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VinciaEW.cc
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// VinciaEW.cc is a part of the PYTHIA event generator.
// Copyright (C) 2024 Peter Skands, 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.
// Function definitions (not found in the header) for Vincia's EW
// shower class and related auxiliary methods. Main author is Rob
// Verheyen.
#include "Pythia8/VinciaEW.h"
namespace Pythia8 {
using namespace VinciaConstants;
//==========================================================================
// Class calculating amplitudes.
//--------------------------------------------------------------------------
// Initialize with maps.
void AmpCalculator::init(EWParticleData* dataIn,
unordered_map< pair<int, int>, vector<pair<int, int> > >* cluMapFinalIn,
unordered_map< pair<int, int>, vector<pair<int, int> > >* cluMapInitialIn) {
if (!isInitPtr) return;
// Store maps.
dataPtr = dataIn;
cluMapFinal = cluMapFinalIn;
cluMapInitial = cluMapInitialIn;
if (dataPtr == nullptr) return;
isInit = true;
// Set some global EW constants.
mw = dataPtr->mass(24);
mw2 = pow2(mw);
double mz(dataPtr->mass(23)), mh(dataPtr->mass(25)), cw(mw/mz);
sw2 = 1. - pow2(cw);
sw = sqrt(sw2);
verbose = settingsPtr->mode("Vincia:verbose");
// Store the Breit-Wigner matching mode.
bwMatchMode = settingsPtr->mode("Vincia:bwMatchingMode");
// Set EW event weight to one.
eventWeightSave = 1;
// Get coupling constants - indices are i and j.
// Photon.
vMap[make_pair(1,22)] = -1./3.; vMap[make_pair(11,22)] = -1.;
aMap[make_pair(1,22)] = 0; aMap[make_pair(11,22)] = 0;
vMap[make_pair(2,22)] = 2./3.; vMap[make_pair(12,22)] = 0;
aMap[make_pair(2,22)] = 0; aMap[make_pair(12,22)] = 0;
vMap[make_pair(3,22)] = -1./3.; vMap[make_pair(13,22)] = -1.;
aMap[make_pair(3,22)] = 0; aMap[make_pair(13,22)] = 0;
vMap[make_pair(4,22)] = 2./3.; vMap[make_pair(14,22)] = 0;
aMap[make_pair(4,22)] = 0; aMap[make_pair(14,22)] = 0;
vMap[make_pair(5,22)] = -1./3.; vMap[make_pair(15,22)] = -1.;
aMap[make_pair(5,22)] = 0; aMap[make_pair(15,22)] = 0;
vMap[make_pair(6,22)] = 2./3.; vMap[make_pair(16,22)] = 0;
aMap[make_pair(6,22)] = 0; aMap[make_pair(16,22)] = 0;
// Z.
vMap[make_pair(1,23)] = -(1. - (4./3.)*sw2)/4./sw/cw;
aMap[make_pair(1,23)] = -1./4./sw/cw;
vMap[make_pair(2,23)] = (1. - (8./3.)*sw2)/4./sw/cw;
aMap[make_pair(2,23)] = 1./4./sw/cw;
vMap[make_pair(3,23)] = -(1. - (4./3.)*sw2)/4./sw/cw;
aMap[make_pair(3,23)] = -1./4./sw/cw;
vMap[make_pair(4,23)] = (1. - (8./3.)*sw2)/4./sw/cw;
aMap[make_pair(4,23)] = 1./4./sw/cw;
vMap[make_pair(5,23)] = -(1. - (4./3.)*sw2)/4./sw/cw;
aMap[make_pair(5,23)] = -1./4./sw/cw;
vMap[make_pair(6,23)] = (1. - (8./3.)*sw2)/4./sw/cw;
aMap[make_pair(6,23)] = 1./4./sw/cw;
vMap[make_pair(11,23)] = -(1. - 4.*sw2)/4./sw/cw;
aMap[make_pair(11,23)] = -1./4./sw/cw;
vMap[make_pair(12,23)] = 1./4./sw/cw;
aMap[make_pair(12,23)] = 1./4./sw/cw;
vMap[make_pair(13,23)] = -(1. - 4.*sw2)/4./sw/cw;
aMap[make_pair(13,23)] = -1./4./sw/cw;
vMap[make_pair(14,23)] = 1./4./sw/cw;
aMap[make_pair(14,23)] = 1./4./sw/cw;
vMap[make_pair(15,23)] = -(1. - 4.*sw2)/4./sw/cw;
aMap[make_pair(15,23)] = -1./4./sw/cw;
vMap[make_pair(16,23)] = 1./4./sw/cw;
aMap[make_pair(16,23)] = 1./4./sw/cw;
// W.
double cW(-1/sqrt(8)/sw);
vMap[make_pair(1,24)] = cW; vMap[make_pair(11,24)] = cW;
aMap[make_pair(1,24)] = cW; aMap[make_pair(11,24)] = cW;
vMap[make_pair(2,24)] = cW; vMap[make_pair(12,24)] = cW;
aMap[make_pair(2,24)] = cW; aMap[make_pair(12,24)] = cW;
vMap[make_pair(3,24)] = cW; vMap[make_pair(13,24)] = cW;
aMap[make_pair(3,24)] = cW; aMap[make_pair(13,24)] = cW;
vMap[make_pair(4,24)] = cW; vMap[make_pair(14,24)] = cW;
aMap[make_pair(4,24)] = cW; aMap[make_pair(14,24)] = cW;
vMap[make_pair(5,24)] = cW; vMap[make_pair(15,24)] = cW;
aMap[make_pair(5,24)] = cW; aMap[make_pair(15,24)] = cW;
vMap[make_pair(6,24)] = cW; vMap[make_pair(16,24)] = cW;
aMap[make_pair(6,24)] = cW; aMap[make_pair(16,24)] = cW;
// Higgs (note that a mass factor is not included here).
gMap[make_pair(1,25)] = 1/mw/2./sw; gMap[make_pair(6,25)] = 1/mw/2./sw;
gMap[make_pair(2,25)] = 1/mw/2./sw; gMap[make_pair(11,25)] = 1/mw/2./sw;
gMap[make_pair(3,25)] = 1/mw/2./sw; gMap[make_pair(13,25)] = 1/mw/2./sw;
gMap[make_pair(4,25)] = 1/mw/2./sw; gMap[make_pair(15,25)] = 1/mw/2./sw;
gMap[make_pair(5,25)] = 1/mw/2./sw;
// Bosonic couplings.
gMap[make_pair(24, 22)] = 1; gMap[make_pair(23, -24)] = cw/sw;
gMap[make_pair(24, 23)] = cw/sw; gMap[make_pair(23, 25)] = mz/cw/sw;
gMap[make_pair(-24, 22)] = -1; gMap[make_pair(24, 25)] = mw/sw;
gMap[make_pair(-24, 23)] = -cw/sw; gMap[make_pair(-24, 25)] = mw/sw;
gMap[make_pair(22, -24)] = 1;
gMap[make_pair(25, 25)] = 3.*pow2(mh)/2./mw/sw;
// CKM matrix.
vCKM[make_pair(1,2)] = settingsPtr->parm("StandardModel:Vud");
vCKM[make_pair(2,1)] = settingsPtr->parm("StandardModel:Vud");
vCKM[make_pair(1,4)] = settingsPtr->parm("StandardModel:Vcd");
vCKM[make_pair(4,1)] = settingsPtr->parm("StandardModel:Vcd");
vCKM[make_pair(1,6)] = settingsPtr->parm("StandardModel:Vtd");
vCKM[make_pair(6,1)] = settingsPtr->parm("StandardModel:Vtd");
vCKM[make_pair(3,2)] = settingsPtr->parm("StandardModel:Vus");
vCKM[make_pair(2,3)] = settingsPtr->parm("StandardModel:Vus");
vCKM[make_pair(3,4)] = settingsPtr->parm("StandardModel:Vcs");
vCKM[make_pair(4,3)] = settingsPtr->parm("StandardModel:Vcs");
vCKM[make_pair(3,6)] = settingsPtr->parm("StandardModel:Vts");
vCKM[make_pair(6,3)] = settingsPtr->parm("StandardModel:Vts");
vCKM[make_pair(5,2)] = settingsPtr->parm("StandardModel:Vub");
vCKM[make_pair(2,5)] = settingsPtr->parm("StandardModel:Vub");
vCKM[make_pair(5,4)] = settingsPtr->parm("StandardModel:Vcb");
vCKM[make_pair(4,5)] = settingsPtr->parm("StandardModel:Vcb");
vCKM[make_pair(5,6)] = settingsPtr->parm("StandardModel:Vtb");
vCKM[make_pair(6,5)] = settingsPtr->parm("StandardModel:Vtb");
// Overestimate constants for Breit-Wigner sampling.
cBW[6] = {1.2618863, 1.0986116, 0.0352201, 1.1040597};
cBW[23] = {1.1699582, 1.0668744, 0.0338234, 1.1567254};
cBW[24] = {1.2091010, 1.0854375, 0.0317986, 1.1629825};
cBW[25] = {1.1864117, 1.0818452, 0.0069201, 1.1963023};
// Compute total width for all resonances and set Breit-Wigner
// overestimate normalizations.
for(auto itRes = dataPtr->begin() ; itRes != dataPtr->end(); ++itRes) {
if (!itRes->second.isRes) continue;
int id(abs(itRes->first.first)), pol(itRes->first.second);
double mass(itRes->second.mass);
// Compute width for the on-shell mass.
double width = getTotalWidth(id, mass, pol);
// Update information.
itRes->second.width = width;
}
// Spin assignment vectors.
fermionPols.push_back(-1);
fermionPols.push_back(1);
vectorPols.push_back(1);
vectorPols.push_back(0);
vectorPols.push_back(-1);
scalarPols.push_back(0);
}
//--------------------------------------------------------------------------
// Spinor products used for the calculation of the amplitudes.
complex AmpCalculator::spinProd(int pol, const Vec4& k1, const Vec4& k2) {
// Check if k1 or k2 accidentally align with the direction of basis vectors.
if ( ( (k2.e() - k2.px()==0.) || (k1.e() - k1.px()==0.) ) ) {
loggerPtr->WARNING_MSG("momentum aligned exactly with basis direction");
return complex(0.,0.);
}
// Explicit expression for a spinor product.
complex sNow(0., 0.);
if (pol == 1) {
sNow = complex(k1.py(), k1.pz())
* sqrt( complex((k2.e() - k2.px())/(k1.e() - k1.px()), 0) )
- complex(k2.py(), k2.pz())
* sqrt( complex((k1.e() - k1.px())/(k2.e() - k2.px()), 0) );
} else if (pol == -1) {
sNow = complex(k2.py(), -k2.pz())
* sqrt( complex((k1.e() - k1.px())/(k2.e() - k2.px()), 0) )
- complex(k1.py(), -k1.pz())
* sqrt( complex((k2.e() - k2.px())/(k1.e() - k1.px()), 0) );
}
// Check result is valid.
if (isnan(double(sNow.real())) || isnan(double(sNow.imag()))) {
loggerPtr->WARNING_MSG("nan encountered");
return complex(0.,0.);
} else if (isinf(double(sNow.real())) || isinf(double(sNow.imag()))) {
loggerPtr->WARNING_MSG("inf encountered");
return complex(0.,0.);
}
return sNow;
}
complex AmpCalculator::spinProd(int pol, const Vec4& k1, const Vec4& p1,
const Vec4& k2) {
Vec4 p1Flat = spinProdFlat(__METHOD_NAME__, k1, p1);
return spinProd(pol, k1, p1Flat)*spinProd(-pol, p1Flat, k2);
}
complex AmpCalculator::spinProd(int pol, const Vec4 &k1, const Vec4& p1,
const Vec4& p2, const Vec4& k2) {
Vec4 p1Flat = spinProdFlat(__METHOD_NAME__, k1, p1);
return spinProd(pol, k1, p1Flat)*spinProd(-pol, p1Flat, p2, k2);
}
complex AmpCalculator::spinProd(int pol, const Vec4& k1, const Vec4& p1,
const Vec4& p2, const Vec4& p3, const Vec4& k2) {
Vec4 p1Flat = spinProdFlat(__METHOD_NAME__, k1, p1);
return spinProd(pol, k1, p1Flat)*spinProd(-pol, p1Flat, p2, p3, k2);
}
complex AmpCalculator::spinProd(int pol, const Vec4& k1, const Vec4& p1,
const Vec4& p2, const Vec4& p3, const Vec4& p4, const Vec4& k2) {
Vec4 p1Flat = spinProdFlat(__METHOD_NAME__, k1, p1);
return spinProd(pol, k1, p1Flat)*spinProd(-pol, p1Flat, p2, p3, p4, k2);
}
Vec4 AmpCalculator::spinProdFlat(
string method, const Vec4& k1, const Vec4& p1) {
if (p1*k1 == 0) {
if (p1.mCalc()/p1.e() > MILLI) {
stringstream ss;
ss << "zero denominator in flattening slashed momentum "
<< "num = " << 0.5*p1.m2Calc() << " denom = " << p1*k1;
loggerPtr->errorMsg(method, ss.str());
}
return p1;
} else return p1 - 0.5*p1.m2Calc()/(p1*k1)*k1;
}
//--------------------------------------------------------------------------
// Initialize couplings.
void AmpCalculator::initCoup(bool va, int id1, int id2, int pol, bool m) {
if (va) {
v = vMap[make_pair(abs(id1), abs(id2))];
a = aMap[make_pair(abs(id1), abs(id2))];
vPls = v + pol*a;
vMin = v - pol*a;
} else if (id1 != 0) g = m ? gMap[make_pair(abs(id1), id2)] : 0;
}
//--------------------------------------------------------------------------
// Initialize an FSR branching amplitude.
void AmpCalculator::initFSRAmp(bool va, int id1, int id2, int pol,
const Vec4& pi, const Vec4 &pj, const double& mMot, const double& widthQ2) {
// Masses.
mMot2 = pow2(mMot);
mi = max(0., pi.mCalc()); mi2 = pow2(mi);
mj = max(0., pj.mCalc()); mj2 = pow2(mj);
fsrQ2 = complex((pi + pj).m2Calc() - mMot2, mMot*widthQ2);
// Reference vectors.
kij = pi + pj; kij.e(1); kij.flip3(); kij.rescale3(1./kij.pAbs());
ki = pi; ki.e(1); ki.flip3(); ki.rescale3(1./ki.pAbs());
kj = pj; kj.e(1); kj.flip3(); kj.rescale3(1./kj.pAbs());
pij = pi + pj;
wij = sqrt(2*(pij.e() + pij.pAbs())); wij2 = pow2(wij);
wi = sqrt(2*(pi.e() + pi.pAbs())); wi2 = pow2(wi);
wj = sqrt(2*(pj.e() + pj.pAbs())); wj2 = pow2(wj);
M = 0;
// Couplings.
initCoup(va, id1, id2, pol, true);
}
//--------------------------------------------------------------------------
// Check for zero denominator in an FSR amplitude.
bool AmpCalculator::zdenFSRAmp(const string& method, const Vec4& pi,
const Vec4& pj, bool check) {
if (check || (fsrQ2.real() == 0 && fsrQ2.imag() == 0)) {
if (verbose >= Logger::NORMAL) {
stringstream ss;
ss << "zero denominator encountered."
<< "\n wij =" << wij << " wi = " << wi << " wj2 = " << wj2
<< "\n mj = " << mj << " Q2 = " << fsrQ2
<< "\n pi = " << pi << " pj = " << pj;
loggerPtr->warningMsg(method, ss.str());
} return true;
} else return false;
}
//--------------------------------------------------------------------------
// Initialize an ISR branching amplitude.
void AmpCalculator::initISRAmp(bool va, int id1, int id2, int pol,
const Vec4& pa, const Vec4 &pj, double& mA) {
// Masses (disable mass corrections in ISR).
mA = 0; mA2 = 0;
ma = 0; ma2 = 0;
mj = max(0., pj.mCalc()); mj2 = pow2(mj);
isrQ2 = -(pa - pj).m2Calc() + mA2;
// Reference vectors.
kaj = pa - pj; kaj.e(1); kaj.flip3(); kaj.rescale3(1./kaj.pAbs());
ka = pa; ka.e(1); ka.flip3(); ka.rescale3(1./ka.pAbs());
kj = pj; kj.e(1); kj.flip3(); kj.rescale3(1./kj.pAbs());
paj = pa - pj;
waj = sqrt(2*(paj.e() + paj.pAbs())); waj2 = pow2(waj);
wa = sqrt(2*(pa.e() + pa.pAbs())); wa2 = pow2(wa);
wj = sqrt(2*(pj.e() + pj.pAbs())); wj2 = pow2(wj);
M = 0;
// Couplings.
initCoup(va, id1, id2, pol, false);
}
//--------------------------------------------------------------------------
// Check for zero denominator in an ISR amplitude.
bool AmpCalculator::zdenISRAmp(const string& method, const Vec4& pa,
const Vec4& pj, bool check) {
if (check || isrQ2 == 0) {
if (verbose >= Logger::NORMAL) {
stringstream ss;
ss << "zero denominator encountered."
<< "\n waj =" << waj << " wa = " << wa << " wj2 = " << wj2
<< "\n mj = " << mj << " Q2 = " << isrQ2
<< "\n pa = " << pa << " pj = " << pj;
loggerPtr->warningMsg(method, ss.str());
} return true;
} else return false;
}
//--------------------------------------------------------------------------
// Branching Amplitudes.
// These functions still have the option to compute branching kernels with a
// width.
// FSR: f->fV.
complex AmpCalculator::ftofvFSRAmp(const Vec4& pi, const Vec4& pj, int idMot,
int idi, int idj, double mMot, double widthQ2, int polMot, int poli,
int polj) {
// Initialize.
initFSRAmp(true, idMot, idj, polMot, pi, pj, mMot, widthQ2);
if (zdenFSRAmp(__METHOD_NAME__, pi, pj, wij == 0 || wi == 0 || wj2 == 0 ||
(mj == 0. && polj == 0) )) return M;
// Calculate amplitude.
// Transverse polarizations, all defined with hel -pol.
if (abs(polj) == 1) {
complex kikj = spinProd(-polMot, ki, kj);
complex kipikj = spinProd(-polMot, ki, pi, kj);
complex kipjkj = spinProd(-polMot, ki, pj, kj);
complex kipipjkj = spinProd(-polMot, ki, pi, pj, kj);
complex kjkij = spinProd(-polMot, kj, kij);
complex kjpijkij = spinProd(-polMot, kj, pij, kij);
complex kjpjkij = spinProd(-polMot, kj, pj, kij);
complex kjpjpijkij = spinProd(-polMot, kj, pj, pij, kij);
double trvFac = sqrt(2)*polMot/wi/wij/wj2;
if ((poli == polMot) && (polj == polMot))
M = -trvFac*(vMin*kipipjkj*kjpijkij
- vPls*mi*mMot*kikj*kjpjkij)/fsrQ2;
else if ((poli == polMot) && (polj == -polMot))
M = -trvFac*(vMin*kipikj*conj(-kjpjpijkij)
- vPls*mi*mMot*kipjkj*conj(-kjkij))/fsrQ2;
else if ((poli == -polMot) && (polj == polMot))
M = trvFac*(mMot*vPls*conj(kipikj)*kjpjkij
- mi*vMin*conj(kipjkj)*kjpijkij)/fsrQ2;
else if ((poli == -polMot) && (polj == -polMot))
M = trvFac*(mMot*vPls*conj(-kipipjkj)*conj(-kjkij)
- mi*vMin*conj(-kikj)*conj(-kjpjpijkij))/fsrQ2;
// Longitudinal polarizations.
} else if (polj == 0) {
double lonFac = 1./mj/wi/wij;
if (poli == polMot)
M = lonFac*(mMot2*vMin*spinProd(-polMot, ki, pi, kij)
- mi2*vMin*spinProd(-polMot, ki, pij, kij)
+ mi*mMot*vPls*spinProd(-polMot, ki, pj, kij)
- 2*mj2/wj2*vMin*spinProd(-polMot, ki, pi, kj, pij, kij)
- 2*mj2/wj2*vPls*mMot*mi*spinProd(-polMot, ki, kj, kij)
)/fsrQ2;
else if (poli == -polMot)
M = lonFac*(mi*vMin*( spinProd(-polMot, ki, pj, pij, kij)
- 2*mj2/wj2*spinProd(-polMot, ki, kj, pij, kij))
+ mMot*vPls*( spinProd(-polMot, ki, pi, pj, kij)
- 2*mj2/wj2*spinProd(-polMot, ki, pi, kj, kij)) )/fsrQ2;
}
// Multiply by CKM matrix - only for q+W.
if (abs(idj) == 24 && abs(idi) < 7)
M *= vCKM[make_pair(abs(idMot), abs(idi))];
return M;
}
//--------------------------------------------------------------------------
// FSR: f->fH.
complex AmpCalculator::ftofhFSRAmp(const Vec4& pi, const Vec4& pj, int idMot,
int, int idj, double, double widthQ2, int polMot, int poli, int) {
// Initialize.
initFSRAmp(false, idMot, idj, polMot, pi, pj, max(0., pi.mCalc()), widthQ2);
if (zdenFSRAmp(__METHOD_NAME__, pi, pj, wij == 0 || wi == 0)) return M;
// Calculate amplitude.
double fac = mi*g/wi/wij;
if (poli == polMot) M = fac*mi*spinProd(-polMot, ki, pi + pij, kij)/fsrQ2;
else if (poli == -polMot) M = fac*(spinProd(-polMot, ki, pi, pij, kij)
+ mi2*spinProd(-polMot, ki, kij))/fsrQ2;
return M;
}
//--------------------------------------------------------------------------
// FSR: fbar->fbarV.
complex AmpCalculator::fbartofbarvFSRAmp(const Vec4& pi, const Vec4& pj,
int idMot, int idi, int idj, double mMot, double widthQ2, int polMot,
int poli, int polj) {
// Initialize.
initFSRAmp(true, idMot, idj, polMot, pi, pj, mMot, widthQ2);
if (zdenFSRAmp(__METHOD_NAME__, pi, pj, wij == 0 || wi == 0 || wj2 == 0 ||
(mj == 0. && polj == 0))) return M;
// Calculate amplitude.
// Transverse polarizations, all defined with hel pol.
if (abs(polj) == 1) {
complex kijkj = spinProd(polMot, kij, kj);
complex kijpijkj = spinProd(polMot, kij, pij, kj);
complex kijpjkj = spinProd(polMot, kij, pj, kj);
complex kijpijpjkj = spinProd(polMot, kij, pij, pj, kj);
complex kjki = spinProd(polMot, kj, ki);
complex kjpiki = spinProd(polMot, kj, pi, ki);
complex kjpjki = spinProd(polMot, kj, pj, ki);
complex kjpjpiki = spinProd(polMot, kj, pj, pi, ki);
double trvFac = sqrt(2)*polMot/wi/wij/wj2;
if ((poli == polMot) && (polj == polMot))
M = -trvFac*(vPls*kijpijkj*conj(-kjpjpiki)
- vMin*mi*mMot*kijpjkj*conj(-kjki))/fsrQ2;
else if ((poli == polMot) && (polj == -polMot))
M = -trvFac*(vPls*kijpijpjkj*kjpiki
- vMin*mi*mMot*kijkj*kjpjki)/fsrQ2;
else if ((poli == -polMot) && (polj == polMot))
M = -trvFac*(mMot*vMin*kijpjkj*conj(kjpiki)
- mi*vPls*kijpijkj*conj(kjpjki))/fsrQ2;
else if ((poli == -polMot) && (polj == -polMot))
M = -trvFac*(mMot*vMin*kijkj*kjpjpiki
- mi*vPls*kijpijpjkj*kjki)/fsrQ2;
// Longitudinal polarizations.
} else if (polj == 0) {
double lonFac = 1./mj/wi/wij;
if (poli == polMot)
M = -lonFac*(mMot2*vPls*spinProd(polMot, kij, pi, ki)
- mi2*vPls*spinProd(polMot, kij, pij, ki)
+ mi*mMot*vMin*spinProd(polMot, kij, pj, ki)
- 2*mj2/wj2*vPls*spinProd(polMot, kij, pij, kj, pi, ki)
- 2*mj2/wj2*vMin*mMot*mi*spinProd(polMot, kij, kj, ki)
)/fsrQ2;
else if (poli == -polMot)
M = -lonFac*(mi*vPls*( spinProd(polMot, kij, pij, pj, ki)
- 2*mj2/wj2*spinProd(polMot, kij, pij, kj, ki))
+ mMot*vMin*( spinProd(polMot, kij, pj, pi, ki)
- 2*mj2/wj2*spinProd(polMot, kij, kj, pi, ki)) )/fsrQ2;
}
// Multiply by CKM matrix - only for q+W.
if (abs(idj) == 24 && abs(idi) < 7)
M *= vCKM[make_pair(abs(idMot), abs(idi))];
return M;
}
//--------------------------------------------------------------------------
// FSR: fbar->fbarH.
complex AmpCalculator::fbartofbarhFSRAmp(const Vec4& pi, const Vec4& pj,
int idMot, int, int idj, double, double widthQ2, int polMot, int poli, int) {
// Initialize.
initFSRAmp(false, idMot, idj, polMot, pi, pj, max(0., pi.mCalc()), widthQ2);
if (zdenFSRAmp(__METHOD_NAME__, pi, pj, wij == 0 || wi == 0)) return M;
// Calculate amplitude.
double fac = mi*g/wi/wij;
if (poli == polMot) M = fac*mi*spinProd(polMot, kij, pij + pi, ki)/fsrQ2;
else if (poli == -polMot) M = fac*(spinProd(polMot, kij, pij, pi, ki)
+ mi2*spinProd(polMot, kij, ki))/fsrQ2;
return M;
}
//--------------------------------------------------------------------------
// FSR: VT->ffbar.
complex AmpCalculator::vTtoffbarFSRAmp(const Vec4& pi, const Vec4& pj,
int idMot, int idi, int idj, double mMot, double widthQ2, int polMot,
int poli, int polj) {
// Initialize.
initFSRAmp(true, idi, idMot, polMot, pi, pj, mMot, widthQ2);
if (zdenFSRAmp(__METHOD_NAME__, pi, pj, wij2 == 0 || wi == 0 || wj == 0))
return M;
// Calculate amplitude.
// All defined with hel -pol.
complex kikij = spinProd(-polMot, ki, kij);
complex kipikij = spinProd(-polMot, ki, pi, kij);
complex kipijkij = spinProd(-polMot, ki, pij, kij);
complex kipipijkij = spinProd(-polMot, ki, pi, pij, kij);
complex kijkj = spinProd(-polMot, kij, kj);
complex kijpjkj = spinProd(-polMot, kij, pj, kj);
complex kijpijkj = spinProd(-polMot, kij, pij, kj);
complex kijpijpjkj = spinProd(-polMot, kij, pij, pj, kj);
double trvFac = sqrt(2)*polMot/wi/wj/wij2;
if (poli == polMot && polj == -polMot)
M = trvFac*(vMin*kipikij*kijpijpjkj
+ vPls*mi*mj*kipijkij*kijkj)/fsrQ2;
else if (poli == -polMot && polj == polMot)
M = trvFac*(vPls*kipipijkij*kijpjkj
+ vMin*mi*mj*kikij*kijpijkj)/fsrQ2;
else if (poli == polMot && polj == polMot)
M = trvFac*(vPls*mi*kipijkij*kijpjkj
+ vMin*mj*kipikij*kijpijkj)/fsrQ2;
else if (poli == -polMot && polj == -polMot)
M = trvFac*(vMin*mi*kikij*kijpijpjkj
+ vPls*mj*kipipijkij*kijkj)/fsrQ2;
// Multiply by CKM matrix - only for W->qqbar.
if (abs(idMot) == 24 && abs(idi) < 7)
M *= vCKM[make_pair(abs(idi), abs(idj))];
return M;
}
//--------------------------------------------------------------------------
// FSR: VT->VH.
complex AmpCalculator::vTtovhFSRAmp(const Vec4& pi, const Vec4& pj, int idMot,
int, int idj, double mMot, double widthQ2, int polMot, int poli, int) {
// Initialize.
initFSRAmp(false, idMot, idj, polMot, pi, pj, mMot, widthQ2);
if (zdenFSRAmp(__METHOD_NAME__, pi, pj, wij2 == 0 || wi2 == 0 ||
( mMot == 0. && poli == 0 ))) return M;
// Calculate amplitude.
double trtrFac = g/wij2/wi2;
if (poli == polMot)
M = -trtrFac*spinProd(-polMot, kij, pij, ki)
*spinProd(-polMot, kij, pi, ki)/fsrQ2;
else if (poli == -polMot)
M = -trtrFac*spinProd(-polMot, ki, kij)
*spinProd(-polMot, kij, pij, pi, ki)/fsrQ2;
else if (poli == 0)
M = -g*polMot/sqrt(2)/wij2/mMot*(spinProd(-polMot, kij, pij, pi, kij)
- 2*mMot2/wi2*spinProd(-polMot, kij, pij, ki, kij) )/fsrQ2;
return M;
}
//--------------------------------------------------------------------------
// FSR: VT->VV.
complex AmpCalculator::vTtovvFSRAmp(const Vec4& pi, const Vec4& pj, int idMot,
int, int idj, double mMot, double widthQ2, int polMot, int poli,
int polj) {
// Initialize.
initFSRAmp(false, idMot, idj, polMot, pi, pj, mMot, widthQ2);
if (zdenFSRAmp(__METHOD_NAME__, pi, pj, wij2 == 0 || wi2 == 0 || wj2 == 0 ||
( mi == 0. && poli == 0 ) || ( mj == 0. && polj == 0 ) )) return M;
// u = pol, d = -pol, z = 0, p = mom.
complex uiuj = -1/wi2/wj2*spinProd(-polMot, ki, pi, pj, kj)
*spinProd(-polMot, kj, ki);
complex uidj = -1/wi2/wj2*spinProd(-polMot, ki, pi, kj)
*spinProd(-polMot, ki, pj, kj);
complex diuj = conj(uidj);
complex didj = conj(uiuj);
complex uidij = -1/wi2/wij2*spinProd(-polMot, ki, pi, kij)
*spinProd(-polMot, ki, pij, kij);
complex didij = -1/wi2/wij2*spinProd(polMot, ki, pi, pij, kij)
*spinProd(polMot, kij, ki);
complex ujdij = -1/wj2/wij2*spinProd(-polMot, kj, pj, kij)
*spinProd(-polMot, kj, pij, kij);
complex djdij = -1/wj2/wij2*spinProd(polMot, kj, pj, pij, kij)
*spinProd(polMot, kij, kj);
complex piuj = polMot/sqrt(2)/wj2*spinProd(-polMot, kj, pj, pi, kj);
complex pidj = conj(piuj);
complex pjui = polMot/sqrt(2)/wi2*spinProd(-polMot, ki, pi, pj, ki);
complex pjdi = conj(pjui);
complex pidij = -polMot/sqrt(2)/wij2*spinProd(polMot, kij, pij, pi, kij);
// Calculate amplitude.
if (abs(poli) == 1 && abs(polj) == 1) {
if ((poli == polMot) && (polj == polMot))
M = 2*g*(pjui*ujdij - piuj*uidij + pidij*uiuj)/fsrQ2;
else if ((poli == polMot) && (polj == -polMot))
M = 2*g*(pjui*djdij - pidj*uidij + pidij*uidj)/fsrQ2;
else if ((poli == -polMot) && (polj == polMot))
M = 2*g*(pjdi*ujdij - piuj*didij + pidij*diuj)/fsrQ2;
else if ((poli == -polMot) && (polj == -polMot))
M = 2*g*(pjdi*djdij - pidj*didij + pidij*didj)/fsrQ2;
} else if (abs(poli) == 1 && polj == 0) {
complex uizj = polMot/sqrt(2)/wi2/mj*
(spinProd(-polMot, ki, pi, pj, ki)
- 2*mj2/wj2*spinProd(-polMot, ki, pi, kj, ki) );
complex dizj = conj(uizj);
complex pizj = (0.5*(mMot2 - mi2 - mj2) - 2*mj2/wj2*(pi*kj))/mj;
complex zjdij = -polMot/sqrt(2)/wij2/mj*(
spinProd(polMot, kij, pij, pj, kij)
- 2*mj2/wj2*spinProd(polMot, kij, pij, kj, kij) );
if (poli == polMot)
M = 2*g*(pjui*zjdij - pizj*uidij + pidij*uizj)/fsrQ2;
else if (poli == -polMot)
M = 2*g*(pjdi*zjdij - pizj*didij + pidij*dizj)/fsrQ2;
} else if (poli == 0 && abs(polj) == 1) {
complex ziuj = polMot/sqrt(2)/wj2/mi*
(spinProd(-polMot, kj, pj, pi, kj)
- 2*mi2/wi2*spinProd(-polMot, kj, pj, ki, kj) );
complex zidj = conj(ziuj);
complex zidij = -polMot/sqrt(2)/wij2/mi*
(spinProd(polMot, kij, pij, pi, kij)
- 2*mi2/wi2*spinProd(polMot, kij, pij, ki, kij) );
complex pjzi = (0.5*(mMot2 - mi2 - mj2) - 2*mi2/wi2*(pj*ki))/mi;
if (polj == polMot)
M = 2*g*(pjzi*ujdij - piuj*zidij + pidij*ziuj)/fsrQ2;
else if (polj == -polMot)
M = 2*g*(pjzi*djdij - pidj*zidij + pidij*zidj)/fsrQ2;
} else if (poli == 0 && polj == 0) {
complex pizj = (0.5*(mMot2 - mi2 - mj2) - 2*mj2/wj2*(pi*kj))/mj;
complex pjzi = (0.5*(mMot2 - mi2 - mj2) - 2*mi2/wi2*(pj*ki))/mi;
complex zizj = (0.5*(mMot2 - mi2 - mj2) - 2*mi2/wi2*(ki*pj)
- 2*mj2/wj2*(kj*pi) - 4*mi2*mj2/wi2/wj2*(ki*kj))/mi/mj;
complex zidij = -polMot/sqrt(2)/wij2/mi*
(spinProd(polMot, kij, pij, pi, kij)
- 2*mi2/wi2*spinProd(polMot, kij, pij, ki, kij) );
complex zjdij = -polMot/sqrt(2)/wij2/mj*(
spinProd(polMot, kij, pij, pj, kij)
- 2*mj2/wj2*spinProd(polMot, kij, pij, kj, kij) );
M = 2*g*(pjzi*zjdij - pizj*zidij + pidij*zizj)/fsrQ2;
}
return M;
}
//--------------------------------------------------------------------------
// FSR: VL->ffbar.
complex AmpCalculator::vLtoffbarFSRAmp(const Vec4& pi, const Vec4& pj,
int idMot, int idi, int idj, double mMot, double widthQ2, int,
int poli, int polj) {
// Initialize.
initFSRAmp(true, idi, idMot, 1, pi, pj, mMot, widthQ2);
if (zdenFSRAmp(__METHOD_NAME__, pi, pj, wij2 == 0 || wi == 0 || wj == 0 ||
mMot == 0)) return M;
// Calculate amplitude.
double lonFac = 1/wi/wj/mMot;
if (poli == 1 && polj == -1)
M = lonFac*(vMin*pow2(mi)*spinProd(-1, ki, pj, kj)
+ vMin*pow2(mj)*spinProd(-1, ki, pi, kj)
- vPls*mi*mj*spinProd(-1, ki, pij, kj)
+ 2*vPls*mi*mj*pow2(mMot)/wij2*spinProd(-1, ki, kij, kj)
- 2*vMin*pow2(mMot)/wij2*spinProd(-1, ki, pi, kij, pj, kj)
)/fsrQ2;
else if (poli == -1 && polj == 1)
M = lonFac*(vPls*pow2(mi)*spinProd(1, ki, pj, kj)
+ vPls*pow2(mj)*spinProd(1, ki, pi, kj)
- vMin*mi*mj*spinProd(1, ki, pij, kj)
+ 2*vMin*mi*mj*pow2(mMot)/wij2*spinProd(1, ki, kij, kj)
- 2*vPls*pow2(mMot)/wij2*spinProd(1, ki, pi, kij, pj, kj)
)/fsrQ2;
else if (poli == 1 && polj == 1)
M = lonFac*(mi*vPls*spinProd(-1, ki, pij, pj, kj)
- 2*mi*vPls*pow2(mMot)/wij2*spinProd(-1, ki, kij, pj, kj)
- mj*vMin*spinProd(-1, ki, pi, pij, kj)
+ 2*mj*vMin*pow2(mMot)/wij2*spinProd(-1, ki, pi, kij, kj)
)/fsrQ2;
else if (poli == -1 && polj == -1)
M = lonFac*(mi*vMin*spinProd(1, ki, pij, pj, kj)
- 2*mi*vMin*pow2(mMot)/wij2*spinProd(1, ki, kij, pj, kj)
- mj*vPls*spinProd(1, ki, pi, pij, kj)
+ 2*mj*vPls*pow2(mMot)/wij2*spinProd(1, ki, pi, kij, kj)
)/fsrQ2;
// Multiply by CKM matrix - only for W->qqbar.
if (abs(idMot) == 24 && abs(idi) < 7)
M *= vCKM[make_pair(abs(idi), abs(idj))];
return M;
}
//--------------------------------------------------------------------------
// FSR: VL->VH.
complex AmpCalculator::vLtovhFSRAmp(const Vec4& pi, const Vec4& pj, int idMot,
int, int idj, double mMot, double widthQ2, int polMot, int poli, int) {
// Initialize.
initFSRAmp(false, idMot, idj, polMot, pi, pj, mMot, widthQ2);
if (zdenFSRAmp(__METHOD_NAME__, pi, pj, wij2 == 0 || wi2 == 0 || wj2 == 0 ||
( mMot == 0. && poli == 0 ))) return M;
// Calculate amplitude.
if (poli == 1)
M = -g/sqrt(2)/wi2/mMot*(spinProd(-1, ki, pi, pij, ki)
- 2*mMot/wij2*spinProd(-1, ki, pi, kij, ki) )/fsrQ2;
else if (poli == -1)
M = g/sqrt(2)/wi2/mMot*(spinProd( 1, ki, pi, pij, ki)
- 2*mMot/wij2*spinProd( 1, ki, pi, kij, ki) )/fsrQ2;
else if (poli == 0)
M = -g/mMot2*(0.5*pow2(mj) + mMot2*(wi2/wij2 + wj2/wi2))/fsrQ2;
return M;
}
//--------------------------------------------------------------------------
// FSR: VL->VV.
complex AmpCalculator::vLtovvFSRAmp(const Vec4& pi, const Vec4& pj, int idMot,
int, int idj, double mMot, double widthQ2, int polMot, int poli,
int polj) {
// Initialize.
initFSRAmp(false, idMot, idj, polMot, pi, pj, mMot, widthQ2);
if (zdenFSRAmp(__METHOD_NAME__, pi, pj,
wij2 == 0 || wi2 == 0 || wj2 == 0 || mMot == 0 ||
( mi == 0. && poli == 0 ) || ( mj == 0. && polj == 0 ))) return M;
// u = pol, d = -pol, z = 0, p = mom.
complex uiuj = -1/wi2/wj2*spinProd(-1, ki, pi, pj, kj)*spinProd(-1, kj, ki);
complex uidj = -1/wi2/wj2*spinProd(-1, ki, pi, kj)*spinProd(-1, ki, pj, kj);
complex diuj = conj(uidj);
complex didj = conj(uiuj);
complex uizij = 1/sqrt(2)/wi2/mMot*( spinProd(-1, ki, pi, pij, ki)
- 2*mMot2/wij2*spinProd(-1, ki, pi, kij, ki) );
complex dizij = conj(uizij);
complex zizij = ( 0.5*(mMot2 + mi2 - mj2) - 2*mi2/wi2*(ki*pij)
- 2*mMot2/wij2*(kij*pi) - 4*mi2*mMot2/wi2/wij2*(ki*kij) )/mi/mMot;
complex ujzij = 1/sqrt(2)/wj2/mMot*( spinProd(-1, kj, pj, pij, kj)
- 2*mMot2/wij2*spinProd(-1, kj, pj, kij, kj) );
complex djzij = conj(ujzij);
complex piuj = 1/sqrt(2)/wj2*spinProd(-1, kj, pj, pi, kj);
complex pidj = conj(piuj);
complex pjui = 1/sqrt(2)/wi2*spinProd(-1, ki, pi, pj, ki);
complex pjdi = conj(pjui);
complex pizij = (0.5*(mMot2 + mi2 - mj2) - 2*mMot2/wij2*(kij*pi))/mMot;
// Calculate amplitude.
if (abs(poli) == 1 && abs(polj) == 1) {
if (poli == 1 && polj == 1)
M = 2*g*(pjui*ujzij - piuj*uizij + pizij*uiuj)/fsrQ2;
else if (poli == 1 && polj == -1)
M = 2*g*(pjui*djzij - pidj*uizij + pizij*uidj)/fsrQ2;
else if (poli == -1 && polj == 1)
M = 2*g*(pjdi*ujzij - piuj*dizij + pizij*diuj)/fsrQ2;
else if (poli == -1 && polj == -1)
M = 2*g*(pjdi*djzij - pidj*dizij + pizij*didj)/fsrQ2;
} else if (abs(poli) == 1 && polj == 0) {
complex uizj = 1/sqrt(2)/wi2/mj*
(spinProd(-1, ki, pi, pj, ki) - 2*mj2/wj2*spinProd(-1, ki, pi, kj, ki) );
complex dizj = conj(uizj);
complex zjzij = ( 0.5*(mMot2 - mi2 + mj2) - 2*mj2/wj2*(kj*pij)
- 2*mMot2/wij2*(kij*pj) - 4*mj2*mMot2/wj2/wij2*(kj*kij) )/mj/mMot;
complex pizj = (0.5*(mMot2 - mi2 - mj2) - 2*mj2/wj2*(pi*kj))/mj;
if (poli == 1) M = 2*g*(pjui*zjzij - pizj*uizij + pizij*uizj)/fsrQ2;
else if (poli == -1) M = 2*g*(pjdi*zjzij - pizj*dizij + pizij*dizj)/fsrQ2;
} else if (poli == 0 && abs(polj) == 1) {
complex ziuj = 1/sqrt(2)/wj2/mi*( spinProd(-1, kj, pj, pi, kj)
- 2*mi2/wi2*spinProd(-1, kj, pj, ki, kj) );
complex zidj = conj(ziuj);
complex pjzi = (0.5*(mMot2 - mi2 - mj2) - 2*mi2/wi2*(pj*ki))/mi;
if (polj == 1) M = 2*g*(pjzi*ujzij - piuj*zizij + pizij*ziuj)/fsrQ2;
else if (polj == -1) M = 2*g*(pjzi*djzij - pidj*zizij + pizij*zidj)/fsrQ2;
} else if (poli == 0 && polj == 0) {
complex zizj = ( 0.5*(mMot2 - mi2 - mj2) - 2*mi2/wi2*(ki*pj)
- 2*mj2/wj2*(kj*pi) - 4*mi2*mj2/wi2/wj2*(ki*kj) )/mi/mj;
complex pizj = (0.5*(mMot2 - mi2 - mj2) - 2*mj2/wj2*(pi*kj))/mj;
complex pjzi = (0.5*(mMot2 - mi2 - mj2) - 2*mi2/wi2*(pj*ki))/mi;
complex zjzij = ( 0.5*(mMot2 - mi2 + mj2) - 2*mj2/wj2*(kj*pij)
- 2*mMot2/wij2*(kij*pj) - 4*mj2*mMot2/wj2/wij2*(kj*kij) )/mj/mMot;
M = 2*g*(pjzi*zjzij - pizj*zizij + pizij*zizj)/fsrQ2;
}
return M;
}
//--------------------------------------------------------------------------
// FSR: H->ffbar.
complex AmpCalculator::htoffbarFSRAmp(const Vec4& pi, const Vec4& pj,
int idMot, int idi, int, double mMot, double widthQ2, int polMot,
int poli, int polj) {
// Initialize.
initFSRAmp(false, idi, idMot, polMot, pi, pj, mMot, widthQ2);
if (zdenFSRAmp(__METHOD_NAME__, pi, pj, wi == 0 || wj == 0)) return M;
// Calculate amplitude (mi = mj).
double fac = mi*g/wi/wj;
if (poli == 1 && polj == -1)
M = fac*(mi*spinProd(-1, ki, pj, kj) - mj*spinProd(-1, ki, pi, kj) )/fsrQ2;
else if (poli == -1 && polj == 1)
M = fac*(mi*spinProd(-1, ki, pj, kj) - mj*spinProd(-1, ki, pi, kj) )/fsrQ2;
else if (poli == 1 && polj == 1)
M = fac*(spinProd(-1, ki, pi, pj, kj) - mi*mj*spinProd(-1, ki, kj) )/fsrQ2;
else if (poli == -1 && polj == -1)
M = fac*(spinProd(1, ki, pi, pj, kj) - mi*mj*spinProd(1, ki, kj) )/fsrQ2;
return M;
}
//--------------------------------------------------------------------------
// FSR: H->VV.
complex AmpCalculator::htovvFSRAmp(const Vec4& pi, const Vec4& pj, int idMot,
int idi, int, double mMot, double widthQ2, int polMot, int poli, int polj) {
// Initialize.
initFSRAmp(false, idi, idMot, polMot, pi, pj, mMot, widthQ2);
if (zdenFSRAmp(__METHOD_NAME__, pi, pj, wi2 == 0 || wj2 == 0 || mi == 0 ||
mj == 0)) return M;
// Calculate amplitude.
double trtrFac = g/wi2/wj2;
if (poli == 1 && polj == 1 )
M = -trtrFac*spinProd(-1, kj, ki)*spinProd(-1, ki, pi, pj, kj)/fsrQ2;
else if (poli == -1 && polj == -1 )
M = -trtrFac*spinProd( 1, kj, ki)*spinProd( 1 , ki, pi, pj, kj)/fsrQ2;
else if (poli == 1 && polj == -1 )
M = -trtrFac*spinProd(-1, ki, pi, kj)*spinProd(-1, ki, pj, kj)/fsrQ2;
else if (poli == -1 && polj == 1 )
M = -trtrFac*spinProd( 1, ki, pi, kj)*spinProd( 1, ki, pj, kj)/fsrQ2;
else if (poli == 0 && polj == 1 )
M = g/sqrt(2)/wj2/mi*(spinProd(-1, kj, pj, pi, kj)
- 2*mi2/wi2*spinProd(-1, kj, pj, ki, kj))/fsrQ2;
else if (poli == 0 && polj == -1 )
M = -g/sqrt(2)/wj2/mi*(spinProd( 1, kj, pj, pi, kj)
- 2*mi2/wi2*spinProd( 1, kj, pj, ki, kj))/fsrQ2;
else if (poli == 1 && polj == 0)
M = g/sqrt(2)/wi2/mj*(spinProd(-1, ki, pi, pj, ki)
- 2*mj2/wi2*spinProd(-1, ki, pi, kj, ki))/fsrQ2;
else if (poli == -1 && polj == 0)
M = -g/sqrt(2)/wi2/mj*(spinProd( 1, ki, pi, pj, ki)
- 2*mj2/wi2*spinProd(1 , ki, pi, kj, ki))/fsrQ2;
else if (poli == 0 && polj == 0)
M = g/mi/mj*(0.5*(mMot2 - mi2 - mj2) - mj2*wi2/wj2 - mi2*wj2/wi2)/fsrQ2;
return M;
}
//--------------------------------------------------------------------------
// FSR: H->HH.
complex AmpCalculator::htohhFSRAmp(const Vec4& pi, const Vec4& pj, int idMot,
int idi, int, double mMot, double widthQ2, int polMot, int, int) {
// Initialize.
initFSRAmp(false, idi, idMot, polMot, pi, pj, mMot, widthQ2);
if (zdenFSRAmp(__METHOD_NAME__, pi, pj, false)) return M;
// Calculate amplitude.
M = g/fsrQ2;
return M;
}
//--------------------------------------------------------------------------
// ISR: f->fV.
complex AmpCalculator::ftofvISRAmp(const Vec4& pa, const Vec4& pj, int idA,
int ida, int idj, double mA, int polA, int pola, int polj) {
// Initialize.
initISRAmp(true, idA, idj, polA, pa, pj, mA);
if (zdenISRAmp(__METHOD_NAME__, pa, pj, waj == 0 || wa == 0 || wj2 == 0 ||
( mj == 0. && polj == 0 ))) return M;
// Calculate amplitude (all defined with hel -pol).
if (abs(pola) == 1 && abs(polj) == 1) {
complex kajkj = spinProd(-polA, kaj, kj);
complex kajpajkj = spinProd(-polA, kaj, paj, kj);
complex kajpjkj = spinProd(-polA, kaj, pj, kj);
complex kajpajpjkj = spinProd(-polA, kaj, paj, pj, kj);
complex kjka = spinProd(-polA, kj, ka);
complex kjpaka = spinProd(-polA, kj, pa, ka);
complex kjpjka = spinProd(-polA, kj, pj, ka);
complex kjpjpaka = spinProd(-polA, kj, pj, pa, ka);
double trvFac = sqrt(2)*polA/wa/waj/wj2/isrQ2;
if (pola == polA && polj == polA)
M = trvFac*(vMin*kajpajpjkj*kjpaka - vPls*ma*mA*kajkj*kjpjka);
else if (pola == polA && polj == -polA)
M = trvFac*(vMin*kajpajkj*conj(-kjpjpaka)
- vPls*ma*mA*kajpjkj*conj(-kjka));
else if (pola == -polA && polj == polA)
M = trvFac*(mA*vPls*kajkj*kjpjpaka - ma*vMin*kajpajpjkj*kjka);
else if (pola == -polA && polj == -polA)
M = trvFac*(mA*vPls*kajpjkj*conj(kjpaka)
- ma*vMin*kajpajkj*conj(kjpjka));
} else if (abs(pola) == 1 && polj == 0) {
double lonFac = 1./mj/wa/waj/isrQ2;
if (pola == polA)
M = -lonFac*(ma2*vMin*spinProd(-polA, kaj, paj, ka)
- mA2*vMin*spinProd(-polA, kaj, pa, ka)
+ ma*mA*vPls*spinProd(-polA, kaj, pj, ka)
- 2*mj2/wj2*vMin*spinProd(-polA, kaj, paj, kj, pa, ka)
- 2*mj2/wj2*vPls*mA*ma*spinProd(-polA, kaj, kj, ka) );
else if (pola == -polA)
M = -lonFac*(ma*vMin*( spinProd(-polA, kaj, paj, pj, ka)
- 2*mj2/wj2*spinProd(-polA, kaj, paj, kj, ka) )
+ mA*vPls*( spinProd(-polA, kaj, pj, pa, ka)
- 2*mj2/wj2*spinProd(-polA, kaj, kj, pa, ka)) );
}
// Multiply by CKM matrix - only for q+W.
if (abs(idj) == 24 && abs(ida) < 7)
M *= vCKM[make_pair(abs(idA), abs(ida))];
return M;
}
//--------------------------------------------------------------------------
// ISR: f->fH.
complex AmpCalculator::ftofhISRAmp(const Vec4& pa, const Vec4& pj, int idA,
int, int idj, double mA, int polA, int pola, int) {
// Initialize.
initISRAmp(false, idA, idj, polA, pa, pj, mA);
if (zdenISRAmp(__METHOD_NAME__, pa, pj, waj == 0 || wa == 0)) return M;
// Calculate amplitude.
double fac = mA*g/wa/waj/isrQ2;
if (pola == polA) M = -fac*ma*( spinProd(-polA, kaj, paj + pa, ka));
else if (pola == -polA) M = -fac*( spinProd(-polA, kaj, paj, pa, ka)
+ ma2*spinProd(-polA, kaj, ka));
return M;
}
//--------------------------------------------------------------------------
// ISR: fbar->fbarV.
complex AmpCalculator::fbartofbarvISRAmp(const Vec4& pa, const Vec4& pj,
int idA, int ida, int idj, double mA, int polA, int pola, int polj) {
// Initialize.
initISRAmp(true, idA, idj, polA, pa, pj, mA);
if (zdenISRAmp(__METHOD_NAME__, pa, pj, waj == 0 || wa == 0 || wj2 == 0 ||
(mj == 0. && polj == 0 ))) return M;
// Calculate amplitude.
// All defined with hel pol.
if (abs(pola) == 1 && abs(polj) == 1) {
complex kakj = spinProd(polA, ka, kj);
complex kapakj = spinProd(polA, ka, pa, kj);
complex kapjkj = spinProd(polA, ka, pj, kj);
complex kapapjkj = spinProd(polA, ka, pa, pj, kj);