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// StandardModel.cc is a part of the PYTHIA event generator.
// Copyright (C) 2012 Torbjorn Sjostrand.
// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details.
// Please respect the MCnet Guidelines, see GUIDELINES for details.
// Function definitions (not found in the header) for the AlphaStrong class.
#include "StandardModel.h"
namespace Pythia8 {
//==========================================================================
// The AlphaStrong class.
//--------------------------------------------------------------------------
// Constants: could be changed here if desired, but normally should not.
// These are of technical nature, as described for each.
// Number of iterations to determine Lambda from given alpha_s.
const int AlphaStrong::NITER = 10;
// Masses: m_c, m_b, m_Z. Used for flavour thresholds and normalization scale.
const double AlphaStrong::MC = 1.5;
const double AlphaStrong::MB = 4.8;
const double AlphaStrong::MZ = 91.188;
// Always evaluate running alpha_s above Lambda3 to avoid disaster.
// Safety margin picked to freeze roughly for alpha_s = 10.
const double AlphaStrong::SAFETYMARGIN1 = 1.07;
const double AlphaStrong::SAFETYMARGIN2 = 1.33;
//--------------------------------------------------------------------------
// Initialize alpha_strong calculation by finding Lambda values etc.
void AlphaStrong::init( double valueIn, int orderIn) {
// Order of alpha_s evaluation.
valueRef = valueIn;
order = max( 0, min( 2, orderIn ) );
// Fix alpha_s.
if (order == 0) {
Lambda3Save = Lambda4Save = Lambda5Save = scale2Min = 0.;
// First order alpha_s: match at flavour thresholds.
} else if (order == 1) {
Lambda5Save = MZ * exp( -6. * M_PI / (23. * valueRef) );
Lambda4Save = Lambda5Save * pow(MB/Lambda5Save, 2./25.);
Lambda3Save = Lambda4Save * pow(MC/Lambda4Save, 2./27.);
scale2Min = pow2(SAFETYMARGIN1 * Lambda3Save);
// Second order alpha_s: iterative match at flavour thresholds.
} else {
double b15 = 348. / 529.;
double b14 = 462. / 625.;
double b13 = 64. / 81.;
double b25 = 224687. / 242208.;
double b24 = 548575. / 426888.;
double b23 = 938709. / 663552.;
double logScale, loglogScale, correction, valueIter;
// Find Lambda_5 at m_Z.
Lambda5Save = MZ * exp( -6. * M_PI / (23. * valueRef) );
for (int iter = 0; iter < NITER; ++iter) {
logScale = 2. * log(MZ/Lambda5Save);
loglogScale = log(logScale);
correction = 1. - b15 * loglogScale / logScale
+ pow2(b15 / logScale) * (pow2(loglogScale - 0.5) + b25 - 1.25);
valueIter = valueRef / correction;
Lambda5Save = MZ * exp( -6. * M_PI / (23. * valueIter) );
}
// Find Lambda_4 at m_b.
double logScaleB = 2. * log(MB/Lambda5Save);
double loglogScaleB = log(logScaleB);
double valueB = 12. * M_PI / (23. * logScaleB)
* (1. - b15 * loglogScaleB / logScaleB
+ pow2(b15 / logScaleB) * (pow2(loglogScaleB - 0.5) + b25- 1.25) );
Lambda4Save = Lambda5Save;
for (int iter = 0; iter < NITER; ++iter) {
logScale = 2. * log(MB/Lambda4Save);
loglogScale = log(logScale);
correction = 1. - b14 * loglogScale / logScale
+ pow2(b14 / logScale) * (pow2(loglogScale - 0.5) + b24 - 1.25);
valueIter = valueB / correction;
Lambda4Save = MB * exp( -6. * M_PI / (25. * valueIter) );
}
// Find Lambda_3 at m_c.
double logScaleC = 2. * log(MC/Lambda4Save);
double loglogScaleC = log(logScaleC);
double valueC = 12. * M_PI / (25. * logScaleC)
* (1. - b14 * loglogScaleC / logScaleC
+ pow2(b14 / logScaleC) * (pow2(loglogScaleC - 0.5) + b24 - 1.25) );
Lambda3Save = Lambda4Save;
for (int iter = 0; iter < NITER; ++iter) {
logScale = 2. * log(MC/Lambda3Save);
loglogScale = log(logScale);
correction = 1. - b13 * loglogScale / logScale
+ pow2(b13 / logScale) * (pow2(loglogScale - 0.5) + b23 - 1.25);
valueIter = valueC / correction;
Lambda3Save = MC * exp( -6. * M_PI / (27. * valueIter) );
}
scale2Min = pow2(SAFETYMARGIN2 * Lambda3Save);
}
// Save squares of mass and Lambda values as well.
mc2 = pow2(MC);
mb2 = pow2(MB);
Lambda3Save2 = pow2(Lambda3Save);
Lambda4Save2 = pow2(Lambda4Save);
Lambda5Save2 = pow2(Lambda5Save);
valueNow = valueIn;
scale2Now = MZ * MZ;
isInit = true;
}
//--------------------------------------------------------------------------
// Calculate alpha_s value
double AlphaStrong::alphaS( double scale2) {
// Check for initialization and ensure minimal scale2 value.
if (!isInit) return 0.;
if (scale2 < scale2Min) scale2 = scale2Min;
// If equal to old scale then same answer.
if (scale2 == scale2Now && (order < 2 || lastCallToFull)) return valueNow;
scale2Now = scale2;
lastCallToFull = true;
// Fix alpha_s.
if (order == 0) {
valueNow = valueRef;
// First order alpha_s: differs by mass region.
} else if (order == 1) {
if (scale2 > mb2)
valueNow = 12. * M_PI / (23. * log(scale2/Lambda5Save2));
else if (scale2 > mc2)
valueNow = 12. * M_PI / (25. * log(scale2/Lambda4Save2));
else valueNow = 12. * M_PI / (27. * log(scale2/Lambda3Save2));
// Second order alpha_s: differs by mass region.
} else {
double Lambda2, b0, b1, b2;
if (scale2 > mb2) {
Lambda2 = Lambda5Save2;
b0 = 23.;
b1 = 348. / 529.;
b2 = 224687. / 242208.;
} else if (scale2 > mc2) {
Lambda2 = Lambda4Save2;
b0 = 25.;
b1 = 462. / 625.;
b2 = 548575. / 426888.;
} else {
Lambda2 = Lambda3Save2;
b0 = 27.;
b1 = 64. / 81.;
b2 = 938709. / 663552.;
}
double logScale = log(scale2/Lambda2);
double loglogScale = log(logScale);
valueNow = 12. * M_PI / (b0 * logScale)
* ( 1. - b1 * loglogScale / logScale
+ pow2(b1 / logScale) * (pow2(loglogScale - 0.5) + b2 - 1.25) );
}
// Done.
return valueNow;
}
//--------------------------------------------------------------------------
// Calculate alpha_s value, but only use up to first-order piece.
// (To be combined with alphaS2OrdCorr.)
double AlphaStrong::alphaS1Ord( double scale2) {
// Check for initialization and ensure minimal scale2 value.
if (!isInit) return 0.;
if (scale2 < scale2Min) scale2 = scale2Min;
// If equal to old scale then same answer.
if (scale2 == scale2Now && (order < 2 || !lastCallToFull)) return valueNow;
scale2Now = scale2;
lastCallToFull = false;
// Fix alpha_S.
if (order == 0) {
valueNow = valueRef;
// First/second order alpha_s: differs by mass region.
} else {
if (scale2 > mb2)
valueNow = 12. * M_PI / (23. * log(scale2/Lambda5Save2));
else if (scale2 > mc2)
valueNow = 12. * M_PI / (25. * log(scale2/Lambda4Save2));
else valueNow = 12. * M_PI / (27. * log(scale2/Lambda3Save2));
}
// Done.
return valueNow;
}
//--------------------------------------------------------------------------
// Calculates the second-order extra factor in alpha_s.
// (To be combined with alphaS1Ord.)
double AlphaStrong::alphaS2OrdCorr( double scale2) {
// Check for initialization and ensure minimal scale2 value.
if (!isInit) return 1.;
if (scale2 < scale2Min) scale2 = scale2Min;
// Only meaningful for second order calculations.
if (order < 2) return 1.;
// Second order correction term: differs by mass region.
double Lambda2, b1, b2;
if (scale2 > mb2) {
Lambda2 = Lambda5Save2;
b1 = 348. / 529.;
b2 = 224687. / 242208.;
} else if (scale2 > mc2) {
Lambda2 = Lambda4Save2;
b1 = 462. / 625.;
b2 = 548575. / 426888.;
} else {
Lambda2 = Lambda3Save2;
b1 = 64. / 81.;
b2 = 938709. / 663552.;
}
double logScale = log(scale2/Lambda2);
double loglogScale = log(logScale);
return ( 1. - b1 * loglogScale / logScale
+ pow2(b1 / logScale) * (pow2(loglogScale - 0.5) + b2 - 1.25) );
}
//==========================================================================
// The AlphaEM class.
//--------------------------------------------------------------------------
// Definitions of static variables.
// Z0 mass. Used for normalization scale.
const double AlphaEM::MZ = 91.188;
// Effective thresholds for electron, muon, light quarks, tau+c, b.
const double AlphaEM::Q2STEP[5] = {0.26e-6, 0.011, 0.25, 3.5, 90.};
// Running coefficients are sum charge2 / 3 pi in pure QED, here slightly
// enhanced for quarks to approximately account for QCD corrections.
const double AlphaEM::BRUNDEF[5] = {0.1061, 0.2122, 0.460, 0.700, 0.725};
//--------------------------------------------------------------------------
// Initialize alpha_EM calculation.
void AlphaEM::init(int orderIn, Settings* settingsPtr) {
// Order. Read in alpha_EM value at 0 and m_Z, and mass of Z.
order = orderIn;
alpEM0 = settingsPtr->parm("StandardModel:alphaEM0");
alpEMmZ = settingsPtr->parm("StandardModel:alphaEMmZ");
mZ2 = MZ * MZ;
// AlphaEM values at matching scales and matching b value.
if (order <= 0) return;
for (int i = 0; i < 5; ++i) bRun[i] = BRUNDEF[i];
// Step down from mZ to tau/charm threshold.
alpEMstep[4] = alpEMmZ / ( 1. + alpEMmZ * bRun[4]
* log(mZ2 / Q2STEP[4]) );
alpEMstep[3] = alpEMstep[4] / ( 1. - alpEMstep[4] * bRun[3]
* log(Q2STEP[3] / Q2STEP[4]) );
// Step up from me to light-quark threshold.
alpEMstep[0] = alpEM0;
alpEMstep[1] = alpEMstep[0] / ( 1. - alpEMstep[0] * bRun[0]
* log(Q2STEP[1] / Q2STEP[0]) );
alpEMstep[2] = alpEMstep[1] / ( 1. - alpEMstep[1] * bRun[1]
* log(Q2STEP[2] / Q2STEP[1]) );
// Fit b in range between light-quark and tau/charm to join smoothly.
bRun[2] = (1./alpEMstep[3] - 1./alpEMstep[2])
/ log(Q2STEP[2] / Q2STEP[3]);
}
//--------------------------------------------------------------------------
// Calculate alpha_EM value
double AlphaEM::alphaEM( double scale2) {
// Fix alphaEM; for order = -1 fixed at m_Z.
if (order == 0) return alpEM0;
if (order < 0) return alpEMmZ;
// Running alphaEM.
for (int i = 4; i >= 0; --i) if (scale2 > Q2STEP[i])
return alpEMstep[i] / (1. - bRun[i] * alpEMstep[i]
* log(scale2 / Q2STEP[i]) );
return alpEM0;
}
//==========================================================================
// The CoupSM class.
//--------------------------------------------------------------------------
// Definitions of static variables: charges and axial couplings.
const double CoupSM::efSave[20] = { 0., -1./3., 2./3., -1./3., 2./3., -1./3.,
2./3., -1./3., 2./3., 0., 0., -1., 0., -1., 0., -1., 0., -1., 0., 0.};
const double CoupSM::afSave[20] = { 0., -1., 1., -1., 1., -1., 1., -1., 1.,
0., 0., -1., 1., -1., 1., -1., 1., -1., 1., 0.};
//--------------------------------------------------------------------------
// Initialize electroweak mixing angle and couplings, and CKM matrix elements.
void CoupSM::init(Settings& settings, Rndm* rndmPtrIn) {
// Store input pointer;
rndmPtr = rndmPtrIn;
// Initialize the local AlphaStrong instance.
double alphaSvalue = settings.parm("SigmaProcess:alphaSvalue");
int alphaSorder = settings.mode("SigmaProcess:alphaSorder");
alphaSlocal.init( alphaSvalue, alphaSorder);
// Initialize the local AlphaEM instance.
int order = settings.mode("SigmaProcess:alphaEMorder");
alphaEMlocal.init( order, &settings);
// Read in electroweak mixing angle and the Fermi constant.
s2tW = settings.parm("StandardModel:sin2thetaW");
c2tW = 1. - s2tW;
s2tWbar = settings.parm("StandardModel:sin2thetaWbar");
GFermi = settings.parm("StandardModel:GF");
// Initialize electroweak couplings.
for (int i = 0; i < 20; ++i) {
vfSave[i] = afSave[i] - 4. * s2tWbar * efSave[i];
lfSave[i] = afSave[i] - 2. * s2tWbar * efSave[i];
rfSave[i] = - 2. * s2tWbar * efSave[i];
ef2Save[i] = pow2(efSave[i]);
vf2Save[i] = pow2(vfSave[i]);
af2Save[i] = pow2(afSave[i]);
efvfSave[i] = efSave[i] * vfSave[i];
vf2af2Save[i] = vf2Save[i] + af2Save[i];
}
// Read in CKM matrix element values and store them.
VCKMsave[1][1] = settings.parm("StandardModel:Vud");
VCKMsave[1][2] = settings.parm("StandardModel:Vus");
VCKMsave[1][3] = settings.parm("StandardModel:Vub");
VCKMsave[2][1] = settings.parm("StandardModel:Vcd");
VCKMsave[2][2] = settings.parm("StandardModel:Vcs");
VCKMsave[2][3] = settings.parm("StandardModel:Vcb");
VCKMsave[3][1] = settings.parm("StandardModel:Vtd");
VCKMsave[3][2] = settings.parm("StandardModel:Vts");
VCKMsave[3][3] = settings.parm("StandardModel:Vtb");
// Also allow for the potential existence of a fourth generation.
VCKMsave[1][4] = settings.parm("FourthGeneration:VubPrime");
VCKMsave[2][4] = settings.parm("FourthGeneration:VcbPrime");
VCKMsave[3][4] = settings.parm("FourthGeneration:VtbPrime");
VCKMsave[4][1] = settings.parm("FourthGeneration:VtPrimed");
VCKMsave[4][2] = settings.parm("FourthGeneration:VtPrimes");
VCKMsave[4][3] = settings.parm("FourthGeneration:VtPrimeb");
VCKMsave[4][4] = settings.parm("FourthGeneration:VtPrimebPrime");
// Calculate squares of matrix elements.
for(int i = 1; i < 5; ++i) for(int j = 1; j < 5; ++j)
V2CKMsave[i][j] = pow2(VCKMsave[i][j]);
// Sum VCKM^2_out sum for given incoming flavour, excluding top as partner.
V2CKMout[1] = V2CKMsave[1][1] + V2CKMsave[2][1];
V2CKMout[2] = V2CKMsave[1][1] + V2CKMsave[1][2] + V2CKMsave[1][3];
V2CKMout[3] = V2CKMsave[1][2] + V2CKMsave[2][2];
V2CKMout[4] = V2CKMsave[2][1] + V2CKMsave[2][2] + V2CKMsave[2][3];
V2CKMout[5] = V2CKMsave[1][3] + V2CKMsave[2][3];
V2CKMout[6] = V2CKMsave[3][1] + V2CKMsave[3][2] + V2CKMsave[3][3];
V2CKMout[7] = V2CKMsave[1][4] + V2CKMsave[2][4];
V2CKMout[8] = V2CKMsave[4][1] + V2CKMsave[4][2] + V2CKMsave[4][3];
for (int i = 11; i <= 18; ++i) V2CKMout[i] = 1.;
}
//--------------------------------------------------------------------------
// Return CKM value for incoming flavours (sign irrelevant).
double CoupSM::VCKMid(int id1, int id2) {
// Use absolute sign (want to cover both f -> f' W and f fbar' -> W).
int id1Abs = abs(id1);
int id2Abs = abs(id2);
if (id1Abs == 0 || id2Abs == 0 || (id1Abs + id2Abs)%2 != 1) return 0.;
// Ensure proper order before reading out from VCKMsave or lepton match.
if (id1Abs%2 == 1) swap(id1Abs, id2Abs);
if (id1Abs <= 8 && id2Abs <= 8) return VCKMsave[id1Abs/2][(id2Abs + 1)/2];
if ( (id1Abs == 12 || id1Abs == 14 || id1Abs == 16 || id1Abs == 18)
&& id2Abs == id1Abs - 1 ) return 1.;
// No more valid cases.
return 0.;
}
//--------------------------------------------------------------------------
// Return squared CKM value for incoming flavours (sign irrelevant).
double CoupSM::V2CKMid(int id1, int id2) {
// Use absolute sign (want to cover both f -> f' W and f fbar' -> W).
int id1Abs = abs(id1);
int id2Abs = abs(id2);
if (id1Abs == 0 || id2Abs == 0 || (id1Abs + id2Abs)%2 != 1) return 0.;
// Ensure proper order before reading out from V2CKMsave or lepton match.
if (id1Abs%2 == 1) swap(id1Abs, id2Abs);
if (id1Abs <= 8 && id2Abs <= 8) return V2CKMsave[id1Abs/2][(id2Abs + 1)/2];
if ( (id1Abs == 12 || id1Abs == 14 || id1Abs == 16 || id1Abs == 18)
&& id2Abs == id1Abs - 1 ) return 1.;
// No more valid cases.
return 0.;
}
//--------------------------------------------------------------------------
// Pick an outgoing flavour for given incoming one, given CKM mixing.
int CoupSM::V2CKMpick(int id) {
// Initial values.
int idIn = abs(id);
int idOut = 0;
// Quarks: need to make random choice.
if (idIn >= 1 && idIn <= 8) {
double V2CKMrndm = rndmPtr->flat() * V2CKMout[idIn];
if (idIn == 1) idOut = (V2CKMrndm < V2CKMsave[1][1]) ? 2 : 4;
else if (idIn == 2) idOut = (V2CKMrndm < V2CKMsave[1][1]) ? 1
: ( (V2CKMrndm < V2CKMsave[1][1] + V2CKMsave[1][2]) ? 3 : 5 );
else if (idIn == 3) idOut = (V2CKMrndm < V2CKMsave[1][2]) ? 2 : 4;
else if (idIn == 4) idOut = (V2CKMrndm < V2CKMsave[2][1]) ? 1
: ( (V2CKMrndm < V2CKMsave[2][1] + V2CKMsave[2][2]) ? 3 : 5 );
else if (idIn == 5) idOut = (V2CKMrndm < V2CKMsave[1][3]) ? 2 : 4;
else if (idIn == 6) idOut = (V2CKMrndm < V2CKMsave[3][1]) ? 1
: ( (V2CKMrndm < V2CKMsave[3][1] + V2CKMsave[3][2]) ? 3 : 5 );
else if (idIn == 7) idOut = (V2CKMrndm < V2CKMsave[1][4]) ? 2 : 4;
else if (idIn == 8) idOut = (V2CKMrndm < V2CKMsave[4][1]) ? 1
: ( (V2CKMrndm < V2CKMsave[4][1] + V2CKMsave[4][2]) ? 3 : 5 );
// Leptons: unambiguous.
} else if (idIn >= 11 && idIn <= 18) {
if (idIn%2 == 1) idOut = idIn + 1;
else idOut = idIn - 1;
}
// Done. Return with sign.
return ( (id > 0) ? idOut : -idOut );
}
//==========================================================================
} // end namespace Pythia8
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