Skip all bosons
        if ( event[i].idAbs() != 21
          && event[i].idAbs() != 22
          && event[i].idAbs() != 23
          && event[i].idAbs() != 24
          && system[j] > 0
          && event[system[i]].isFinal()
          && event[system[j]].isFinal()
          && event[system[i]].id() == -1*event[system[j]].id()) {
          // If we want to check if only one flavour of quarks
          // exists
          if (abs(flav) > 0 && event[system[i]].idAbs() != flav)
            return false;
          // Remove index and break
          system[i] = 0;
          system[j] = 0;
          break;
        }
        // If flavour of outgoing and incoming partons match,
        // remove both partons and continue.
        // Skip all bosons
        if ( event[i].idAbs() != 21
          && event[i].idAbs() != 22
          && event[i].idAbs() != 23
          && event[i].idAbs() != 24
          && system[j] > 0
          && event[system[i]].isFinal() != event[system[j]].isFinal()
          && event[system[i]].id() == event[system[j]].id()) {
          // If we want to check if only one flavour of quarks
          // exists
          if (abs(flav) > 0 && event[system[i]].idAbs() != flav)
            return false;
          // Remove index and break
          system[i] = 0;
          system[j] = 0;
          break;
        }

      }
    }

  // The colour singlet is a flavour singlet if for all quarks,
  // an antiquark was found
  bool isFlavSing = true;
  for(int i=0; i < int(system.size()); ++i)
    if ( system[i] != 0 )
      isFlavSing = false;

  // Return
  return isFlavSing;

}

//--------------------------------------------------------------------------

// Function to check if rad,emt,rec triple is allowed for clustering
// IN int rad,emt,rec : Positions (in event record) of the three
//                      particles considered for clustering
//    Event event     : Reference event

bool History::allowedClustering( int rad, int emt, int rec, int partner,
                const Event& event ) {

  // Declare output
  bool allowed = true;

  // CONSTRUCT SOME PROPERTIES FOR LATER INVESTIGATION

  // Check if the triple forms a colour singlett
  bool isSing = isSinglett(rad,emt,partner,event);
  int type = (event[rad].isFinal()) ? 1 :-1;
  // Get flavour of radiator after potential clustering
  int radBeforeFlav = getRadBeforeFlav(rad,emt,event);
  // Get colours of the radiator before the potential clustering
  int radBeforeCol = getRadBeforeCol(rad,emt,event);
  int radBeforeAcl = getRadBeforeAcol(rad,emt,event);
  // Get colour partner of reclustered parton
  vector<int> radBeforeColP = getReclusteredPartners(rad, emt, event);

  // Count coloured partons in hard process
  int nPartonInHard = 0;
  for(int i=0; i < int(event.size()); ++i)
    // Check all final state partons
    if ( event[i].isFinal()
      && event[i].colType() != 0
      && mergingHooksPtr->hardProcess->matchesAnyOutgoing(i, event) )
      nPartonInHard++;

  // Count number of initial state partons
  int nInitialPartons = 0;
  for(int i=0; i < int(event.size()); ++i)
    if ( event[i].status() == -21
      && event[i].colType() != 0 )
      nInitialPartons++;

  // Get number of non-charged final state particles
  int nFinalEW = 0;
  for(int i=0; i < int(event.size()); ++i)
    if ( event[i].isFinal()
      &&(  event[i].id() == 22
        || event[i].id() == 23
        || event[i].id() == 24
        ||(event[i].idAbs() > 10 && event[i].idAbs() < 20)
        ||(event[i].idAbs() > 1000010 && event[i].idAbs() < 1000020)
        ||(event[i].idAbs() > 2000010 && event[i].idAbs() < 2000020) ))
      nFinalEW++;

  // Check if event after potential clustering contains an even
  // number of quarks and/or antiquarks
  // (otherwise no electroweak vertex could be formed!)
  // Get number of final quarks
  int nFinalQuark = 0;
  // Get number of excluded final state quarks as well
  int nFinalQuarkExc = 0;
  for(int i=0; i < int(event.size()); ++i) {
    if (i !=rad && i != emt && i != rec) {
      if (event[i].isFinal() && abs(event[i].colType()) == 1 ) {
        if ( !mergingHooksPtr->hardProcess->matchesAnyOutgoing(i,event) )
          nFinalQuark++;
        else
          nFinalQuarkExc++;
      }
    }
  }

  // Add recoiler to number of final quarks
  if (event[rec].isFinal() && event[rec].isQuark()) nFinalQuark++;
  // Add radiator after clustering to number of final quarks
  if ( event[rad].isFinal()
    && abs(particleDataPtr->colType(radBeforeFlav)) == 1) nFinalQuark++;

  // Get number of initial quarks
  int nInitialQuark = 0;
  if (type == 1) {
    if (event[rec].isFinal()) {
      if (event[3].isQuark()) nInitialQuark++;
      if (event[4].isQuark()) nInitialQuark++;
    } else {
      int iOtherIn = (rec == 3) ? 4 : 3;
      if (event[rec].isQuark()) nInitialQuark++;
      if (event[iOtherIn].isQuark()) nInitialQuark++;
    }
  } else {
    // Add recoiler to number of initial quarks
    if (event[rec].isQuark()) nInitialQuark++;
    // Add radiator after clustering to number of initial quarks
    if (abs(radBeforeFlav) < 10) nInitialQuark++;
  }

  // BEGIN CHECKING THE CLUSTERING

  // Do not allow clusterings that lead to a disallowed proton content.
  int proton[] = {1,2,3,4,5,21,22,23,24};
  bool isInProton = false;
  for(int i=0; i < 9; ++i)
    if (abs(radBeforeFlav) == proton[i]) isInProton = true;
  if (type == -1 && !isInProton) return false;

  // Check if colour is conserved
  vector<int> unmatchedCol;
  vector<int> unmatchedAcl;
  // Check all unmatched colours
  for ( int i = 0; i < event.size(); ++i)
    if ( i != emt && i != rad
      && (event[i].isFinal() || event[i].status() == -21)
      && event[i].colType() != 0 ) {

      int colP = getColPartner(i,event);
      int aclP = getAcolPartner(i,event);

      if (event[i].col() > 0
        && (colP == emt || colP == rad || colP == 0) )
        unmatchedCol.push_back(i);
      if (event[i].acol() > 0
        && (aclP == emt || aclP == rad || aclP == 0) )
        unmatchedAcl.push_back(i);

    }

  // If more than one colour or more than one anticolour are unmatched,
  // there is no way to make this clustering work
  if (int(unmatchedCol.size()) + int(unmatchedAcl.size()) > 2)
    return false;

  // If triple forms colour singlett, check that resulting state
  // matches hard core process
  if (isSing)
    allowed = false;
  if ( isSing && event[rec].isQuark()
    && abs(particleDataPtr->colType(radBeforeFlav)) == 1)
    allowed = true;

  // Never recluster any outgoing partons of the core V -> qqbar' splitting!
  if ( mergingHooksPtr->hardProcess->matchesAnyOutgoing(emt,event) ) {
    // Check if any other particle could replace "emt" as part of the candidate
    // core process. If so, replace emt with the new candidate and allow the
    // clustering.
    bool canReplace = mergingHooksPtr->hardProcess->findOtherCandidates(emt,
                        event, true);
    if (canReplace) allowed = true;
    else allowed = false;
  }

  // Never allow clustering of any outgoing partons of the hard process
  // which would change the flavour of one of the hard process partons!
  if ( mergingHooksPtr->hardProcess->matchesAnyOutgoing(rad,event)
      && event[rad].id() != radBeforeFlav )
    allowed = false;

  // Ensure quark number conservation.
  if ( (nInitialQuark + nFinalQuark + nFinalQuarkExc)%2 != 0 )
    allowed = false;

  // Disallow final state splittings that lead to a purely gluonic final
  // state, while having a completely colour-connected initial state.
  // This means that the clustering is discarded if it does not lead to the
  // t-channel gluon needed to connect the final state to a qq~ initial state.
  // Here, partons excluded from clustering are not counted as possible
  // partners to form a t-channel gluon
  vector<int> in;
  for(int i=0; i < int(event.size()); ++i)
    if ( i!=emt && i!=rad && i!=rec
      && (event[i].mother1() == 1 || event[i].mother1() == 2))
      in.push_back(event[i].id());
  if (!event[rad].isFinal()) in.push_back(radBeforeFlav);
  if (!event[rec].isFinal()) in.push_back(event[rec].id());
  vector<int> out;
  for(int i=0; i < int(event.size()); ++i)
    if ( i!=emt && i!=rad && i!=rec && event[i].isFinal())
      out.push_back(event[i].id());
  if (event[rad].isFinal()) out.push_back(radBeforeFlav);
  if (event[rec].isFinal()) out.push_back(event[rec].id());
  if (event[3].col() == event[4].acol()
    && event[3].acol() == event[4].col()
    && !mergingHooksPtr->allowEffectiveVertex( in, out)
    && nFinalQuark == 0){
    // Careful if rad and rec are the only quarks in the final state, but
    // were both excluded from the list of final state quarks.
    int nTripletts = abs(event[rec].colType())
                   + abs(particleDataPtr->colType(radBeforeFlav));
    if (event[3].isGluon())                            allowed = false;
    else if (nTripletts != 2 && nFinalQuarkExc%2 == 0) allowed = false;
  }

  // If only gluons in initial state and no quarks in final state,
  // reject (no electroweak vertex can be formed)
  if (nFinalEW != 0 && nInitialQuark == 0
    && nFinalQuark == 0 && nFinalQuarkExc == 0)
    allowed = false;

  // Minimal phase space checks.
  if ( abs((event[rad].p()+type*event[emt].p()+event[rec].p()).pz())
     > (event[rad].p()+type*event[emt].p()+event[rec].p()).e()
    || (type == -1
      && (event[rad].p()-event[emt].p()+event[rec].p()).m2Calc() < 0.))
    return false;

  // No problems with gluon radiation
  if (event[emt].id() == 21) return allowed;

  // No problems with gluino radiation
  if (event[emt].id() == 1000021) return allowed;

  // When calling History from within aMC@NLO, don't be too zealous about
  // checking the color configuration, since aMC@NLO can pass
  // subleading flows to History. Thus, already return here.
  if (mergingHooksPtr->doRuntimeAMCATNLOInterface()) return allowed;

  // Save all hard process candidates
  vector<int> outgoingParticles;
  int nOut1 = int(mergingHooksPtr->hardProcess->PosOutgoing1.size());
  for ( int i=0; i < nOut1;  ++i ) {
    int iPos = mergingHooksPtr->hardProcess->PosOutgoing1[i];
    outgoingParticles.push_back(
                      mergingHooksPtr->hardProcess->state[iPos].id() );
  }
  int nOut2 = int(mergingHooksPtr->hardProcess->PosOutgoing2.size());
  for ( int i=0; i < nOut2; ++i ) {
    int iPos = mergingHooksPtr->hardProcess->PosOutgoing2[i];
    outgoingParticles.push_back(
                      mergingHooksPtr->hardProcess->state[iPos].id() );
  }

  // Start more involved checks. g -> q_1 qbar_1 splittings are
  // particularly problematic if more than one quark of the emitted
  // flavour is present.
  // Count number of initial quarks of radiator or emitted flavour
  vector<int> iInQuarkFlav;
  for(int i=0; i < int(event.size()); ++i)
    // Check all initial state partons
    if ( i != emt && i != rad
      && event[i].status() == -21
      && event[i].idAbs() == event[emt].idAbs() )
      iInQuarkFlav.push_back(i);

  // Count number of final quarks of radiator or emitted flavour
  vector<int> iOutQuarkFlav;
  for(int i=0; i < int(event.size()); ++i)
  // Check all final state partons
  if ( i != emt && i != rad
    && event[i].isFinal()
    && event[i].idAbs() == event[emt].idAbs() ) {

    // Loop through final state hard particles. If one matches, remove the
    // matching one, and do not count.
    bool matchOut = false;
    for (int j = 0; j < int(outgoingParticles.size()); ++j)
    if ( event[i].idAbs() == abs(outgoingParticles[j])) {
      matchOut = true;
      outgoingParticles[j] = 99;
    }
    if (!matchOut) iOutQuarkFlav.push_back(i);

  }

  // Save number of potentially dangerous quarks
  int nInQuarkFlav  = int(iInQuarkFlav.size());
  int nOutQuarkFlav = int(iOutQuarkFlav.size());

  // Easiest problem 0:
  // Radiator before splitting exactly matches the partner
  // after the splitting
  if ( event[partner].isFinal()
    && event[partner].id()   == 21
    && radBeforeFlav         == 21
    && event[partner].col()  == radBeforeCol
    && event[partner].acol() == radBeforeAcl)
    return false;

  // If there are no ambiguities in qqbar pairs, return
  if (nInQuarkFlav + nOutQuarkFlav == 0)
    return allowed;

  // Save all quarks and gluons that will not change colour
  vector<int> gluon;
  vector<int> quark;
  vector<int> antiq;
  vector<int> partons;
  for(int i=0; i < int(event.size()); ++i)
    // Check initial and final state partons
    if ( i!=emt && i!=rad
      && event[i].colType() != 0
      && (event[i].isFinal() || event[i].status() == -21) ) {
      // Save index
      partons.push_back(i);
      // Split into components
      if (event[i].colType() == 2)
        gluon.push_back(i);
      else if (event[i].colType() ==  1)
        quark.push_back(i);
      else if (event[i].colType() == -1)
        antiq.push_back(i);
    }

  // We split up the test of the g->qq splitting into final state
  // and initial state problems
  bool isFSRg2qq = ((type == 1) && (event[rad].id() == -1*event[emt].id()) );
  bool isISRg2qq = ((type ==-1) && (event[rad].id() ==    event[emt].id()) );

  // First check general things about colour connections
  // Check that clustering does not produce a gluon that is exactly
  // matched in the final state, or does not have any colour connections
  if ( (isFSRg2qq || isISRg2qq)
    && int(quark.size()) + int(antiq.size())
     + int(gluon.size()) > nPartonInHard ) {

      vector<int> colours;
      vector<int> anticolours;
      // Add the colour and anticolour of the gluon before the emission
      // to the list, bookkeep initial colour as final anticolour, and
      // initial anticolour as final colour
      if (type == 1) {
        colours.push_back(radBeforeCol);
        anticolours.push_back(radBeforeAcl);
      } else {
        colours.push_back(radBeforeAcl);
        anticolours.push_back(radBeforeCol);
      }
      // Now store gluon colours and anticolours.
      for(int i=0; i < int(gluon.size()); ++i)
        if (event[gluon[i]].isFinal()) {
          colours.push_back(event[gluon[i]].col());
          anticolours.push_back(event[gluon[i]].acol());
        } else {
          colours.push_back(event[gluon[i]].acol());
          anticolours.push_back(event[gluon[i]].col());
        }

      // Loop through colours and check if any match with
      // anticolours. If colour matches, remove from list
      for(int i=0; i < int(colours.size()); ++i)
        for(int j=0; j < int(anticolours.size()); ++j)
          if (colours[i] > 0 && anticolours[j] > 0
            && colours[i] == anticolours[j]) {
            colours[i] = 0;
            anticolours[j] = 0;
          }


      // If all gluon anticolours and all colours matched, disallow
      // the clustering
      bool allMatched = true;
      for(int i=0; i < int(colours.size()); ++i)
        if (colours[i] != 0)
          allMatched = false;
      for(int i=0; i < int(anticolours.size()); ++i)
        if (anticolours[i] != 0)
          allMatched = false;

      if (allMatched)
        return false;

      // Now add the colours of the hard process, and check if all
      // colours match.
      for(int i=0; i < int(quark.size()); ++i)
        if ( event[quark[i]].isFinal()
        && mergingHooksPtr->hardProcess->matchesAnyOutgoing(quark[i], event) )
          colours.push_back(event[quark[i]].col());

      for(int i=0; i < int(antiq.size()); ++i)
        if ( event[antiq[i]].isFinal()
        && mergingHooksPtr->hardProcess->matchesAnyOutgoing(antiq[i], event) )
          anticolours.push_back(event[antiq[i]].acol());

      // Loop through colours again and check if any match with
      // anticolours. If colour matches, remove from list
      for(int i=0; i < int(colours.size()); ++i)

        for(int j=0; j < int(anticolours.size()); ++j)
          if (colours[i] > 0 && anticolours[j] > 0
            && colours[i] == anticolours[j]) {
            colours[i] = 0;
            anticolours[j] = 0;
          }

      // Check if clustering would produce the hard process
      int nNotInHard = 0;
      for ( int i=0; i < int(quark.size()); ++i )
        if ( !mergingHooksPtr->hardProcess->matchesAnyOutgoing( quark[i],
              event) )
          nNotInHard++;
      for ( int i=0; i < int(antiq.size()); ++i )
        if ( !mergingHooksPtr->hardProcess->matchesAnyOutgoing( antiq[i],
              event) )
          nNotInHard++;
      for(int i=0; i < int(gluon.size()); ++i)
        if ( event[gluon[i]].isFinal() )
          nNotInHard++;
      if ( type == 1 )
          nNotInHard++;

      // If all colours are matched now, and since we have more quarks than
      // present in the hard process, disallow the clustering
      allMatched = true;
      for(int i=0; i < int(colours.size()); ++i)
        if (colours[i] != 0)
          allMatched = false;
      for(int i=0; i < int(anticolours.size()); ++i)
        if (anticolours[i] != 0)
          allMatched = false;

      if (allMatched && nNotInHard > 0)
        return false;

  }

  // FSR PROBLEMS

  if (isFSRg2qq && nInQuarkFlav + nOutQuarkFlav > 0) {

    // Easiest problem 1:
    // RECLUSTERED FINAL STATE GLUON MATCHES INITIAL STATE GLUON
    for(int i=0; i < int(gluon.size()); ++i) {
      if (!event[gluon[i]].isFinal()
        && event[gluon[i]].col()  == radBeforeCol
        && event[gluon[i]].acol() == radBeforeAcl)
        return false;
    }

    // Easiest problem 2:
    // RECLUSTERED FINAL STATE GLUON MATCHES FINAL STATE GLUON
    for(int i=0; i < int(gluon.size()); ++i) {
      if (event[gluon[i]].isFinal()
        && event[gluon[i]].col()  == radBeforeAcl
        && event[gluon[i]].acol() == radBeforeCol)
        return false;
    }

    // Easiest problem 3:
    // RECLUSTERED FINAL STATE GLUON MATCHES FINAL STATE Q-QBAR PAIR
    if ( int(radBeforeColP.size()) == 2
      && event[radBeforeColP[0]].isFinal()
      && event[radBeforeColP[1]].isFinal()
      && event[radBeforeColP[0]].id() == -1*event[radBeforeColP[1]].id() ) {

      // This clustering is allowed if there is no colour in the
      // initial state
      if (nInitialPartons > 0)
        return false;
    }

    // Next-to-easiest problem 1:
    // RECLUSTERED FINAL STATE GLUON MATCHES ONE FINAL STARE Q_1
    // AND ONE INITIAL STATE Q_1
    if ( int(radBeforeColP.size()) == 2
      && ((  event[radBeforeColP[0]].status() == -21
          && event[radBeforeColP[1]].isFinal())
        ||(  event[radBeforeColP[0]].isFinal()
          && event[radBeforeColP[1]].status() == -21))
      && event[radBeforeColP[0]].id() == event[radBeforeColP[1]].id() ) {

      // In principle, clustering this splitting can disconnect
      // the colour lines of a graph. However, the colours can be connected
      // again if a final or initial partons of the correct flavour exists.

      // Check which of the partners are final / initial
      int incoming = (event[radBeforeColP[0]].isFinal())
                   ? radBeforeColP[1] : radBeforeColP[0];
      int outgoing = (event[radBeforeColP[0]].isFinal())
                   ? radBeforeColP[0] : radBeforeColP[1];

      // Loop through event to find "recovery partons"
      bool clusPossible = false;
      for(int i=0; i < int(event.size()); ++i)
        if (  i != emt && i != rad
          &&  i != incoming && i != outgoing
          && !mergingHooksPtr->hardProcess->matchesAnyOutgoing(i,event) ) {
          // Check if an incoming parton matches
          if ( event[i].status() == -21
            && (event[i].id() ==    event[outgoing].id()
              ||event[i].id() == -1*event[incoming].id()) )
          clusPossible = true;
          // Check if a final parton matches
          if ( event[i].isFinal()
            && (event[i].id() == -1*event[outgoing].id()
              ||event[i].id() ==    event[incoming].id()) )
          clusPossible = true;
        }

      // There can be a further complication: If e.g. in
      // t-channel photon exchange topologies, both incoming
      // partons are quarks, and form colour singlets with any
      // number of final state partons, at least try to
      // recluster as much as possible.
      // For this, check if the incoming parton
      // connected to the radiator is connected to a
      // colour and flavour singlet
      vector<int> excludeIn1;
      for(int i=0; i < 4; ++i)
        excludeIn1.push_back(0);
      vector<int> colSingletIn1;
      int flavIn1Type = (event[incoming].id() > 0) ? 1 : -1;
      // Try finding colour singlets
      bool isColSingIn1  = getColSinglet(flavIn1Type,incoming,event,
                             excludeIn1,colSingletIn1);
      // Check if colour singlet also is a flavour singlet
      bool isFlavSingIn1 = isFlavSinglet(event,colSingletIn1);

      // Check if the incoming parton not
      // connected to the radiator is connected to a
      // colour and flavour singlet
      int incoming2 = (incoming == 3) ? 4 : 3;
      vector<int> excludeIn2;
      for(int i=0; i < 4; ++i)
        excludeIn2.push_back(0);
      vector<int> colSingletIn2;
      int flavIn2Type = (event[incoming2].id() > 0) ? 1 : -1;
      // Try finding colour singlets
      bool isColSingIn2  = getColSinglet(flavIn2Type,incoming2,event,
                             excludeIn2,colSingletIn2);
      // Check if colour singlet also is a flavour singlet
      bool isFlavSingIn2 = isFlavSinglet(event,colSingletIn2);

      // If no "recovery clustering" is possible, reject clustering
      if (!clusPossible
        && (!isColSingIn1 || !isFlavSingIn1
         || !isColSingIn2 || !isFlavSingIn2))
        return false;

    }

    // Next-to-easiest problem 2:
    // FINAL STATE Q-QBAR CLUSTERING DISCONNECTS SINGLETT SUBSYSTEM WITH
    // FINAL STATE Q-QBAR PAIR FROM GRAPH

    // Prepare to check for colour singlet combinations of final state quarks
    // Start by building a list of partons to exclude when checking for
    // colour singlet combinations
    int flav = event[emt].id();
    vector<int> exclude;
    exclude.push_back(emt);
    exclude.push_back(rad);
    exclude.push_back(radBeforeColP[0]);
    exclude.push_back(radBeforeColP[1]);
    vector<int> colSinglet;
    // Now find parton from which to start checking colour singlets
    int iOther = -1;
    // Loop through event to find a parton of correct flavour
    for(int i=0; i < int(event.size()); ++i)
      // Check final state for parton equalling emitted flavour.
      // Exclude the colour system coupled to the clustering
      if ( i != emt
        && i != rad
        && i != radBeforeColP[0]
        && i != radBeforeColP[1]
        && event[i].isFinal() ) {
        // Stop if one parton of the correct flavour is found
        if (event[i].id() == flav) {
          iOther = i;
          break;
        }
      }
    // Save the type of flavour
    int flavType = (iOther > 0 && event[iOther].id() > 0) ? 1
                 : (iOther > 0) ? -1 : 0;
    // Try finding colour singlets
    bool isColSing = getColSinglet(flavType,iOther,event,exclude,colSinglet);
    // Check if colour singlet also is a flavour singlet
    bool isFlavSing = isFlavSinglet(event,colSinglet);

    // Check if the colour singlet is precisely contained in the hard process.
    // If so, then we're safe to recluster.
    bool isHardSys = true;
    for(int i=0; i < int(colSinglet.size()); ++i)
      isHardSys = mergingHooksPtr->hardProcess->matchesAnyOutgoing(
        colSinglet[i], event);

    // Nearly there...
    // If the decoupled colour singlet system is NOT contained in the hard
    // process, we need to check the whole final state.
    if (isColSing && isFlavSing && !isHardSys) {

      // In a final check, ensure that the final state does not only
      // consist of colour singlets that are also flavour singlets
      // of the identical (!) flavours
      // Loop through event and save all final state partons
      vector<int> allFinal;
      for(int i=0; i < int(event.size()); ++i)
        if ( event[i].isFinal() )
          allFinal.push_back(i);

      // Check if all final partons form a colour singlet
      bool isFullColSing  = isColSinglet(event,allFinal);
      // Check if all final partons form a flavour singlet
      bool isFullFlavSing = isFlavSinglet(event,allFinal,flav);

      // If all final quarks are of identical flavour,
      // no possible clustering should be discriminated.
      // Otherwise, disallow
      if (!isFullColSing || !isFullFlavSing)
        return false;
    }
  }

  // ISR PROBLEMS

  if (isISRg2qq && nInQuarkFlav + nOutQuarkFlav > 0) {

    // Easiest problem 1:
    // RECLUSTERED INITIAL STATE GLUON MATCHES FINAL STATE GLUON
    for(int i=0; i < int(gluon.size()); ++i) {
      if (event[gluon[i]].isFinal()
        && event[gluon[i]].col()  == radBeforeCol
        && event[gluon[i]].acol() == radBeforeAcl)
        return false;
    }

    // Easiest problem 2:
    // RECLUSTERED INITIAL STATE GLUON MATCHES INITIAL STATE GLUON
    for(int i=0; i < int(gluon.size()); ++i) {
      if (event[gluon[i]].status() == -21
        && event[gluon[i]].acol()  == radBeforeCol
        && event[gluon[i]].col() == radBeforeAcl)
        return false;
    }

    // Next-to-easiest problem 1:
    // RECLUSTERED INITIAL STATE GLUON MATCHES FINAL STATE Q-QBAR PAIR
    if ( int(radBeforeColP.size()) == 2
      && event[radBeforeColP[0]].isFinal()
      && event[radBeforeColP[1]].isFinal()
      && event[radBeforeColP[0]].id() == -1*event[radBeforeColP[1]].id() ) {

      // In principle, clustering this splitting can disconnect
      // the colour lines of a graph. However, the colours can be connected
      // again if final state partons of the correct (anti)flavour, or
      // initial state partons of the correct flavour exist
      // Loop through event to check
      bool clusPossible = false;
      for(int i=0; i < int(event.size()); ++i)
        if ( i != emt && i != rad
          && i != radBeforeColP[0]
          && i != radBeforeColP[1]
          && !mergingHooksPtr->hardProcess->matchesAnyOutgoing(i,event) ) {
          if (event[i].status() == -21
            && ( event[radBeforeColP[0]].id() == event[i].id()
              || event[radBeforeColP[1]].id() == event[i].id() ))

            clusPossible = true;
          if (event[i].isFinal()
            && ( event[radBeforeColP[0]].id() == -1*event[i].id()
              || event[radBeforeColP[1]].id() == -1*event[i].id() ))
            clusPossible = true;
        }

      // There can be a further complication: If e.g. in
      // t-channel photon exchange topologies, both incoming
      // partons are quarks, and form colour singlets with any
      // number of final state partons, at least try to
      // recluster as much as possible.
      // For this, check if the incoming parton
      // connected to the radiator is connected to a
      // colour and flavour singlet
      int incoming1 = 3;
      vector<int> excludeIn1;
      for(int i=0; i < 4; ++i)
        excludeIn1.push_back(0);
      vector<int> colSingletIn1;
      int flavIn1Type = (event[incoming1].id() > 0) ? 1 : -1;
      // Try finding colour singlets
      bool isColSingIn1  = getColSinglet(flavIn1Type,incoming1,event,
                             excludeIn1,colSingletIn1);
      // Check if colour singlet also is a flavour singlet
      bool isFlavSingIn1 = isFlavSinglet(event,colSingletIn1);

      // Check if the incoming parton not
      // connected to the radiator is connected to a
      // colour and flavour singlet
      int incoming2 = 4;
      vector<int> excludeIn2;
      for(int i=0; i < 4; ++i)
        excludeIn2.push_back(0);
      vector<int> colSingletIn2;
      int flavIn2Type = (event[incoming2].id() > 0) ? 1 : -1;
      // Try finding colour singlets
      bool isColSingIn2  = getColSinglet(flavIn2Type,incoming2,event,
                             excludeIn2,colSingletIn2);
      // Check if colour singlet also is a flavour singlet
      bool isFlavSingIn2 = isFlavSinglet(event,colSingletIn2);

      // If no "recovery clustering" is possible, reject clustering
      if (!clusPossible
        && (!isColSingIn1 || !isFlavSingIn1
         || !isColSingIn2 || !isFlavSingIn2))
        return false;

    }

  }

  // Done
  return allowed;
}

//--------------------------------------------------------------------------

// Function to check if rad,emt,rec triple is results in
// colour singlet radBefore+recBefore
// IN int rad,emt,rec : Positions (in event record) of the three
//                      particles considered for clustering
//    Event event     : Reference event

bool History::isSinglett( int rad, int emt, int rec, const Event& event ) {

  int radCol = event[rad].col();
  int emtCol = event[emt].col();
  int recCol = event[rec].col();
  int radAcl = event[rad].acol();
  int emtAcl = event[emt].acol();
  int recAcl = event[rec].acol();
  int recType = event[rec].isFinal() ? 1 : -1;

  bool isSing = false;

  if ( ( recType == -1
       && radCol + emtCol == recCol && radAcl + emtAcl == recAcl)
    ||( recType == 1
       && radCol + emtCol == recAcl && radAcl + emtAcl == recCol) )
    isSing = true;

  return isSing;

}

//--------------------------------------------------------------------------

// Function to check if event is sensibly constructed: Meaning
// that all colour indices are contracted and that the charge in
// initial and final states matches
// IN  event : event to be checked
// OUT TRUE  : event is properly construced
//     FALSE : event not valid

bool History::validEvent( const Event& event ) {

  // Check if event is coloured
  bool validColour = true;
  for ( int i = 0; i < event.size(); ++i)
   // Check colour of quarks
   if ( event[i].isFinal() && event[i].colType() == 1
          // No corresponding anticolour in final state
       && ( FindCol(event[i].col(),i,0,event,1,true) == 0
          // No corresponding colour in initial state
         && FindCol(event[i].col(),i,0,event,2,true) == 0 )) {
     validColour = false;
     break;
   // Check anticolour of antiquarks
   } else if ( event[i].isFinal() && event[i].colType() == -1
          // No corresponding colour in final state
       && ( FindCol(event[i].acol(),i,0,event,2,true) == 0
          // No corresponding anticolour in initial state
         && FindCol(event[i].acol(),i,0,event,1,true) == 0 )) {
     validColour = false;
     break;
   // No uncontracted colour (anticolour) charge of gluons
   } else if ( event[i].isFinal() && event[i].colType() == 2
          // No corresponding anticolour in final state
       && ( FindCol(event[i].col(),i,0,event,1,true) == 0
          // No corresponding colour in initial state
         && FindCol(event[i].col(),i,0,event,2,true) == 0 )
          // No corresponding colour in final state
       && ( FindCol(event[i].acol(),i,0,event,2,true) == 0
          // No corresponding anticolour in initial state
         && FindCol(event[i].acol(),i,0,event,1,true) == 0 )) {
     validColour = false;
     break;
   }

  // Check charge sum in initial and final state
  bool validCharge = true;
  double initCharge = event[3].charge() + event[4].charge();
  double finalCharge = 0.0;
  for(int i = 0; i < event.size(); ++i)
    if (event[i].isFinal()) finalCharge += event[i].charge();
  if (abs(initCharge-finalCharge) > 1e-12) validCharge = false;

  return (validColour && validCharge);

}

//--------------------------------------------------------------------------

// Function to check whether two clusterings are identical, used
// for finding the history path in the mother -> children direction

bool History::equalClustering( Clustering clus1 , Clustering clus2 ) {
  return (  (clus1.emittor     == clus2.emittor)
         && (clus1.emitted     == clus2.emitted)
         && (clus1.recoiler    == clus2.recoiler)
         && (clus1.partner     == clus2.partner)
         && (clus1.pT()        == clus2.pT())
         && (clus1.spinRadBef  == clus2.spinRadBef)
         && (clus1.spinRad     == clus2.spinRad)
         && (clus1.spinEmt     == clus2.spinEmt)
         && (clus1.spinRec     == clus2.spinRec)
         && (clus1.flavRadBef  == clus2.flavRadBef));
}

//--------------------------------------------------------------------------

// Chose dummy scale for event construction. By default, choose
//     sHat     for 2->Boson(->2)+ n partons processes and
//     M_Boson  for 2->Boson(->)             processes

double History::choseHardScale( const Event& event ) const {

  // Get sHat
  double mHat = (event[3].p() + event[4].p()).mCalc();

  // Find number of final state particles and bosons
  int nFinal = 0;
  int nFinBos= 0;
  int nBosons= 0;
  double mBos = 0.0;
  for(int i = 0; i < event.size(); ++i)
    if ( event[i].isFinal() ) {
      nFinal++;
      // Remember final state unstable bosons
      if ( event[i].idAbs() == 23
        || event[i].idAbs() == 24 ) {
          nFinBos++;
          nBosons++;
          mBos += event[i].m();
      }
    } else if ( abs(event[i].status()) == 22
             && (  event[i].idAbs() == 23
                || event[i].idAbs() == 24 )) {
      nBosons++;
      mBos += event[i].m(); // Real mass
    }

  // Return averaged boson masses
  if ( nBosons > 0 && (nFinal + nFinBos*2) <= 3)
    return (mBos / double(nBosons));
  else return
    mHat;
}


//--------------------------------------------------------------------------

// If the state has an incoming hadron return the flavour of the
// parton entering the hard interaction. Otherwise return 0

int History::getCurrentFlav(const int side) const {
  int in = (side == 1) ? 3 : 4;
  return state[in].id();
}

//--------------------------------------------------------------------------

double History::getCurrentX(const int side) const {
  int in = (side == 1) ? 3 : 4;
  return ( 2.*state[in].e()/state[0].e() );
}

//--------------------------------------------------------------------------

double History::getCurrentZ(const int rad,
  const int rec, const int emt, int idRadBef) const {

  int type = state[rad].isFinal() ? 1 : -1;
  double z = 0.;

  if (type == 1) {

    Vec4 radAfterBranch(state[rad].p());
    Vec4 recAfterBranch(state[rec].p());
    Vec4 emtAfterBranch(state[emt].p());

    // Store masses both after and prior to emission.
    double m2RadAft = radAfterBranch.m2Calc();
    double m2EmtAft = emtAfterBranch.m2Calc();
    double m2RadBef = 0.;
    if ( state[rad].idAbs() != 21 && state[rad].idAbs() != 22
      && state[emt].idAbs() != 24 && state[rad].idAbs() != state[emt].idAbs())
      m2RadBef = m2RadAft;
    else if ( state[emt].idAbs() == 24) {
      if (idRadBef != 0)
        m2RadBef = pow2(particleDataPtr->m0(abs(idRadBef)));
    }

    double Qsq   = (radAfterBranch + emtAfterBranch).m2Calc();

    // Calculate dipole invariant mass.
    double m2final
      = (radAfterBranch + recAfterBranch + emtAfterBranch).m2Calc();
    // More complicated for initial state recoiler.
    if ( !state[rec].isFinal() ){
      double mar2  = m2final - 2. * Qsq + 2. * m2RadBef;
       recAfterBranch *=  (1. - (Qsq - m2RadBef)/(mar2 - m2RadBef))
                         /(1. + (Qsq - m2RadBef)/(mar2 - m2RadBef));
       // If Qsq is larger than mar2 the event is not kinematically possible.
       // Just return random z, since clustering will be discarded.
       if (Qsq > mar2) return 0.5;
    }

    Vec4   sum   = radAfterBranch + recAfterBranch + emtAfterBranch;
    double m2Dip = sum.m2Calc();
    // Construct 2->3 variables for FSR
    double x1 = 2. * (sum * radAfterBranch) / m2Dip;
    double x2 = 2. * (sum * recAfterBranch) / m2Dip;

    // Prepare for more complicated z definition for massive splittings.
    double lambda13 = sqrt( pow2(Qsq - m2RadAft - m2EmtAft )
                         - 4.*m2RadAft*m2EmtAft);
    double k1 = ( Qsq - lambda13 + (m2EmtAft - m2RadAft ) ) / ( 2. * Qsq );
    double k3 = ( Qsq - lambda13 - (m2EmtAft - m2RadAft ) ) / ( 2. * Qsq );
    // Calculate z of splitting, different for FSR
    z = 1./ ( 1- k1 -k3) * ( x1 / (2.-x2) - k3);

  } else {
    // Construct momenta of dipole before/after splitting for ISR
    Vec4 qBR(state[rad].p() - state[emt].p() + state[rec].p());
    Vec4 qAR(state[rad].p() + state[rec].p());
    // Calculate z of splitting, different for ISR
    z = (qBR.m2Calc())/( qAR.m2Calc());
  }

  return z;

}

//--------------------------------------------------------------------------

// Function to compute "pythia pT separation" from Particle input

double History::pTLund(const Event& event, int rad, int emt, int rec,
  int ShowerType, int idRadBef) {

  // Signal failures when calling History from within aMC@NLO.
  bool signal = mergingHooksPtr->doRuntimeAMCATNLOInterface();

  Particle RadAfterBranch = event[rad];
  Particle EmtAfterBranch = event[emt];
  Particle RecAfterBranch = event[rec];

  // Use external shower for merging.
  if ( mergingHooksPtr->useShowerPlugin() ) {
    map<string,double> stateVars;
    bool isFSR = showers->timesPtr->isTimelike(event, rad, emt, rec, "");
    if (isFSR) {
      string name = showers->timesPtr->getSplittingName(event, rad, emt,
        rec).front();
      stateVars   = showers->timesPtr->getStateVariables(event, rad, emt, rec,
        name);
    } else {
      string name = showers->spacePtr->getSplittingName(event, rad, emt,
        rec).front();
      stateVars   = showers->spacePtr->getStateVariables(event, rad, emt, rec,
        name);
    }

    return ( (stateVars.size() > 0 && stateVars.find("t") != stateVars.end())
             ? sqrt(stateVars["t"]) : -1.0 );
  }

  // Save type: 1 = FSR pT definition, else ISR definition
  int Type   = ShowerType;
  // Calculate virtuality of splitting
  int sign = (Type==1) ? 1 : -1;
  Vec4 Q(RadAfterBranch.p() + sign*EmtAfterBranch.p());
  double Qsq = sign * Q.m2Calc();

  // If tiny Q^2 there won't be a viable configuration. In this case, return
  // a small value for signalling.
  if (abs(Qsq)<1e-6) return (signal ? 1e-6 : 0.0);

  // Construct 2->3 variables for FSR
  Vec4 radAft(RadAfterBranch.p());
  Vec4 recAft(RecAfterBranch.p());
  Vec4 emtAft(EmtAfterBranch.p());

  // Store masses both after and prior to emission.
  double m2RadAft = radAft.m2Calc();
  double m2EmtAft = emtAft.m2Calc();

  double m2RadBef = 0.;
  if ( RadAfterBranch.idAbs() != 21 && RadAfterBranch.idAbs() != 22
       && EmtAfterBranch.idAbs() != 24
     && RadAfterBranch.idAbs() != EmtAfterBranch.idAbs() )
    m2RadBef = m2RadAft;
  else if (EmtAfterBranch.idAbs() == 24) {
    if (idRadBef != 0)
      m2RadBef = pow2(particleDataPtr->m0(abs(idRadBef)));
  } else if (!RadAfterBranch.isFinal()) {
    if (RadAfterBranch.idAbs() == 21 && EmtAfterBranch.idAbs() != 21)
      m2RadBef = m2EmtAft;
  }

  // Calculate dipole invariant mass.
  double m2final = (radAft + recAft + emtAft).m2Calc();
  // More complicated for initial state recoiler.
  if ( !RecAfterBranch.isFinal() && RadAfterBranch.isFinal() ){
    double mar2  = m2final - 2. * Qsq + 2. * m2RadBef;
     recAft *=  (1. - (Qsq - m2RadBef)/(mar2 - m2RadBef))
               /(1. + (Qsq - m2RadBef)/(mar2 - m2RadBef));
     // Reclustering not kinematically possible if Qsq is larger than mar2.
     if (Qsq > mar2) return (signal ? 1e10 : 0.0);
  }

  Vec4   sum   = radAft + recAft + emtAft;
  double m2Dip = sum.m2Calc();
  double x1 = 2. * (sum * radAft) / m2Dip;
  double x2 = 2. * (sum * recAft) / m2Dip;

  // Construct momenta of dipole before/after splitting for ISR
  double q2BR = (RadAfterBranch.p() - EmtAfterBranch.p()
               + RecAfterBranch.p()).m2Calc();
  double q2AR = (RadAfterBranch.p() + RecAfterBranch.p()).m2Calc();

  // Check that dipole mass after intial-state emission is positive.
  // If not, the emission is not kinematically allowed and the pT should
  // be zero.
  if (Type != 1 && q2BR < 0.) return (signal ? 1e-5 : 0.0);

  // Prepare for more complicated z definition for massive splittings.
  double lambda13 = sqrt( pow2(Qsq - m2RadAft - m2EmtAft )
    - 4. * m2RadAft*m2EmtAft );
  double k1 = ( Qsq - lambda13 + (m2EmtAft - m2RadAft ) ) / ( 2. * Qsq );
  double k3 = ( Qsq - lambda13 - (m2EmtAft - m2RadAft ) ) / ( 2. * Qsq );

  // Calculate z of splitting, different for FSR and ISR
  double z = (Type==1) ? 1./ ( 1- k1 -k3) * ( x1 / (2.-x2) - k3)
                     : q2BR / q2AR;

  // Separation of splitting, different for FSR and ISR
  double pTpyth = (Type==1) ? z*(1.-z) : (1.-z);

  // pT^2 = separation*virtuality
  if (Type == 1) pTpyth *= (Qsq - m2RadBef);
  else           pTpyth *= Qsq;

  // Check for threshold in ISR, only relevant for c and b.
  // Use pT2 = (1 - z) * (Qsq + m^2).
  if ( Type != 1) {
    if ( (RadAfterBranch.idAbs() == 4 || EmtAfterBranch.idAbs() == 4)
         && RadAfterBranch.idAbs() != EmtAfterBranch.idAbs()) {
      if (pTpyth < 2 * pow2(particleDataPtr->m0(4)))
        pTpyth = (Qsq + pow2(particleDataPtr->m0(4)) ) * (1. - q2BR/q2AR);
    } else if ( (RadAfterBranch.idAbs() == 5 || EmtAfterBranch.idAbs() == 5)
                && RadAfterBranch.idAbs() != EmtAfterBranch.idAbs()) {
      if (pTpyth < 2 * pow2(particleDataPtr->m0(5)))
        pTpyth = (Qsq + pow2(particleDataPtr->m0(5)) ) * (1. - q2BR/q2AR);
    }
  }

  if ( pTpyth < 0. ) return (signal ? 1e-6 : 0.0);

  // Return pT
  return sqrt(pTpyth);

}

//--------------------------------------------------------------------------

// Function to return the position of the initial line before (or after)
// a single (!) splitting.

int History::posChangedIncoming(const Event& event, bool before) {

  // Check for initial state splittings.
  // Consider a splitting to exist if both mother and sister were found.
  // Find sister
  int iSister = 0;
  for (int i =0; i < event.size(); ++i)
    if (event[i].status() == 43) {
      iSister = i;
      break;
    }
  // Find mother
  int iMother = 0;
  if (iSister > 0) iMother = event[iSister].mother1();

  // Initial state splitting has been found.
  if (iSister > 0 && iMother > 0) {

    // Find flavour, mother flavour
    int flavSister  = event[iSister].id();
    int flavMother  = event[iMother].id();

    // Find splitting flavour
    int flavDaughter = 0;
    if ( abs(flavMother) < 21 && flavSister     == 21)
      flavDaughter = flavMother;
    else if ( flavMother     == 21 && flavSister     == 21)
      flavDaughter = flavMother;
    else if ( flavMother     == 21 && abs(flavSister) < 21)
      flavDaughter = -1*flavSister;
    else if ( abs(flavMother) < 21 && abs(flavSister) < 21)
      flavDaughter = 21;

    // Find initial state (!) daughter
    int iDaughter = 0;
    for (int i =0; i < event.size(); ++i)
      if ( !event[i].isFinal()
        && event[i].mother1() == iMother
        && event[i].id()      == flavDaughter )
        iDaughter = i;

    // Done for initial state splitting.
    if ( !before ) return iMother;
    else return iDaughter;

  }

  // Check for final state splittings with initial state recoiler.
  // Consider a splitting to exist if both mother and daughter were found.
  // Find new mother
  iMother = 0;
  for (int i =0; i < event.size(); ++i)
    if ( abs(event[i].status()) == 53 || abs(event[i].status()) == 54) {
      iMother = i;
      break;
    }
  // Find daughter
  int iDaughter = 0;
  if (iMother > 0) iDaughter = event[iMother].daughter1();

  // Done if final state splitting has been found.
  if (iDaughter > 0 && iMother > 0) {

    // Done for final state splitting.
    if ( !before ) return iMother;
    else return iDaughter;

  }

  // If no splitting has been found, return zero.
  return 0;

}

//--------------------------------------------------------------------------

// Function to give back the ratio of PDFs and PDF * splitting kernels needed
// to convert a splitting at scale pdfScale, chosen with running PDFs, to a
// splitting chosen with PDFs at a fixed scale mu. As needed to properly count
// emissions.

double History::pdfFactor( const Event& event, const int type,
  double pdfScale, double mu ) {

  double weight = 1.;

  // Final state splittings
  if (type >= 3) {

    // Find new mother
    int iMother = 0;
    for (int i =0; i < event.size(); ++i)
      if ( abs(event[i].status()) == 53 || abs(event[i].status()) == 54) {
        iMother = i;
        break;
      }
    int flavMother = event[iMother].id();

    // Done if no initial state recoiler was found
    if ( iMother == 0 ) return 1.;

    // Find daughter
    int iDaughter    = event[iMother].daughter1();
    int flavDaughter = event[iDaughter].id();

    // Find x values
    double xMother = 2.*event[iMother].e() / event[0].e();
    double xDaughter = 2.*event[iDaughter].e() / event[0].e();

    // Calculate PDF ratios
    int sideSplit = ( event[iMother].pz() > 0.) ? 1 : -1;
    double pdfDen1, pdfDen2, pdfNum1, pdfNum2;
    if ( sideSplit == 1 ) {
      // Find PDFs
      pdfDen1 = max(1e-15,beamA.xfISR(0, flavDaughter, xDaughter, pow2(mu)) );
      pdfNum1 = beamA.xfISR(0, flavDaughter, xDaughter, pow2(pdfScale) );
      pdfNum2 = beamA.xfISR(0, flavMother, xMother, pow2(mu) );
      pdfDen2 = max(1e-15,beamA.xfISR(0,flavMother, xMother, pow2(pdfScale)) );
    } else {
      // Find PDFs
      pdfDen1 = max(1e-15,beamB.xfISR(0, flavDaughter, xDaughter, pow2(mu)) );
      pdfNum1 = beamB.xfISR(0, flavDaughter, xDaughter, pow2(pdfScale) );
      pdfNum2 = beamB.xfISR(0, flavMother, xMother, pow2(mu) );
      pdfDen2 = max(1e-15,beamB.xfISR(0,flavMother, xMother, pow2(pdfScale)) );
    }

    // The magnitude of the PDF ratio in FSR is limited to one. If that was
    // the case, return one.
    if ( pdfDen2/pdfNum1 > 1. ) return 1.;

    // Calculate PDF weight to reweight emission to emission evaluated at
    // constant factorisation scale. No need to include the splitting kernel in
    // the weight, since it will drop out anyway.
    weight = (pdfNum1/pdfDen1) * (pdfNum2)/(pdfDen2);

  // Initial state splittings
  } else if (type == 2) {

    // Find sister
    int iSister = 0;
    for (int i =0; i < event.size(); ++i)
      if (event[i].status() == 43) {
        iSister = i;
        break;
      }
    int flavSister = event[iSister].id();

    // Find mother
    int iMother    = event[iSister].mother1();
    int flavMother = event[iMother].id();

    // Find splitting flavour
    int flavDaughter = 0;
    if ( abs(flavMother) < 21 && flavSister     == 21)
      flavDaughter = flavMother;
    else if ( flavMother     == 21 && flavSister     == 21)
      flavDaughter = flavMother;
    else if ( flavMother     == 21 && abs(flavSister) < 21)
      flavDaughter = -1*flavSister;
    else if ( abs(flavMother) < 21 && abs(flavSister) < 21)
      flavDaughter = 21;

    // Find x values
    double xMother = 2.*event[iMother].e() / event[0].e();

    // Find initial state (!) daughter
    int iDaughter = 0;
    for (int i =0; i < event.size(); ++i)
      if ( !event[i].isFinal()
        && event[i].mother1() == iMother
        && event[i].id()      == flavDaughter )
        iDaughter = i;
    double xDaughter = 2.*event[iDaughter].e() / event[0].e();

    // Calculate PDF weight to reweight emission to emission evaluated at
    // constant factorisation scale. No need to include the splitting kernel
    // in the weight, since it will drop out anyway.
    int sideSplit = ( event[iMother].pz() > 0.) ? 1 : -1;
    double ratio1 = getPDFratio( sideSplit, false, false, flavDaughter,
                      xDaughter, pdfScale, flavDaughter, xDaughter, mu );
    double ratio2 = getPDFratio( sideSplit, false, false, flavMother,
                      xMother, mu, flavMother, xMother, pdfScale );

    weight = ratio1*ratio2;

  // Do nothing for MPI
  } else {
    weight = 1.;
  }

  // Done
  return weight;
}

//--------------------------------------------------------------------------

// Function giving the product of splitting kernels and PDFs so that the
// resulting flavour is given by flav. This is used as a helper routine
// to dgauss

double History::integrand(int flav, double x, double scaleInt, double z) {

  // Declare constants
  double CF = 4./3.;
  double TR = 1./2.;
  double CA = 3.;

  double result = 0.;

  // Integrate NLL sudakov remainder
  if (flav==0) {

    AlphaStrong* as = mergingHooksPtr->AlphaS_ISR();
    double asNow = (*as).alphaS(z);
    result = 1./z *asNow*asNow* ( log(scaleInt/z) -3./2. );

  // Integrand for PDF ratios. Careful about factors if 1/z, since formulae
  // are expressed in terms if f(x,mu), while Pythia uses x*f(x,mu)!
  } else if (flav==21) {

    double measure1 = 1./(1. - z);
    double measure2 = 1.;

    double integrand1 =
      2.*CA
      * z * getPDFratio( 2, false, true, 21, x/z, scaleInt, 21, x, scaleInt )
    - 2.*CA;

    double integrand2 =
      // G -> G terms
      2.*CA  *((1. -z)/z + z*(1.-z))
      * getPDFratio( 2, false, true, 21, x/z, scaleInt, 21, x, scaleInt )
      // G -> Q terms
    + CF * ((1+pow(1-z,2))/z)
      *( getPDFratio(2,false,true,1,x/z,scaleInt,21,x,scaleInt)
       + getPDFratio(2,false,true,-1,x/z,scaleInt,21,x,scaleInt)
       + getPDFratio(2,false,true,2,x/z,scaleInt,21,x,scaleInt)
       + getPDFratio(2,false,true,-2,x/z,scaleInt,21,x,scaleInt)
       + getPDFratio(2,false,true,3,x/z,scaleInt,21,x,scaleInt)
       + getPDFratio(2,false,true,-3,x/z,scaleInt,21,x,scaleInt)
       + getPDFratio(2,false,true,4,x/z,scaleInt,21,x,scaleInt)
       + getPDFratio(2,false,true,-4,x/z,scaleInt,21,x,scaleInt) );

    // Done
    result = integrand1*measure1 + integrand2*measure2;

  } else {

    double measure1 = 1./(1. -z);
    double measure2 = 1.;

    // Q -> Q terms
    double integrand1 =
      CF * (1+pow(z,2))
      * getPDFratio(2,false,true,flav,x/z,scaleInt,flav,x,scaleInt)
    - 2.*CF;

    // Q -> G terms
    double integrand2 =
    + TR * (pow(z,2) + pow(1-z,2))
      * getPDFratio(2,false,true,21,x/z,scaleInt,flav,x,scaleInt);

    // Done
    result = measure1*integrand1 + measure2*integrand2;
  }

  return result;

}

//--------------------------------------------------------------------------

// Function providing a list of possible new flavours after a w emssion
// from the input flavour.

vector<int> History::posFlavCKM(int flav) {

  // absolute values!
  int flavAbs = abs(flav);

  vector<int> flavRadBefs;
  // (e,mu,tau)
  if (flavAbs > 10 && flavAbs % 2 == 1)
    flavRadBefs.push_back(flavAbs + 1);
  // (neutrinoes)
  else if (flavAbs > 10 && flavAbs % 2 == 0)
    flavRadBefs.push_back(flavAbs - 1);
  // Full CKM for quarks.
  else if (flavAbs < 10 && flavAbs % 2 == 1) {
    flavRadBefs.push_back(2);
    flavRadBefs.push_back(4);
    flavRadBefs.push_back(6);
  }
  else if (flavAbs < 10 && flavAbs % 2 == 0) {
    flavRadBefs.push_back(1);
    flavRadBefs.push_back(3);
    flavRadBefs.push_back(5);
  }

  // Return the possible flavours.
  return flavRadBefs;
}

//--------------------------------------------------------------------------

// Check if the new flavour structure is possible.
// If clusType is 1 final clustering is assumed, otherwise initial clustering
// is assumed.

bool History::checkFlavour(vector<int>& flavCounts, int flavRad,
                           int flavRadBef, int clusType) {

  // Loop over event.
  for(int k = 0; k < 20; ++k) {
    // Find changes from this W emission.
    int cor = 0;
    if (abs(flavRad) == k) {
      cor = -1;
      if (flavRad < 0) cor = 1;
    }

    if (abs(flavRadBef) == k) {
      cor = 1;
      if (flavRadBef < 0) cor = -1;
    }

    // if flavour and flavRadBef is the same, no correction.
    if (flavRadBef == flavRad) cor = 0;

    // Check if flavour is consistent.
    if (clusType == 1) {
      if (flavCounts[k] + cor != 0) return false;
    }
    else
      if (flavCounts[k] - cor != 0) return false;
  }

 // No more checks.
 return true;

}

//--------------------------------------------------------------------------

// Reverse the boost carried out by the ISR.
// The three first momenta are given by the ME,
// the last two are filled in by this function.
void History::reverseBoostISR(Vec4& pMother, Vec4& pSister, Vec4& pPartner,
  Vec4& pDaughter, Vec4& pRecoiler, int sign, double eCM, double& phi ) {

  // Find rotation by phi that would have been done for a
  // splitting daughter -> mother + sister
  phi = pSister.phi();
  // Find rotation with -phi
  RotBstMatrix rot_by_mphi;
  rot_by_mphi.rot(0.,-phi);
  // Find rotation with +phi
  RotBstMatrix rot_by_pphi;
  rot_by_pphi.rot(0.,phi);

  // Get mother and partner x values
  // x1 after isr
  double x1 = 2. * pMother.e() / eCM;
  // x2 after isr
  double x2 = 2. * pPartner.e() / eCM;

  // Find z of the splitting
  Vec4 qDip( pMother - pSister);
  Vec4 qAfter(pMother + pPartner);
  Vec4 qBefore(qDip + pPartner);
  double z = qBefore.m2Calc() / qAfter.m2Calc();

  // Calculate e_CM^2 before the splitting.
  double x1New = z*x1; // x1 before isr
  double x2New = x2;   // x2 before isr
  double sHat = x1New*x2New*eCM*eCM;

  // Construct daughter and recoiler momenta before the splitting.
  // (Note: For final result, only needs to be boosted into
  //        frame with unchanged "recoiler" momentum)
  Vec4 pDaughterBef( 0., 0.,  sign*0.5*sqrt(sHat), 0.5*sqrt(sHat));
  Vec4 pRecoilerBef( 0., 0., -sign*0.5*sqrt(sHat), 0.5*sqrt(sHat));

  // Rotate momenta defined in the lab frame by phi
  pMother.rotbst( rot_by_mphi );
  pSister.rotbst( rot_by_mphi );
  pPartner.rotbst( rot_by_mphi );

  // Find boost from lab frame to rest frame of
  // off-shell daughter + on-shell recoiler dipole
  pDaughter.p( pMother - pSister);
  pRecoiler.p( pPartner );
  RotBstMatrix from_CM_to_DRoff;
  if (sign == 1)
    from_CM_to_DRoff.toCMframe(pDaughter, pRecoiler);
  else
    from_CM_to_DRoff.toCMframe(pRecoiler, pDaughter);

  // Rotate and boost all momenta to rest frame of off-shell daughter +
  // on-shell recoiler dipole
  pMother.rotbst( from_CM_to_DRoff );
  pPartner.rotbst( from_CM_to_DRoff );
  pSister.rotbst( from_CM_to_DRoff );

  // Find longitudinal boost from on-shell daughter + on-shell recoiler
  // dipole rest frame to the frame in which the recoiler momentum (x-value)
  // does not change in the splitting process.
  RotBstMatrix from_DR_to_CM;
  from_DR_to_CM.bst( 0., 0., sign*( x1New - x2New ) / ( x1New + x2New ) );

  // Boost all momenta into the "unchanged recoiler" frame, thereby
  // correcting for momentum mismatch by transferring the recoil to all
  // final state particles.
  pDaughterBef.rotbst( from_DR_to_CM );
  pRecoilerBef.rotbst( from_DR_to_CM );

  // Ensure that radiator and recoiler are massless to
  // very good accuracy.
  if ( abs(pRecoilerBef.mCalc()) > 1e-7 ) {
    double pzSign = (pRecoilerBef.pz() > 0.) ? 1. : -1.;
    double eRec   = pRecoilerBef.e();
    pRecoilerBef.p(0., 0., pzSign*eRec, eRec);
  }
  if ( abs(pDaughterBef.mCalc()) > 1e-7 ) {
    double pzSign = (pDaughterBef.pz() > 0.) ? 1. : -1.;
    double eDau   = pDaughterBef.e();
    pDaughterBef.p(0., 0., pzSign*eDau, eDau);
  }

  // Done.
  return;
}


//--------------------------------------------------------------------------

// Check if an event reclustered into a 2 -> 2 dijet.
// (Only enabled if W reclustering is used).
bool History::isQCD2to2(const Event& event) {

  if (!mergingHooksPtr->doWeakClustering()) return false;

  int nFinalPartons = 0, nFinal = 0;;
  for (int i = 0;i < event.size();++i)
    if (event[i].isFinal()) {
      nFinal++;
      if ( event[i].idAbs() < 10 || event[i].idAbs() == 21)
        nFinalPartons++;
    }
  if (nFinalPartons == 2 && nFinal == 2) return true;
  else return false;

}

//--------------------------------------------------------------------------


// Check if an event reclustered into a 2 -> 1 Drell-Yan.
// (Only enabled if W reclustering is used).
bool History::isEW2to1(const Event& event) {

  if (!mergingHooksPtr->doWeakClustering()) return false;

  int nVector = 0;
  for (int i = 0;i < event.size();++i) {
    if (event[i].isFinal()) {
      if (event[i].idAbs() == 23 ||
         event[i].idAbs() == 24 ||
         event[i].idAbs() == 22) nVector++;
      else return false;
    }
  }

  // Only true if a single vector boson as outgoing process.
  if (nVector == 1) return true;

  // Done
  return false;

}

//--------------------------------------------------------------------------

// Set selected child indices.
void History::setSelectedChild() {
  if (mother == 0) return;
  for (int i = 0;i < int(mother->children.size());++i)
    if (mother->children[i] == this) mother->selectedChild = i;
  mother->setSelectedChild();
}

//--------------------------------------------------------------------------

void History::setupSimpleWeakShower(int nSteps) {

  // Go back to original 2 to 2 process.
  if (selectedChild != -1) {
    children[selectedChild]->setupSimpleWeakShower(nSteps+1);
    return;
  }

  // Defining needed containers.
  vector<int> mode, fermionLines;
  vector<Vec4> mom;
  vector<pair<int,int> > dipoles;

  // Setup hard process.
  setupWeakHard(mode,fermionLines, mom);

  // Setup dipoles
  if (isQCD2to2(state)) {
    // Add dipoles.
    if (state[3].idAbs() < 10) dipoles.push_back(make_pair(3,4));
    if (state[4].idAbs() < 10) dipoles.push_back(make_pair(4,3));
    if (state[5].idAbs() < 10) dipoles.push_back(make_pair(5,6));
    if (state[6].idAbs() < 10) dipoles.push_back(make_pair(6,5));
  } else if (isEW2to1(state)) {
      if (state[3].idAbs() < 10) dipoles.push_back(make_pair(3,4));
      if (state[4].idAbs() < 10) dipoles.push_back(make_pair(4,3));
  }

  // Update the dipoles untill the desired number of emissions is reached.
  transferSimpleWeakShower(mode, mom, fermionLines, dipoles, nSteps);
}

//--------------------------------------------------------------------------

// Update weak dipoles after an emission.
void History::transferSimpleWeakShower(vector<int> &mode, vector<Vec4> &mom,
  vector<int> fermionLines, vector<pair<int,int> > &dipoles,
  int nSteps) {

  // store information in info pointer when reached last step.
  if (nSteps == 0) {
    infoPtr->setWeakModes(mode);
    infoPtr->setWeakDipoles(dipoles);
    infoPtr->setWeakMomenta(mom);
    infoPtr->setWeak2to2lines(fermionLines);
    return;
  }

  // Find the transfer map.
  map<int,int> stateTransfer;
  findStateTransfer(stateTransfer);

  // Update modes, fermion lines and dipoles.
  vector<int> modeNew = updateWeakModes(mode, stateTransfer);
  vector<int> fermionLinesNew = updateWeakFermionLines(fermionLines,
    stateTransfer);
  vector<pair<int, int> > dipolesNew = updateWeakDipoles(dipoles,
    stateTransfer);

  // Recursive call to transfer to desired final step.
  mother->transferSimpleWeakShower(modeNew, mom, fermionLinesNew, dipolesNew,
    nSteps - 1);
}

//--------------------------------------------------------------------------

// Update the weak modes after an emission.
vector<int> History::updateWeakModes(vector<int>& mode,
  map<int,int>& stateTransfer) {

  vector<int> modeNew(mode.size() + 1,0);

  // Update all modes not involved in emission.
  for (map<int,int>::iterator it = stateTransfer.begin();
       it != stateTransfer.end(); ++it)
    modeNew[it->second] = mode[it->first];

  modeNew[clusterIn.emitted] = mode[clusterIn.radBef];

  // Update splittings.
  // g -> q Q mark as s-channel.
  if (state[clusterIn.radBef].idAbs() == 21 &&
      mother->state[clusterIn.emittor].idAbs() != 21)  {
    // Set FSR dipole to S-channel.
    if (state[clusterIn.radBef].status() > 0) modeNew[clusterIn.emittor] = 1;
    // Set ISR dipole depending on recoiler.
    else {
      if (modeNew[clusterIn.emittor] == 1);
      else if ( mother->state[clusterIn.recoiler].id() == 21)
        modeNew[clusterIn.emittor] = 2;
      else if ( mother->state[clusterIn.recoiler].id()
             == mother->state[clusterIn.emittor].id() )
        modeNew[clusterIn.emittor] = 4;
      else modeNew[clusterIn.emittor] = 3;
    }
    // Emitted is always FSR.
    modeNew[clusterIn.emitted] = 1;
  }

  // ISR q -> q g
  if (state[clusterIn.radBef].idAbs() < 10 &&
      mother->state[clusterIn.emittor].idAbs() == 21)  {
    if (state[clusterIn.radBef].status() < 0) {
      modeNew[clusterIn.emitted] = 1;
    }
  }

  // gamma -> q Q mark as s-channel
  if (state[clusterIn.radBef].idAbs() == 22) {
    // Only FSR particles change to S-channel.
    if (state[clusterIn.radBef].status() > 0) modeNew[clusterIn.emittor] = 1;
    // Set ISR dipole depending on recoiler.
    else {
      if (modeNew[clusterIn.emittor] == 1);
      else if ( mother->state[clusterIn.recoiler].id() == 21)
        modeNew[clusterIn.emittor] = 2;
      else if ( mother->state[clusterIn.recoiler].id()
             == mother->state[clusterIn.emittor].id() )
        modeNew[clusterIn.emittor] = 4;
      else modeNew[clusterIn.emittor] = 3;
    }
    // Emitted is always FSR.
    modeNew[clusterIn.emitted] = 1;
  }
  return modeNew;
}

//--------------------------------------------------------------------------

// Update the fermion lines for the 2 -> 2 process. This is needed for
// the weak probabilities.
vector<int> History::updateWeakFermionLines(vector<int> fermionLines,
  map<int,int>& stateTransfer) {

  // Update fermion lines to 2-to-2 process.
  if (!fermionLines.empty()) {
    // Initial state lines always goes back to radiator.
    fermionLines[0] = stateTransfer[fermionLines[0]];
    fermionLines[1] = stateTransfer[fermionLines[1]];

    // If not involved in splitting just update index.
    bool lines[2] = {false,false};
    if (fermionLines[2] != clusterIn.radBef)
      fermionLines[2] = stateTransfer[fermionLines[2]];
    else lines[0] = true;
    if (fermionLines[3] != clusterIn.radBef)
      fermionLines[3] = stateTransfer[fermionLines[3]];
    else lines[1] = true;

    // If involved in splitting follow the fermion line.
    for (int i = 0;i < 2; ++i) {
      if (lines[i]) {
        if (state[fermionLines[2 + i]].isQuark() ||
            state[fermionLines[2 + i]].isLepton()) {
          if (mother->state[clusterIn.emittor].isQuark() ||
              mother->state[clusterIn.emittor].isLepton())
            fermionLines[2 + i] = clusterIn.emittor;
          else fermionLines[2 + i] = clusterIn.emitted;
        }
        // Stop tracing if gluon splitting.
        else fermionLines[2 + i] = 0;
      }
    }
  }
  return fermionLines;
}

//--------------------------------------------------------------------------

// Update the list of weak dipoles. This is needed to setup the PS correctly.
vector<pair<int,int> > History::updateWeakDipoles(
  vector<pair<int,int> > &dipoles, map<int,int>& stateTransfer) {

  vector<pair<int,int> > dipolesNew;
  for (int i = 0;i < int(dipoles.size());++i) {
    int iRecNew = -1, iRadNew = -1;

    // Find new radiator.
    if (dipoles[i].first != clusterIn.radBef)
      iRadNew = stateTransfer[dipoles[i].first];
    // FSR emission follow the quark line.
    else if (state[clusterIn.radBef].status() > 0) {
      if (mother->state[clusterIn.emitted].id() ==
        state[clusterIn.radBef].id())
        iRadNew = clusterIn.emitted;
      else iRadNew = clusterIn.emittor;
    // OSR emission always choose the emittor.
    } else if (mother->state[clusterIn.emittor].idAbs() < 10)
      iRadNew = clusterIn.emittor;

    // If no radiator is found skip the dipole.
    if (iRadNew == -1) continue;

    // Find new recoiler
    if (dipoles[i].second != clusterIn.radBef)
      iRecNew = stateTransfer[dipoles[i].second];
    // FSR emission follow the quark line.
    else if (state[clusterIn.radBef].status() > 0) {
      // If g -> g g, choose the one with the highest invariant mass.
      if (mother->state[clusterIn.emitted].id() == 21 &&
          mother->state[clusterIn.emittor].id() == 21) {
        double m1 = (mother->state[clusterIn.emitted].p()
          + mother->state[iRadNew].p()).m2Calc();
        double m2 = (mother->state[clusterIn.emittor].p()
          + mother->state[iRadNew].p()).m2Calc();
        iRecNew = (m1 > m2) ? clusterIn.emitted : clusterIn.emittor;
      }
      // Otherwise choose matching flavour.
      else if (mother->state[clusterIn.emitted].id() ==
        state[clusterIn.radBef].id())
        iRecNew = clusterIn.emitted;
      else  iRecNew = clusterIn.emittor;
      // ISR emission always choose the emittor.
    } else iRecNew = clusterIn.emittor;

    dipolesNew.push_back(make_pair(iRadNew,iRecNew));
  }

  // If g -> q qbar add new dipoles.
  if (state[clusterIn.radBef].idAbs() == 21 &&
      mother->state[clusterIn.emittor].idAbs() != 21) {
    // FSR.
    if (state[clusterIn.radBef].status() > 0) {
      dipolesNew.push_back(make_pair(clusterIn.emittor,clusterIn.emitted));
      dipolesNew.push_back(make_pair(clusterIn.emitted,clusterIn.emittor));
    // ISR.
    } else {
      int iRad = clusterIn.emittor;
      int iRec = (iRad == 3) ? 4 : 3;
      dipolesNew.push_back(make_pair(iRad,iRec));
      dipolesNew.push_back(make_pair(clusterIn.emitted,findISRRecoiler()));
    }
  }

  // if an ISR quark goes into a gluon.
  if (state[clusterIn.radBef].idAbs() < 10 &&
      mother->state[clusterIn.emittor].idAbs() == 21 &&
      state[clusterIn.radBef].status() < 0)
    dipolesNew.push_back(make_pair(clusterIn.emitted,findISRRecoiler()));

  return dipolesNew;
}

//--------------------------------------------------------------------------

// Setup the hard process information needed for calculating weak probabilities
// and setting up the shower.
void History::setupWeakHard(vector<int>& mode, vector<int>& fermionLines,
    vector<Vec4>& mom) {

  if (!isQCD2to2(state)) {
    // Not a 2 -> 2 process, mark everything as s-channel.
    mode.resize(state.size(), 1);
  } else {

    // Store momenta.
    for (int i = 0;i < 4; ++i) {
      mom.push_back(state[3 + i].p());
      fermionLines.push_back(3 + i);
    }
    // All gluon case, everything is s-channel.
    if ( state[3].idAbs() == 21 && state[4].idAbs() == 21 &&
         state[5].idAbs() == 21 && state[6].idAbs() == 21)
      mode.resize(state.size(), 1);

    // s-channel if quark-anti quark final state or gluon final state.
    else if (state[5].id() == -state[6].id() ||
             (state[5].idAbs() == 21 && state[6].idAbs() == 21))
      mode.resize(state.size(), 1);

    // t-channel gluon.
    else if (state[5].idAbs() == 21 || state[6].idAbs() == 21) {
      mode.resize(state.size(), 2);
      if (state[3].id() != state[5].id()) {
        swap(mom[0], mom[1]);
        swap(mom[2], mom[3]);
      }
    }

    // Double (different) quark t-channel.
    else if (state[5].id() != state[6].id()) {
      mode.resize(state.size(), 3);
      if (state[3].id() != state[5].id()) {
        swap(mom[0], mom[1]);
        swap(mom[2], mom[3]);
      }
    }

    // 4 quarks of the same type.
    // (might need to try both combinations).
    else if (state[5].id() == state[6].id()) {
      mode.resize(state.size(), 4);
    }
  }
}

//--------------------------------------------------------------------------

// Function to retrieve scale information from external showers.

double History::getShowerPluginScale(const Event& event, int rad, int emt,
  int rec, string key, double scalePythia) {

  // Done if no shower plugin is used.
  if ( !mergingHooksPtr->useShowerPlugin() ) return scalePythia;

  // Retrieve state variables.
  map<string,double> stateVars;
  bool isFSR = showers->timesPtr->isTimelike(event, rad, emt, rec, "");
  if (isFSR) {
    string name = showers->timesPtr->getSplittingName(event, rad, emt,
      rec).front();
    stateVars   = showers->timesPtr->getStateVariables(event, rad, emt, rec,
      name);
  } else {
    string name = showers->spacePtr->getSplittingName(event, rad, emt,
      rec).front();
    stateVars   = showers->spacePtr->getStateVariables(event, rad, emt, rec,
      name);
  }

  return ( (stateVars.size() > 0 && stateVars.find(key) != stateVars.end())
           ? stateVars[key] : -1.0 );

}

//==========================================================================

} // end namespace Pythia8