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SigmaExtraDim.cc
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// SigmaExtraDim.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.
// Author: Stefan Ask for the *LED* routines.
// Function definitions (not found in the header) for the
// extra-dimensional simulation classes.
#include "Pythia8/SigmaExtraDim.h"
namespace Pythia8 {
//==========================================================================
// ampLedS (amplitude) method for LED graviton tree level exchange.
// Based on Eq. (8) in JHEP 1105 (2011) 092, arXiv:1101.4919.
complex ampLedS(double x, double n, double L, double M) {
complex cS(0., 0.);
if (n <= 0) return cS;
// Constants.
double exp1 = n - 2;
double exp2 = n + 2;
double rC = sqrt(pow(M_PI,n)) * pow(L,exp1)
/ (gammaReal(n/2.) * pow(M,exp2));
// Base functions, F1 and F2.
complex I(0., 1.);
if (x < 0) {
double sqrX = sqrt(-x);
if (int(n) % 2 == 0) {
cS = -log(abs(1 - 1/x));
} else {
cS = (2.*atan(sqrX) - M_PI)/sqrX;
}
} else if ((x > 0) && (x < 1)) {
double sqrX = sqrt(x);
if (int(n) % 2 == 0) {
cS = -log(abs(1 - 1/x)) - M_PI*I;
} else {
double rat = (sqrX + 1)/(sqrX - 1);
cS = log(abs(rat))/sqrX - M_PI*I/sqrX;
}
} else if (x > 1){
double sqrX = sqrt(x);
if (int(n) % 2 == 0) {
cS = -log(abs(1 - 1/x));
} else {
double rat = (sqrX + 1)/(sqrX - 1);
cS = log(abs(rat))/sqrX;
}
}
// Recursive part.
int nL;
int nD;
if (int(n) % 2 == 0) {
nL = int(n/2.);
nD = 2;
} else {
nL = int((n + 1)/2.);
nD = 1;
}
for (int i=1; i<nL; ++i) {
cS = x*cS - 2./nD;
nD += 2;
}
return rC*cS;
}
//--------------------------------------------------------------------------
// Common method, "Mandelstam polynomial", for LED dijet processes.
double funLedG(double x, double y) {
double ret = pow(x,4) + 10. * pow(x,3) * y + 42. * pow2(x) * pow2(y)
+ 64. * x * pow(y,3) + 32. * pow(y,4);
return ret;
}
//==========================================================================
// Sigma1gg2GravitonStar class.
// Cross section for g g -> G* (excited graviton state).
//--------------------------------------------------------------------------
// Initialize process.
void Sigma1gg2GravitonStar::initProc() {
// Store G* mass and width for propagator.
idGstar = 5100039;
mRes = particleDataPtr->m0(idGstar);
GammaRes = particleDataPtr->mWidth(idGstar);
m2Res = mRes*mRes;
GamMRat = GammaRes / mRes;
// SMinBulk = off/on, use universal coupling (kappaMG)
// or individual (Gxx) between graviton and SM particles.
eDsmbulk = flag("ExtraDimensionsG*:SMinBulk");
eDvlvl = false;
if (eDsmbulk) eDvlvl = flag("ExtraDimensionsG*:VLVL");
kappaMG = parm("ExtraDimensionsG*:kappaMG");
for (int i = 0; i < 27; ++i) eDcoupling[i] = 0.;
double tmPcoup = parm("ExtraDimensionsG*:Gqq");
for (int i = 1; i <= 4; ++i) eDcoupling[i] = tmPcoup;
eDcoupling[5] = parm("ExtraDimensionsG*:Gbb");
eDcoupling[6] = parm("ExtraDimensionsG*:Gtt");
tmPcoup = parm("ExtraDimensionsG*:Gll");
for (int i = 11; i <= 16; ++i) eDcoupling[i] = tmPcoup;
eDcoupling[21] = parm("ExtraDimensionsG*:Ggg");
eDcoupling[22] = parm("ExtraDimensionsG*:Ggmgm");
eDcoupling[23] = parm("ExtraDimensionsG*:GZZ");
eDcoupling[24] = parm("ExtraDimensionsG*:GWW");
eDcoupling[25] = parm("ExtraDimensionsG*:Ghh");
// Set pointer to particle properties and decay table.
gStarPtr = particleDataPtr->particleDataEntryPtr(idGstar);
}
//--------------------------------------------------------------------------
// Evaluate sigmaHat(sHat), part independent of incoming flavour.
void Sigma1gg2GravitonStar::sigmaKin() {
// Incoming width for gluons.
double widthIn = mH / (160. * M_PI);
// RS graviton coupling
if (eDsmbulk) widthIn *= 2. * pow2(eDcoupling[21] * mH);
else widthIn *= pow2(kappaMG * mH / mRes);
// Set up Breit-Wigner. Width out only includes open channels.
double sigBW = 5. * M_PI/ ( pow2(sH - m2Res) + pow2(sH * GamMRat) );
double widthOut = gStarPtr->resWidthOpen(idGstar, mH);
// Modify cross section in wings of peak. Done.
sigma = widthIn * sigBW * widthOut;
}
//--------------------------------------------------------------------------
// Select identity, colour and anticolour.
void Sigma1gg2GravitonStar::setIdColAcol() {
// Flavours trivial.
setId( 21, 21, idGstar);
// Colour flow topology.
setColAcol( 1, 2, 2, 1, 0, 0);
}
//--------------------------------------------------------------------------
// Evaluate weight for G* decay angle.
// SA: Angle dist. for decay G* -> W/Z/h, based on
// Phys.Rev. D65 (2002) 075008, [arXiv:hep-ph/0103308v3]
double Sigma1gg2GravitonStar::weightDecay( Event& process, int iResBeg,
int iResEnd) {
// Identity of mother of decaying reseonance(s).
int idMother = process[process[iResBeg].mother1()].idAbs();
// For top decay hand over to standard routine.
if (idMother == 6)
return weightTopDecay( process, iResBeg, iResEnd);
// G* should sit in entry 5.
if (iResBeg != 5 || iResEnd != 5) return 1.;
// Phase space factors. Reconstruct decay angle.
double mr1 = pow2(process[6].m()) / sH;
double mr2 = pow2(process[7].m()) / sH;
double betaf = sqrtpos( pow2(1. - mr1 - mr2) - 4. * mr1 * mr2);
double cosThe = (process[3].p() - process[4].p())
* (process[7].p() - process[6].p()) / (sH * betaf);
// Default is isotropic decay.
double wt = 1.;
// Angular weight for g + g -> G* -> f + fbar.
if (process[6].idAbs() < 19) {
wt = 1. - pow4(cosThe);
// Angular weight for g + g -> G* -> g + g or gamma + gamma.
} else if (process[6].id() == 21 || process[6].id() == 22) {
wt = (1. + 6. * pow2(cosThe) + pow4(cosThe)) / 8.;
// Angular weight for g + g -> G* -> Z + Z or W + W.
} else if (process[6].id() == 23 || process[6].id() == 24) {
double beta2 = pow2(betaf);
double cost2 = pow2(cosThe);
double cost4 = pow2(cost2);
wt = pow2(beta2 - 2.)*(1. - 2.*cost2 + cost4);
// Longitudinal W/Z only.
if(eDvlvl) {
wt /= 4.;
// Transverse W/Z contributions as well.
} else {
double beta4 = pow2(beta2);
double beta8 = pow2(beta4);
wt += 2.*pow2(beta4 - 1.)*beta4*cost4;
wt += 2.*pow2(beta2 - 1.)*(1. - 2.*beta4*cost2 + beta8*cost4);
wt += 2.*(1. + 6.*beta4*cost2 + beta8*cost4);
wt += 8.*(1. - beta2)*(1. - cost4);
wt /= 18.;
}
// Angular weight for g + g -> G* -> h + h
} else if (process[6].id() == 25) {
double beta2 = pow2(betaf);
double cost2 = pow2(cosThe);
double cost4 = pow2(cost2);
wt = pow2(beta2 - 2.)*(1. - 2.*cost2 + cost4);
wt /= 4.;
}
// Done.
return wt;
}
//==========================================================================
// Sigma1ffbar2GravitonStar class.
// Cross section for f fbar -> G* (excited graviton state).
//--------------------------------------------------------------------------
// Initialize process.
void Sigma1ffbar2GravitonStar::initProc() {
// Store G* mass and width for propagator.
idGstar = 5100039;
mRes = particleDataPtr->m0(idGstar);
GammaRes = particleDataPtr->mWidth(idGstar);
m2Res = mRes*mRes;
GamMRat = GammaRes / mRes;
// SMinBulk = off/on, use universal coupling (kappaMG)
// or individual (Gxx) between graviton and SM particles.
eDsmbulk = flag("ExtraDimensionsG*:SMinBulk");
eDvlvl = false;
if (eDsmbulk) eDvlvl = flag("ExtraDimensionsG*:VLVL");
kappaMG = parm("ExtraDimensionsG*:kappaMG");
for (int i = 0; i < 27; ++i) eDcoupling[i] = 0.;
double tmPcoup = parm("ExtraDimensionsG*:Gqq");
for (int i = 1; i <= 4; ++i) eDcoupling[i] = tmPcoup;
eDcoupling[5] = parm("ExtraDimensionsG*:Gbb");
eDcoupling[6] = parm("ExtraDimensionsG*:Gtt");
tmPcoup = parm("ExtraDimensionsG*:Gll");
for (int i = 11; i <= 16; ++i) eDcoupling[i] = tmPcoup;
eDcoupling[21] = parm("ExtraDimensionsG*:Ggg");
eDcoupling[22] = parm("ExtraDimensionsG*:Ggmgm");
eDcoupling[23] = parm("ExtraDimensionsG*:GZZ");
eDcoupling[24] = parm("ExtraDimensionsG*:GWW");
eDcoupling[25] = parm("ExtraDimensionsG*:Ghh");
// Set pointer to particle properties and decay table.
gStarPtr = particleDataPtr->particleDataEntryPtr(idGstar);
}
//--------------------------------------------------------------------------
// Evaluate sigmaHat(sHat), part independent of incoming flavour.
void Sigma1ffbar2GravitonStar::sigmaKin() {
// Incoming width for fermions, disregarding colour factor.
double widthIn = mH / (80. * M_PI);
// Set up Breit-Wigner. Width out only includes open channels.
double sigBW = 5. * M_PI/ ( pow2(sH - m2Res) + pow2(sH * GamMRat) );
double widthOut = gStarPtr->resWidthOpen(idGstar, mH);
// Modify cross section in wings of peak. Done.
sigma0 = widthIn * sigBW * widthOut;
}
//--------------------------------------------------------------------------
// Evaluate sigmaHat(sHat), part dependent of incoming flavour.
double Sigma1ffbar2GravitonStar::sigmaHat() {
double sigma = sigma0;
// RS graviton coupling
if (eDsmbulk) sigma *= 2. * pow2(eDcoupling[min( abs(id1), 26)] * mH);
else sigma *= pow2(kappaMG * mH / mRes);
// If initial quarks, 1/N_C
if (abs(id1) < 9) sigma /= 3.;
return sigma;
}
//--------------------------------------------------------------------------
// Select identity, colour and anticolour.
void Sigma1ffbar2GravitonStar::setIdColAcol() {
// Flavours trivial.
setId( id1, id2, idGstar);
// Colour flow topologies. Swap when antiquarks.
if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0);
else setColAcol( 0, 0, 0, 0, 0, 0);
if (id1 < 0) swapColAcol();
}
//--------------------------------------------------------------------------
// Evaluate weight for G* decay angle.
// SA: Angle dist. for decay G* -> W/Z/h, based on
// Phys.Rev. D65 (2002) 075008, [arXiv:hep-ph/0103308v3]
double Sigma1ffbar2GravitonStar::weightDecay( Event& process, int iResBeg,
int iResEnd) {
// Identity of mother of decaying reseonance(s).
int idMother = process[process[iResBeg].mother1()].idAbs();
// For top decay hand over to standard routine.
if (idMother == 6)
return weightTopDecay( process, iResBeg, iResEnd);
// G* should sit in entry 5.
if (iResBeg != 5 || iResEnd != 5) return 1.;
// Phase space factors. Reconstruct decay angle.
double mr1 = pow2(process[6].m()) / sH;
double mr2 = pow2(process[7].m()) / sH;
double betaf = sqrtpos( pow2(1. - mr1 - mr2) - 4. * mr1 * mr2);
double cosThe = (process[3].p() - process[4].p())
* (process[7].p() - process[6].p()) / (sH * betaf);
// Default is isotropic decay.
double wt = 1.;
// Angular weight for f + fbar -> G* -> f + fbar.
if (process[6].idAbs() < 19) {
wt = (1. - 3. * pow2(cosThe) + 4. * pow4(cosThe)) / 2.;
// Angular weight for f + fbar -> G* -> g + g or gamma + gamma.
} else if (process[6].id() == 21 || process[6].id() == 22) {
wt = 1. - pow4(cosThe);
// Angular weight for f + fbar -> G* -> Z + Z or W + W.
} else if (process[6].id() == 23 || process[6].id() == 24) {
double beta2 = pow2(betaf);
double cost2 = pow2(cosThe);
double cost4 = pow2(cost2);
wt = pow2(beta2 - 2.)*cost2*(1. - cost2);
// Longitudinal W/Z only.
if (eDvlvl) {
wt /= 4.;
// Transverse W/Z contributions as well.
} else {
wt += pow2(beta2 - 1.)*cost2*(1. - cost2);
wt += 2.*(1. - cost4);
wt += (1. - beta2)*(1. - 3.*cost2 + 4.*cost4);
wt /= 8.;
}
// Angular weight for f + fbar -> G* -> h + h
} else if (process[6].id() == 25) {
double beta2 = pow2(betaf);
double cost2 = pow2(cosThe);
wt = pow2(beta2 - 2.)*cost2*(1. - cost2);
wt /= 4.;
}
// Done.
return wt;
}
//==========================================================================
// Sigma1qqbar2KKgluonStar class.
// Cross section for q qbar -> g^*/KK-gluon^* (excited KK-gluon state).
//--------------------------------------------------------------------------
// Initialize process.
void Sigma1qqbar2KKgluonStar::initProc() {
// Store kk-gluon* mass and width for propagator.
idKKgluon = 5100021;
mRes = particleDataPtr->m0(idKKgluon);
GammaRes = particleDataPtr->mWidth(idKKgluon);
m2Res = mRes*mRes;
GamMRat = GammaRes / mRes;
// KK-gluon gv/ga couplings and interference.
for (int i = 0; i < 10; ++i) { eDgv[i] = 0.; eDga[i] = 0.; }
double tmPgL = parm("ExtraDimensionsG*:KKgqL");
double tmPgR = parm("ExtraDimensionsG*:KKgqR");
for (int i = 1; i <= 4; ++i) {
eDgv[i] = 0.5 * (tmPgL + tmPgR);
eDga[i] = 0.5 * (tmPgL - tmPgR);
}
tmPgL = parm("ExtraDimensionsG*:KKgbL");
tmPgR = parm("ExtraDimensionsG*:KKgbR");
eDgv[5] = 0.5 * (tmPgL + tmPgR); eDga[5] = 0.5 * (tmPgL - tmPgR);
tmPgL = parm("ExtraDimensionsG*:KKgtL");
tmPgR = parm("ExtraDimensionsG*:KKgtR");
eDgv[6] = 0.5 * (tmPgL + tmPgR); eDga[6] = 0.5 * (tmPgL - tmPgR);
interfMode = mode("ExtraDimensionsG*:KKintMode");
// Set pointer to particle properties and decay table.
gStarPtr = particleDataPtr->particleDataEntryPtr(idKKgluon);
}
//--------------------------------------------------------------------------
// Evaluate sigmaHat(sHat), part independent of incoming flavour.
void Sigma1qqbar2KKgluonStar::sigmaKin() {
// Incoming width for fermions.
double widthIn = alpS * mH * 4 / 27;
double widthOut = alpS * mH / 6;
// Loop over all decay channels.
sumSM = 0.;
sumInt = 0.;
sumKK = 0.;
for (int i = 0; i < gStarPtr->sizeChannels(); ++i) {
int idAbs = abs( gStarPtr->channel(i).product(0) );
// Only contributions quarks.
if ( idAbs > 0 && idAbs <= 6 ) {
double mf = particleDataPtr->m0(idAbs);
// Check that above threshold. Phase space.
if (mH > 2. * mf + MASSMARGIN) {
double mr = pow2(mf / mH);
double beta = sqrtpos(1. - 4. * mr);
// Store sum of combinations. For outstate only open channels.
int onMode = gStarPtr->channel(i).onMode();
if (onMode == 1 || onMode == 2) {
sumSM += beta * (1. + 2. * mr);
sumInt += beta * eDgv[min(idAbs, 9)] * (1. + 2. * mr);
sumKK += beta * (pow2(eDgv[min(idAbs, 9)]) * (1. + 2.*mr)
+ pow2(eDga[min(idAbs, 9)]) * (1. - 4.*mr));
}
}
}
}
// Set up Breit-Wigner. Width out only includes open channels.
sigSM = widthIn * 12. * M_PI * widthOut / sH2;
sigInt = 2. * sigSM * sH * (sH - m2Res)
/ ( pow2(sH - m2Res) + pow2(sH * GamMRat) );
sigKK = sigSM * sH2 / ( pow2(sH - m2Res) + pow2(sH * GamMRat) );
// Optionally only keep g* or gKK term.
if (interfMode == 1) {sigInt = 0.; sigKK = 0.;}
if (interfMode == 2) {sigSM = 0.; sigInt = 0.;}
}
//--------------------------------------------------------------------------
// Evaluate sigmaHat(sHat), part dependent of incoming flavour.
double Sigma1qqbar2KKgluonStar::sigmaHat() {
// RS graviton coupling.
double sigma = sigSM * sumSM
+ eDgv[min(abs(id1), 9)] * sigInt * sumInt
+ ( pow2(eDgv[min(abs(id1), 9)])
+ pow2(eDga[min(abs(id1), 9)]) ) * sigKK * sumKK;
return sigma;
}
//--------------------------------------------------------------------------
// Select identity, colour and anticolour.
void Sigma1qqbar2KKgluonStar::setIdColAcol() {
// Flavours trivial.
setId( id1, id2, idKKgluon);
// Colour flow topologies. Swap when antiquarks.
setColAcol( 1, 0, 0, 2, 1, 2);
if (id1 < 0) swapColAcol();
}
//--------------------------------------------------------------------------
// Evaluate weight for KK-gluon* decay angle (based on ffbar2gmZ).
double Sigma1qqbar2KKgluonStar::weightDecay( Event& process, int iResBeg,
int iResEnd) {
// Identity of mother of decaying reseonance(s).
int idMother = process[process[iResBeg].mother1()].idAbs();
// For top decay hand over to standard routine.
if (idMother == 6)
return weightTopDecay( process, iResBeg, iResEnd);
// g* should sit in entry 5.
if (iResBeg != 5 || iResEnd != 5) return 1.;
// Couplings for in- and out-flavours (alpS already included).
int idInAbs = process[3].idAbs();
double vi = eDgv[min(idInAbs, 9)];
double ai = eDga[min(idInAbs, 9)];
int idOutAbs = process[6].idAbs();
double vf = eDgv[min(idOutAbs, 9)];
double af = eDga[min(idOutAbs, 9)];
// Phase space factors. (One power of beta left out in formulae.)
double mf = process[6].m();
double mr = mf*mf / sH;
double betaf = sqrtpos(1. - 4. * mr);
// Coefficients of angular expression.
double coefTran = sigSM + vi * sigInt * vf
+ (vi*vi + ai*ai) * sigKK * (vf*vf + pow2(betaf) * af*af);
double coefLong = 4. * mr * ( sigSM + vi * sigInt * vf
+ (vi*vi + ai*ai) * sigKK * vf*vf );
double coefAsym = betaf * ( ai * sigInt * af
+ 4. * vi * ai * sigKK * vf * af );
// Flip asymmetry for in-fermion + out-antifermion.
if (process[3].id() * process[6].id() < 0) coefAsym = -coefAsym;
// Reconstruct decay angle and weight for it.
double cosThe = (process[3].p() - process[4].p())
* (process[7].p() - process[6].p()) / (sH * betaf);
double wtMax = 2. * (coefTran + abs(coefAsym));
double wt = coefTran * (1. + pow2(cosThe))
+ coefLong * (1. - pow2(cosThe)) + 2. * coefAsym * cosThe;
// Done.
return (wt / wtMax);
}
//==========================================================================
// Sigma2gg2GravitonStarg class.
// Cross section for g g -> G* g (excited graviton state).
//--------------------------------------------------------------------------
// Initialize process.
void Sigma2gg2GravitonStarg::initProc() {
// Store G* mass and width for propagator.
idGstar = 5100039;
mRes = particleDataPtr->m0(idGstar);
GammaRes = particleDataPtr->mWidth(idGstar);
m2Res = mRes*mRes;
GamMRat = GammaRes / mRes;
// Overall coupling strength kappa * m_G*.
kappaMG = parm("ExtraDimensionsG*:kappaMG");
// Secondary open width fraction.
openFrac = particleDataPtr->resOpenFrac(idGstar);
}
//--------------------------------------------------------------------------
// Evaluate sigmaHat(sHat), part independent of incoming flavour.
void Sigma2gg2GravitonStarg::sigmaKin() {
// Evaluate cross section. Secondary width for G*.
sigma = (3. * pow2(kappaMG) * alpS) / (32. * sH * m2Res)
* ( pow2(tH2 + tH * uH + uH2) / (sH2 * tH * uH)
+ 2. * (tH2 / uH + uH2 / tH) / sH + 3. * (tH / uH + uH / tH)
+ 2. * (sH / uH + sH/tH) + sH2 / (tH * uH) );
sigma *= openFrac;
}
//--------------------------------------------------------------------------
// Select identity, colour and anticolour.
void Sigma2gg2GravitonStarg::setIdColAcol() {
// Flavours trivial.
setId( 21, 21, idGstar, 21);
// Colour flow topologies: random choice between two mirrors.
if (rndmPtr->flat() < 0.5) setColAcol( 1, 2, 2, 3, 0, 0, 1, 3);
else setColAcol( 1, 2, 3, 1, 0, 0, 3, 2);
}
//--------------------------------------------------------------------------
// Evaluate weight for decay angles: currently G* assumed isotropic.
double Sigma2gg2GravitonStarg::weightDecay( Event& process, int iResBeg,
int iResEnd) {
// Identity of mother of decaying reseonance(s).
int idMother = process[process[iResBeg].mother1()].idAbs();
// For top decay hand over to standard routine.
if (idMother == 6)
return weightTopDecay( process, iResBeg, iResEnd);
// No equations for G* decay so assume isotropic.
return 1.;
}
//==========================================================================
// Sigma2qg2GravitonStarq class.
// Cross section for q g -> G* q (excited graviton state).
//--------------------------------------------------------------------------
// Initialize process.
void Sigma2qg2GravitonStarq::initProc() {
// Store G* mass and width for propagator.
idGstar = 5100039;
mRes = particleDataPtr->m0(idGstar);
GammaRes = particleDataPtr->mWidth(idGstar);
m2Res = mRes*mRes;
GamMRat = GammaRes / mRes;
// Overall coupling strength kappa * m_G*.
kappaMG = parm("ExtraDimensionsG*:kappaMG");
// Secondary open width fraction.
openFrac = particleDataPtr->resOpenFrac(idGstar);
}
//--------------------------------------------------------------------------
// Evaluate sigmaHat(sHat), part independent of incoming flavour.
void Sigma2qg2GravitonStarq::sigmaKin() {
// Evaluate cross section. Secondary width for G*.
sigma = -(pow2(kappaMG) * alpS) / (192. * sH * m2Res )
* ( 4. * (sH2 + uH2) / (tH * sH) + 9. * (sH + uH) / sH + sH / uH
+ uH2 / sH2 + 3. * tH * (4. + sH / uH + uH / sH) / sH
+ 4. * tH2 * (1. / uH + 1. / sH) / sH + 2. * tH2 * tH / (uH * sH2) );
sigma *= openFrac;
}
//--------------------------------------------------------------------------
// Select identity, colour and anticolour.
void Sigma2qg2GravitonStarq::setIdColAcol() {
// Flavour set up for q g -> H q.
int idq = (id2 == 21) ? id1 : id2;
setId( id1, id2, idGstar, idq);
// tH defined between f and f': must swap tHat <-> uHat if q g in.
swapTU = (id2 == 21);
// Colour flow topologies. Swap when antiquarks.
if (id2 == 21) setColAcol( 1, 0, 2, 1, 0, 0, 2, 0);
else setColAcol( 2, 1, 1, 0, 0, 0, 2, 0);
if (idq < 0) swapColAcol();
}
//--------------------------------------------------------------------------
// Evaluate weight for decay angles: currently G* assumed isotropic.
double Sigma2qg2GravitonStarq::weightDecay( Event& process, int iResBeg,
int iResEnd) {
// Identity of mother of decaying reseonance(s).
int idMother = process[process[iResBeg].mother1()].idAbs();
// For top decay hand over to standard routine.
if (idMother == 6)
return weightTopDecay( process, iResBeg, iResEnd);
// No equations for G* decay so assume isotropic.
return 1.;
}
//==========================================================================
// Sigma2qqbar2GravitonStarg class.
// Cross section for q qbar -> G* g (excited graviton state).
//--------------------------------------------------------------------------
// Initialize process.
void Sigma2qqbar2GravitonStarg::initProc() {
// Store G* mass and width for propagator.
idGstar = 5100039;
mRes = particleDataPtr->m0(idGstar);
GammaRes = particleDataPtr->mWidth(idGstar);
m2Res = mRes*mRes;
GamMRat = GammaRes / mRes;
// Overall coupling strength kappa * m_G*.
kappaMG = parm("ExtraDimensionsG*:kappaMG");
// Secondary open width fraction.
openFrac = particleDataPtr->resOpenFrac(idGstar);
}
//--------------------------------------------------------------------------
// Evaluate sigmaHat(sHat), part independent of incoming flavour.
void Sigma2qqbar2GravitonStarg::sigmaKin() {
// Evaluate cross section. Secondary width for G*.
sigma = (pow2(kappaMG) * alpS) / (72. * sH * m2Res)
* ( 4. * (tH2 + uH2) / sH2 + 9. * (tH + uH) / sH
+ (tH2 / uH + uH2 / tH) / sH + 3. * (4. + tH / uH + uH/ tH)
+ 4. * (sH / uH + sH / tH) + 2. * sH2 / (tH * uH) );
sigma *= openFrac;
}
//--------------------------------------------------------------------------
// Select identity, colour and anticolour.
void Sigma2qqbar2GravitonStarg::setIdColAcol() {
// Flavours trivial.
setId( id1, id2, idGstar, 21);
// Colour flow topologies. Swap when antiquarks.
setColAcol( 1, 0, 0, 2, 0, 0, 1, 2);
if (id1 < 0) swapColAcol();
}
//--------------------------------------------------------------------------
// Evaluate weight for decay angles: currently G* assumed isotropic.
double Sigma2qqbar2GravitonStarg::weightDecay( Event& process, int iResBeg,
int iResEnd) {
// Identity of mother of decaying reseonance(s).
int idMother = process[process[iResBeg].mother1()].idAbs();
// For top decay hand over to standard routine.
if (idMother == 6)
return weightTopDecay( process, iResBeg, iResEnd);
// No equations for G* decay so assume isotropic.
return 1.;
}
//==========================================================================
// NOAM: Sigma2ffbar2TEVffbar class.
// Cross section for, f fbar -> gammaKK/ZKK -> F Fbar.
// Process provided by N. Hod et al. and is described in arXiv:XXXX.YYYY
//--------------------------------------------------------------------------
// Initialize process.
void Sigma2ffbar2TEVffbar::initProc() {
// Process name.
if (idNew == 1) nameSave = "f fbar -> d dbar (s-channel gamma_KK/Z_KK)";
if (idNew == 2) nameSave = "f fbar -> u ubar (s-channel gamma_KK/Z_KK)";
if (idNew == 3) nameSave = "f fbar -> s sbar (s-channel gamma_KK/Z_KK)";
if (idNew == 4) nameSave = "f fbar -> c cbar (s-channel gamma_KK/Z_KK)";
if (idNew == 5) nameSave = "f fbar -> b bbar (s-channel gamma_KK/Z_KK)";
if (idNew == 6) nameSave = "f fbar -> t tbar (s-channel gamma_KK/Z_KK)";
if (idNew == 11) nameSave = "f fbar -> e+ e- (s-channel gamma_KK/Z_KK)";
if (idNew == 12) nameSave = "f fbar -> nue nuebar (s-channel gamma_KK/Z_KK)";
if (idNew == 13) nameSave = "f fbar -> mu+ mu- (s-channel gamma_KK/Z_KK)";
if (idNew == 14) nameSave
= "f fbar -> numu numubar (s-channel gamma_KK/Z_KK)";
if (idNew == 15) nameSave = "f fbar -> tau+ tau- (s-channel gamma_KK/Z_KK)";
if (idNew == 16) nameSave
= "f fbar -> nutau nutaubar (s-channel gamma_KK/Z_KK)";
// Allow to pick only gamma* or Z0 part of full gamma*/Z0 expression.
gmZmode = mode("ExtraDimensionsTEV:gmZmode");
// Pick number of KK excitations
nexcitationmax = mode("ExtraDimensionsTEV:nMax");
// Initialize the widths of the KK propogators.
// partial width of the KK photon
wgmKKFactor = 0.;
// total width of the KK photon
wgmKKn = 0.;
// will be proportional to "wZ0" + ttbar addition
wZKKn = 0.;
// Store Z0 mass and width for propagator.
wZ0 = particleDataPtr->mWidth(23);
mRes = particleDataPtr->m0(23);
m2Res = mRes*mRes;
// Store the top mass for the ttbar width calculations
mTop = particleDataPtr->m0(6);
m2Top = mTop*mTop;
// Store the KK mass parameter, equivalent to the mass of the first KK
// excitation: particleDataPtr->m0(5000023);
mStar = (double)parm("ExtraDimensionsTEV:mStar");
// Get alphaEM - relevant for the calculation of the widths
alphaemfixed = parm("StandardModel:alphaEM0");
// initialize imaginari number
mI = complex(0.,1.);
// Sum all partial widths of the KK photon except for the ttbar channel
// which is handeled afterwards seperately
if (gmZmode>=0 && gmZmode<=5) {
for (int i=1 ; i<17 ; i++) {
if (i==7) { i=11; }
// skip the ttbar decay and add its contribution later
if (i==6) { continue; }
if (i<9) {
wgmKKFactor += ( (alphaemfixed / 6.) * 4.
* coupSMPtr->ef(i) * coupSMPtr->ef(i) * 3. );
}
else {
wgmKKFactor += (alphaemfixed / 6.) * 4.
* coupSMPtr->ef(i) * coupSMPtr->ef(i);
}
}
}
// Get the helicity-couplings of the Z0 to all the fermions except top
gMinusF = ( coupSMPtr->t3f(idNew) - coupSMPtr->ef(idNew)
* coupSMPtr->sin2thetaW() )
/ sqrt( coupSMPtr->sin2thetaW()*coupSMPtr->cos2thetaW() );
gPlusF = -1. * coupSMPtr->ef(idNew) * coupSMPtr->sin2thetaW()
/ sqrt( coupSMPtr->sin2thetaW() * coupSMPtr->cos2thetaW() );
// Get the helicity-couplings of the Z0 to the top quark
gMinusTop = ( coupSMPtr->t3f(6) - coupSMPtr->ef(6)
* coupSMPtr->sin2thetaW() )
/ sqrt( coupSMPtr->sin2thetaW()*coupSMPtr->cos2thetaW() );
gPlusTop = -1. * coupSMPtr->ef(6) * coupSMPtr->sin2thetaW()
/ sqrt( coupSMPtr->sin2thetaW() * coupSMPtr->cos2thetaW() );
// calculate the constant factor of the unique ttbar decay width
ttbarwFactorA = pow2(gMinusTop) + pow2(gPlusTop);
ttbarwFactorB = 6.*gMinusTop*gPlusTop - pow2(gMinusTop) - pow2(gPlusTop);
// Secondary open width fraction, relevant for top (or heavier).
openFracPair = 1.;
if ((idNew >=6 && idNew <=8) || idNew == 17 || idNew == 18)
openFracPair = particleDataPtr->resOpenFrac(idNew, -idNew);
}
//--------------------------------------------------------------------------
// For improving the phase-space sampling (there can be 2 resonances)
int Sigma2ffbar2TEVffbar::resonanceB() {
return 23;
}
//--------------------------------------------------------------------------
// For improving the phase-space sampling (there can be 2 resonances)
int Sigma2ffbar2TEVffbar::resonanceA() {
if (gmZmode>=3) {
phaseSpacemHatMin = parm("PhaseSpace:mHatMin");
phaseSpacemHatMax = parm("PhaseSpace:mHatMax");
double mResFirstKKMode = sqrt(pow2(particleDataPtr->m0(23)) + pow2(mStar));
if (mResFirstKKMode/2. <= phaseSpacemHatMax
|| 3*mResFirstKKMode/2. >= phaseSpacemHatMin) { return 5000023; }
else { return 23; }
// no KK terms at all
} else { return 23; }
}
//--------------------------------------------------------------------------
// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour.
void Sigma2ffbar2TEVffbar::sigmaKin() {
// Check that above threshold.
isPhysical = true;
if (mH < m3 + m4 + MASSMARGIN) {
isPhysical = false;
return;
}
// Define average F, Fbar mass so same beta. Phase space.
double s34Avg = 0.5 * (s3 + s4) - 0.25 * pow2(s3 - s4) / sH;
mr = s34Avg / sH;
betaf = sqrtpos(1. - 4. * mr);
// Reconstruct decay angle so can reuse 2 -> 1 cross section.
cosThe = (tH - uH) / (betaf * sH);
}
//--------------------------------------------------------------------------
// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence.
double Sigma2ffbar2TEVffbar::sigmaHat() {
// Fail if below threshold.
if (!isPhysical) return 0.;
// Couplings for in/out-flavours.
int idAbs = abs(id1);
// The couplings of the Z0 to the fermions for in/out flavors
gMinusf = ( coupSMPtr->t3f(idAbs) - coupSMPtr->ef(idAbs)
* coupSMPtr->sin2thetaW() )
/ sqrt( coupSMPtr->sin2thetaW()*coupSMPtr->cos2thetaW() );
gPlusf = -1. * coupSMPtr->ef(idAbs)*coupSMPtr->sin2thetaW()
/ sqrt( coupSMPtr->sin2thetaW()*coupSMPtr->cos2thetaW() );
// Initialize the some values
helicityME2 = 0.;
coefAngular = 0.;
gf=0.;
gF=0.;
gammaProp = complex(0.,0.);
resProp = complex(0.,0.);
gmPropKK = complex(0.,0.);
ZPropKK = complex(0.,0.);
totalProp = complex(0.,0.);
// Sum all initial and final helicity states this corresponds to an
// unpolarized beams and unmeasured polarization final-state
for (double helicityf=-0.5 ; helicityf<=0.5 ; helicityf++) {
for (double helicityF=-0.5 ; helicityF<=0.5 ; helicityF++) {
// the couplings for the initial-final helicity configuration
gF = (helicityF == +0.5) ? gMinusF : gPlusF;
gf = (helicityf == +0.5) ? gMinusf : gPlusf;
// 0=SM gmZ, 1=SM gm, 2=SM Z, 3=SM+KK gmZ, 4=KK gm, 5=KK Z
switch(gmZmode) {
// SM photon and Z0 only
case 0:
gammaProp = coupSMPtr->ef(idAbs)*coupSMPtr->ef(idNew)/sH;
resProp = gf*gF/( sH - m2Res + mI*sH*(wZ0/mRes) );
break;
// SM photon only
case 1:
gammaProp = coupSMPtr->ef(idAbs)*coupSMPtr->ef(idNew)/sH;
break;
// SM Z0 only
case 2:
resProp = gf*gF/( sH - m2Res + mI*sH*(wZ0/mRes) );