diff --git a/Shower/QTilde/SplittingFunctions/SudakovFormFactor.cc b/Shower/QTilde/SplittingFunctions/SudakovFormFactor.cc --- a/Shower/QTilde/SplittingFunctions/SudakovFormFactor.cc +++ b/Shower/QTilde/SplittingFunctions/SudakovFormFactor.cc @@ -1,1224 +1,1225 @@ // -*- C++ -*- // // SudakovFormFactor.cc is a part of Herwig - A multi-purpose Monte Carlo event generator // Copyright (C) 2002-2019 The Herwig Collaboration // // Herwig is licenced under version 3 of the GPL, see COPYING for details. // Please respect the MCnet academic guidelines, see GUIDELINES for details. // // // This is the implementation of the non-inlined, non-templated member // functions of the SudakovFormFactor class. // #include "SudakovFormFactor.h" #include "ThePEG/Interface/ClassDocumentation.h" #include "ThePEG/Persistency/PersistentOStream.h" #include "ThePEG/Persistency/PersistentIStream.h" #include "ThePEG/Interface/Reference.h" #include "ThePEG/Interface/Switch.h" #include "ThePEG/Interface/Parameter.h" #include "Herwig/Shower/QTilde/Kinematics/ShowerKinematics.h" #include "Herwig/Shower/QTilde/Base/ShowerParticle.h" #include "ThePEG/Utilities/DescribeClass.h" #include "Herwig/Shower/QTilde/QTildeShowerHandler.h" #include "Herwig/Shower/QTilde/Kinematics/FS_QTildeShowerKinematics1to2.h" #include "Herwig/Shower/QTilde/Kinematics/IS_QTildeShowerKinematics1to2.h" #include "Herwig/Shower/QTilde/Kinematics/Decay_QTildeShowerKinematics1to2.h" #include "Herwig/Shower/QTilde/Kinematics/KinematicHelpers.h" #include "SudakovCutOff.h" #include using std::array; using namespace Herwig; DescribeClass describeSudakovFormFactor ("Herwig::SudakovFormFactor",""); void SudakovFormFactor::persistentOutput(PersistentOStream & os) const { os << splittingFn_ << alpha_ << pdfmax_ << particles_ << pdffactor_ << cutoff_; } void SudakovFormFactor::persistentInput(PersistentIStream & is, int) { is >> splittingFn_ >> alpha_ >> pdfmax_ >> particles_ >> pdffactor_ >> cutoff_; } void SudakovFormFactor::Init() { static ClassDocumentation documentation ("The SudakovFormFactor class is the base class for the implementation of Sudakov" " form factors in Herwig"); static Reference interfaceSplittingFunction("SplittingFunction", "A reference to the SplittingFunction object", &Herwig::SudakovFormFactor::splittingFn_, false, false, true, false); static Reference interfaceAlpha("Alpha", "A reference to the Alpha object", &Herwig::SudakovFormFactor::alpha_, false, false, true, false); static Reference interfaceCutoff("Cutoff", "A reference to the SudakovCutOff object", &Herwig::SudakovFormFactor::cutoff_, false, false, true, false); static Parameter interfacePDFmax ("PDFmax", "Maximum value of PDF weight. ", &SudakovFormFactor::pdfmax_, 35.0, 1.0, 1000000.0, false, false, Interface::limited); static Switch interfacePDFFactor ("PDFFactor", "Include additional factors in the overestimate for the PDFs", &SudakovFormFactor::pdffactor_, 0, false, false); static SwitchOption interfacePDFFactorNo (interfacePDFFactor, "No", "Don't include any factors", 0); static SwitchOption interfacePDFFactorOverZ (interfacePDFFactor, "OverZ", "Include an additional factor of 1/z", 1); static SwitchOption interfacePDFFactorOverOneMinusZ (interfacePDFFactor, "OverOneMinusZ", "Include an additional factor of 1/(1-z)", 2); static SwitchOption interfacePDFFactorOverZOneMinusZ (interfacePDFFactor, "OverZOneMinusZ", "Include an additional factor of 1/z/(1-z)", 3); static SwitchOption interfacePDFFactorOverRootZ (interfacePDFFactor, "OverRootZ", "Include an additional factor of 1/sqrt(z)", 4); static SwitchOption interfacePDFFactorRootZ (interfacePDFFactor, "RootZ", "Include an additional factor of sqrt(z)", 5); } bool SudakovFormFactor::alphaSVeto(Energy2 pt2) const { double ratio=alphaSVetoRatio(pt2,1.); return UseRandom::rnd() > ratio; } double SudakovFormFactor::alphaSVetoRatio(Energy2 pt2, double factor) const { factor *= ShowerHandler::currentHandler()->renormalizationScaleFactor(); return alpha_->ratio(pt2, factor); } bool SudakovFormFactor::PDFVeto(const Energy2 t, const double x, const tcPDPtr parton0, const tcPDPtr parton1, Ptr::transient_const_pointer beam) const { double ratio=PDFVetoRatio(t,x,parton0,parton1,beam,1.); return UseRandom::rnd() > ratio; } double SudakovFormFactor::PDFVetoRatio(const Energy2 t, const double x, const tcPDPtr parton0, const tcPDPtr parton1, Ptr::transient_const_pointer beam,double factor) const { assert(pdf_); Energy2 theScale = t * sqr(ShowerHandler::currentHandler()->factorizationScaleFactor()*factor); if (theScale < sqr(freeze_)) theScale = sqr(freeze_); const double newpdf=pdf_->xfx(beam,parton0,theScale,x/z()); if(newpdf<=0.) return 0.; const double oldpdf=pdf_->xfx(beam,parton1,theScale,x); if(oldpdf<=0.) return 1.; const double ratio = newpdf/oldpdf; double maxpdf = pdfmax_; switch (pdffactor_) { case 0: break; case 1: maxpdf /= z(); break; case 2: maxpdf /= 1.-z(); break; case 3: maxpdf /= (z()*(1.-z())); break; case 4: maxpdf /= sqrt(z()); break; case 5: maxpdf *= sqrt(z()); break; default : throw Exception() << "SudakovFormFactor::PDFVetoRatio invalid PDFfactor = " << pdffactor_ << Exception::runerror; } if (ratio > maxpdf) { generator()->log() << "PDFVeto warning: Ratio > " << name() << ":PDFmax (by a factor of " << ratio/maxpdf <<") for " << parton0->PDGName() << " to " << parton1->PDGName() << "\n"; } return ratio/maxpdf ; } void SudakovFormFactor::addSplitting(const IdList & in) { bool add=true; for(unsigned int ix=0;ix::iterator it=particles_.begin(); it!=particles_.end();++it) { if(it->size()==in.size()) { bool match=true; for(unsigned int iy=0;iy::iterator itemp=it; --itemp; particles_.erase(it); it = itemp; } } } } void SudakovFormFactor::guesstz(Energy2 t1,unsigned int iopt, const IdList &ids, double enhance,bool ident, double detune, Energy2 &t_main, double &z_main){ unsigned int pdfopt = iopt!=1 ? 0 : pdffactor_; double lower = splittingFn_->integOverP(zlimits_.first ,ids,pdfopt); double upper = splittingFn_->integOverP(zlimits_.second,ids,pdfopt); double c = 1./((upper - lower) * alpha_->overestimateValue()/Constants::twopi*enhance*detune); double r = UseRandom::rnd(); assert(iopt<=2); if(iopt==1) { c/=pdfmax_; //symmetry of FS gluon splitting if(ident) c*=0.5; } else if(iopt==2) c*=-1.; // guessing t if(iopt!=2 || c*log(r)invIntegOverP(lower + UseRandom::rnd() *(upper - lower),ids,pdfopt); } bool SudakovFormFactor::guessTimeLike(Energy2 &t,Energy2 tmin,double enhance, double detune) { Energy2 told = t; // calculate limits on z and if lower>upper return if(!computeTimeLikeLimits(t)) return false; // guess values of t and z guesstz(told,0,ids_,enhance,ids_[1]==ids_[2],detune,t,z_); // actual values for z-limits if(!computeTimeLikeLimits(t)) return false; if(tupper return if(!computeSpaceLikeLimits(t,x)) return false; // guess values of t and z guesstz(told,1,ids_,enhance,ids_[1]==ids_[2],detune,t,z_); // actual values for z-limits if(!computeSpaceLikeLimits(t,x)) return false; if(t zlimits_.second) return true; Energy2 m02 = (ids_[0]->id()!=ParticleID::g && ids_[0]->id()!=ParticleID::gamma) ? masssquared_[0] : Energy2(); Energy2 pt2 = QTildeKinematics::pT2_FSR(t,z(),m02,masssquared_[1],masssquared_[2], masssquared_[1],masssquared_[2]); // if pt2<0 veto if (pt2pT2min()) return true; // otherwise calculate pt and return pT_ = sqrt(pt2); return false; } ShoKinPtr SudakovFormFactor::generateNextTimeBranching(const Energy startingScale, const IdList &ids, const RhoDMatrix & rho, double enhance, double detuning) { // First reset the internal kinematics variables that can // have been eventually set in the previous call to the method. q_ = ZERO; z_ = 0.; phi_ = 0.; // perform initialization Energy2 tmax(sqr(startingScale)),tmin; initialize(ids,tmin); // check max > min if(tmax<=tmin) return ShoKinPtr(); // calculate next value of t using veto algorithm Energy2 t(tmax); // no shower variations to calculate if(ShowerHandler::currentHandler()->showerVariations().empty()){ // Without variations do the usual Veto algorithm // No need for more if-statements in this loop. do { if(!guessTimeLike(t,tmin,enhance,detuning)) break; } while(PSVeto(t) || SplittingFnVeto(z()*(1.-z())*t,ids,true,rho,detuning) || alphaSVeto(splittingFn()->pTScale() ? sqr(z()*(1.-z()))*t : z()*(1.-z())*t)); } else { bool alphaRew(true),PSRew(true),SplitRew(true); do { if(!guessTimeLike(t,tmin,enhance,detuning)) break; PSRew=PSVeto(t); if (PSRew) continue; SplitRew=SplittingFnVeto(z()*(1.-z())*t,ids,true,rho,detuning); alphaRew=alphaSVeto(splittingFn()->pTScale() ? sqr(z()*(1.-z()))*t : z()*(1.-z())*t); double factor=alphaSVetoRatio(splittingFn()->pTScale() ? sqr(z()*(1.-z()))*t : z()*(1.-z())*t,1.)* SplittingFnVetoRatio(z()*(1.-z())*t,ids,true,rho,detuning); tShowerHandlerPtr ch = ShowerHandler::currentHandler(); if( !(SplitRew || alphaRew) ) { //Emission q_ = t > ZERO ? Energy(sqrt(t)) : -1.*MeV; if (q_ <= ZERO) break; } for ( map::const_iterator var = ch->showerVariations().begin(); var != ch->showerVariations().end(); ++var ) { if ( ( ch->firstInteraction() && var->second.firstInteraction ) || ( !ch->firstInteraction() && var->second.secondaryInteractions ) ) { double newfactor = alphaSVetoRatio(splittingFn()->pTScale() ? sqr(z()*(1.-z()))*t : z()*(1.-z())*t,var->second.renormalizationScaleFactor) * SplittingFnVetoRatio(z()*(1.-z())*t,ids,true,rho,detuning); double varied; if ( SplitRew || alphaRew ) { // No Emission varied = (1. - newfactor) / (1. - factor); } else { // Emission varied = newfactor / factor; } map::iterator wi = ch->currentWeights().find(var->first); if ( wi != ch->currentWeights().end() ) wi->second *= varied; else { assert(false); //ch->currentWeights()[var->first] = varied; } } } } while(PSRew || SplitRew || alphaRew); } q_ = t > ZERO ? Energy(sqrt(t)) : -1.*MeV; if(q_ < ZERO) return ShoKinPtr(); // return the ShowerKinematics object return new_ptr(FS_QTildeShowerKinematics1to2(q_,z(),phi(),pT(),this)); } ShoKinPtr SudakovFormFactor:: generateNextSpaceBranching(const Energy startingQ, const IdList &ids, double x, const RhoDMatrix & rho, double enhance, Ptr::transient_const_pointer beam, double detuning) { // First reset the internal kinematics variables that can // have been eventually set in the previous call to the method. q_ = ZERO; z_ = 0.; phi_ = 0.; // perform the initialization Energy2 tmax(sqr(startingQ)),tmin; initialize(ids,tmin); // check max > min if(tmax<=tmin) return ShoKinPtr(); // calculate next value of t using veto algorithm Energy2 t(tmax),pt2(ZERO); // no shower variations if(ShowerHandler::currentHandler()->showerVariations().empty()){ // Without variations do the usual Veto algorithm // No need for more if-statements in this loop. do { if(!guessSpaceLike(t,tmin,x,enhance,detuning)) break; pt2 = QTildeKinematics::pT2_ISR(t,z(),masssquared_[2]); } while(pt2 < cutoff_->pT2min()|| z() > zlimits_.second|| SplittingFnVeto((1.-z())*t/z(),ids,false,rho,detuning)|| alphaSVeto(splittingFn()->pTScale() ? sqr(1.-z())*t : (1.-z())*t)|| PDFVeto(t,x,ids[0],ids[1],beam)); } // shower variations else { bool alphaRew(true),PDFRew(true),ptRew(true),zRew(true),SplitRew(true); do { if(!guessSpaceLike(t,tmin,x,enhance,detuning)) break; pt2 = QTildeKinematics::pT2_ISR(t,z(),masssquared_[2]); ptRew=pt2 < cutoff_->pT2min(); zRew=z() > zlimits_.second; if (ptRew||zRew) continue; SplitRew=SplittingFnVeto((1.-z())*t/z(),ids,false,rho,detuning); alphaRew=alphaSVeto(splittingFn()->pTScale() ? sqr(1.-z())*t : (1.-z())*t); PDFRew=PDFVeto(t,x,ids[0],ids[1],beam); double factor=PDFVetoRatio(t,x,ids[0],ids[1],beam,1.)* alphaSVetoRatio(splittingFn()->pTScale() ? sqr(1.-z())*t : (1.-z())*t,1.)* SplittingFnVetoRatio((1.-z())*t/z(),ids,false,rho,detuning); tShowerHandlerPtr ch = ShowerHandler::currentHandler(); if( !(PDFRew || SplitRew || alphaRew) ) { //Emission q_ = t > ZERO ? Energy(sqrt(t)) : -1.*MeV; if (q_ <= ZERO) break; } for ( map::const_iterator var = ch->showerVariations().begin(); var != ch->showerVariations().end(); ++var ) { if ( ( ch->firstInteraction() && var->second.firstInteraction ) || ( !ch->firstInteraction() && var->second.secondaryInteractions ) ) { double newfactor = PDFVetoRatio(t,x,ids[0],ids[1],beam,var->second.factorizationScaleFactor)* alphaSVetoRatio(splittingFn()->pTScale() ? sqr(1.-z())*t : (1.-z())*t,var->second.renormalizationScaleFactor) *SplittingFnVetoRatio((1.-z())*t/z(),ids,false,rho,detuning); double varied; if( PDFRew || SplitRew || alphaRew) { // No Emission varied = (1. - newfactor) / (1. - factor); } else { // Emission varied = newfactor / factor; } map::iterator wi = ch->currentWeights().find(var->first); if ( wi != ch->currentWeights().end() ) wi->second *= varied; else { assert(false); //ch->currentWeights()[var->first] = varied; } } } } while( PDFRew || SplitRew || alphaRew); } if(t > ZERO && zlimits_.first < zlimits_.second) q_ = sqrt(t); else return ShoKinPtr(); pT_ = sqrt(pt2); // create the ShowerKinematics and return it return new_ptr(IS_QTildeShowerKinematics1to2(q_,z(),phi(),pT(),this)); } void SudakovFormFactor::initialize(const IdList & ids, Energy2 & tmin) { ids_=ids; tmin = 4.*cutoff_->pT2min(); masses_ = cutoff_->virtualMasses(ids); masssquared_.clear(); for(unsigned int ix=0;ix0) tmin=max(masssquared_[ix],tmin); } } ShoKinPtr SudakovFormFactor::generateNextDecayBranching(const Energy startingScale, const Energy stoppingScale, const Energy minmass, const IdList &ids, const RhoDMatrix & rho, double enhance, double detuning) { // First reset the internal kinematics variables that can // have been eventually set in the previous call to this method. q_ = Constants::MaxEnergy; z_ = 0.; phi_ = 0.; // perform initialisation Energy2 tmax(sqr(stoppingScale)),tmin; initialize(ids,tmin); tmin=sqr(startingScale); // check some branching possible if(tmax<=tmin) return ShoKinPtr(); // perform the evolution Energy2 t(tmin),pt2(-MeV2); do { if(!guessDecay(t,tmax,minmass,enhance,detuning)) break; pt2 = QTildeKinematics::pT2_Decay(t,z(),masssquared_[0],masssquared_[2]); } while(SplittingFnVeto((1.-z())*t/z(),ids,true,rho,detuning)|| alphaSVeto(splittingFn()->pTScale() ? sqr(1.-z())*t : (1.-z())*t ) || pt2pT2min() || t*(1.-z())>masssquared_[0]-sqr(minmass)); if(t > ZERO) { q_ = sqrt(t); pT_ = sqrt(pt2); } else return ShoKinPtr(); phi_ = 0.; // create the ShowerKinematics object return new_ptr(Decay_QTildeShowerKinematics1to2(q_,z(),phi(),pT(),this)); } bool SudakovFormFactor::guessDecay(Energy2 &t,Energy2 tmax, Energy minmass, - double enhance, double detune) { + double enhance, double detune) { + minmass = max(minmass,GeV); // previous scale Energy2 told = t; // overestimated limits on z if(tmaxpT2min()+ - 0.25*sqr(masssquared_[2])/tm2)/tm - +0.5*masssquared_[2]/tm2); + 1.-sqrt(masssquared_[2]+cutoff_->pT2min()+ + 0.25*sqr(masssquared_[2])/tm2)/tm + +0.5*masssquared_[2]/tm2); if(zlimits_.secondpT2min()+ 0.25*sqr(masssquared_[2])/tm2)/tm +0.5*masssquared_[2]/tm2); if(t>tmax||zlimits_.secondpT2min(); // special case for gluon radiating if(ids_[0]->id()==ParticleID::g||ids_[0]->id()==ParticleID::gamma) { // no emission possible if(t<16.*(masssquared_[1]+pT2min)) { t=-1.*GeV2; return false; } // overestimate of the limits zlimits_.first = 0.5*(1.-sqrt(1.-4.*sqrt((masssquared_[1]+pT2min)/t))); zlimits_.second = 1.-zlimits_.first; } // special case for radiated particle is gluon else if(ids_[2]->id()==ParticleID::g||ids_[2]->id()==ParticleID::gamma) { zlimits_.first = sqrt((masssquared_[1]+pT2min)/t); zlimits_.second = 1.-sqrt((masssquared_[2]+pT2min)/t); } else if(ids_[1]->id()==ParticleID::g||ids_[1]->id()==ParticleID::gamma) { zlimits_.second = sqrt((masssquared_[2]+pT2min)/t); zlimits_.first = 1.-sqrt((masssquared_[1]+pT2min)/t); } else { zlimits_.first = (masssquared_[1]+pT2min)/t; zlimits_.second = 1.-(masssquared_[2]+pT2min)/t; } if(zlimits_.first>=zlimits_.second) { t=-1.*GeV2; return false; } return true; } bool SudakovFormFactor::computeSpaceLikeLimits(Energy2 & t, double x) { if (t < 1e-20 * GeV2) { t=-1.*GeV2; return false; } // compute the limits zlimits_.first = x; double yy = 1.+0.5*masssquared_[2]/t; zlimits_.second = yy - sqrt(sqr(yy)-1.+cutoff_->pT2min()/t); // return false if lower>upper if(zlimits_.second(particle.parents()[0]) : tShowerParticlePtr(); } else { mother = particle.children().size()==2 ? dynamic_ptr_cast(&particle) : tShowerParticlePtr(); } tShowerParticlePtr partner; while(mother) { tPPtr otherChild; if(forward) { for (unsigned int ix=0;ixchildren().size();++ix) { if(mother->children()[ix]!=child) { otherChild = mother->children()[ix]; break; } } } else { otherChild = mother->children()[1]; } tShowerParticlePtr other = dynamic_ptr_cast(otherChild); if((inter==ShowerInteraction::QCD && otherChild->dataPtr()->coloured()) || (inter==ShowerInteraction::QED && otherChild->dataPtr()->charged())) { partner = other; break; } if(forward && !other->isFinalState()) { partner = dynamic_ptr_cast(mother); break; } child = mother; if(forward) { mother = ! mother->parents().empty() ? dynamic_ptr_cast(mother->parents()[0]) : tShowerParticlePtr(); } else { if(mother->children()[0]->children().size()!=2) break; tShowerParticlePtr mtemp = dynamic_ptr_cast(mother->children()[0]); if(!mtemp) break; else mother=mtemp; } } if(!partner) { if(forward) { partner = dynamic_ptr_cast( child)->partner(); } else { if(mother) { tShowerParticlePtr parent; if(!mother->children().empty()) { parent = dynamic_ptr_cast(mother->children()[0]); } if(!parent) { parent = dynamic_ptr_cast(mother); } partner = parent->partner(); } else { partner = dynamic_ptr_cast(&particle)->partner(); } } } return partner; } pair softPhiMin(double phi0, double phi1, double A, double B, double C, double D) { double c01 = cos(phi0 - phi1); double s01 = sin(phi0 - phi1); double s012(sqr(s01)), c012(sqr(c01)); double A2(A*A), B2(B*B), C2(C*C), D2(D*D); if(abs(B/A)<1e-10 && abs(D/C)<1e-10) return make_pair(phi0,phi0+Constants::pi); double root = sqr(B2)*C2*D2*sqr(s012) + 2.*A*B2*B*C2*C*D*c01*s012 + 2.*A*B2*B*C*D2*D*c01*s012 + 4.*A2*B2*C2*D2*c012 - A2*B2*C2*D2*s012 - A2*B2*sqr(D2)*s012 - sqr(B2)*sqr(C2)*s012 - sqr(B2)*C2*D2*s012 - 4.*A2*A*B*C*D2*D*c01 - 4.*A*B2*B*C2*C*D*c01 + sqr(A2)*sqr(D2) + 2.*A2*B2*C2*D2 + sqr(B2)*sqr(C2); if(root<0.) return make_pair(phi0,phi0+Constants::pi); root = sqrt(root); double denom = (-2.*A*B*C*D*c01 + A2*D2 + B2*C2); double denom2 = (-B*C*c01 + A*D); double num = B2*C*D*s012; double y1 = B*s01*(-C*(num + root) + D*denom) / denom2; double y2 = B*s01*(-C*(num - root) + D*denom) / denom2; double x1 = -(num + root ); double x2 = -(num - root ); if(denom<0.) { y1*=-1.; y2*=-1.; x1*=-1.; x2*=-1.; } return make_pair(atan2(y1,x1) + phi0,atan2(y2,x2) + phi0); } } double SudakovFormFactor::generatePhiForward(ShowerParticle & particle, const IdList & ids, ShoKinPtr kinematics, const RhoDMatrix & rho) { // no correlations, return flat phi if(! dynamic_ptr_cast(ShowerHandler::currentHandler())->correlations()) return Constants::twopi*UseRandom::rnd(); // get the kinematic variables double z = kinematics->z(); Energy2 t = z*(1.-z)*sqr(kinematics->scale()); Energy pT = kinematics->pT(); // if soft correlations Energy2 pipj,pik; bool canBeSoft[2] = {ids[1]->id()==ParticleID::g || ids[1]->id()==ParticleID::gamma, ids[2]->id()==ParticleID::g || ids[2]->id()==ParticleID::gamma }; array pjk; array Ek; Energy Ei,Ej; Energy2 m12(ZERO),m22(ZERO); InvEnergy2 aziMax(ZERO); bool softAllowed = dynamic_ptr_cast(ShowerHandler::currentHandler())->softCorrelations()&& (canBeSoft[0] || canBeSoft[1]); if(softAllowed) { // find the partner for the soft correlations tShowerParticlePtr partner=findCorrelationPartner(particle,true,splittingFn()->interactionType()); // remember we want the softer gluon bool swapOrder = !canBeSoft[1] || (canBeSoft[0] && canBeSoft[1] && z < 0.5); double zFact = !swapOrder ? (1.-z) : z; // compute the transforms to the shower reference frame // first the boost Lorentz5Momentum pVect = particle.showerBasis()->pVector(); Lorentz5Momentum nVect = particle.showerBasis()->nVector(); Boost beta_bb; if(particle.showerBasis()->frame()==ShowerBasis::BackToBack) { beta_bb = -(pVect + nVect).boostVector(); } else if(particle.showerBasis()->frame()==ShowerBasis::Rest) { beta_bb = -pVect.boostVector(); } else assert(false); pVect.boost(beta_bb); nVect.boost(beta_bb); Axis axis; if(particle.showerBasis()->frame()==ShowerBasis::BackToBack) { axis = pVect.vect().unit(); } else if(particle.showerBasis()->frame()==ShowerBasis::Rest) { axis = nVect.vect().unit(); } else assert(false); // and then the rotation LorentzRotation rot; if(axis.perp2()>0.) { double sinth(sqrt(sqr(axis.x())+sqr(axis.y()))); rot.rotate(acos(axis.z()),Axis(-axis.y()/sinth,axis.x()/sinth,0.)); } else if(axis.z()<0.) { rot.rotate(Constants::pi,Axis(1.,0.,0.)); } rot.invert(); pVect *= rot; nVect *= rot; // shower parameters Energy2 pn = pVect*nVect, m2 = pVect.m2(); double alpha0 = particle.showerParameters().alpha; double beta0 = 0.5/alpha0/pn* (sqr(particle.dataPtr()->mass())-sqr(alpha0)*m2+sqr(particle.showerParameters().pt)); Lorentz5Momentum qperp0(particle.showerParameters().ptx, particle.showerParameters().pty,ZERO,ZERO); assert(partner); Lorentz5Momentum pj = partner->momentum(); pj.boost(beta_bb); pj *= rot; // compute the two phi independent dot products pik = 0.5*zFact*(sqr(alpha0)*m2 - sqr(particle.showerParameters().pt) + 2.*alpha0*beta0*pn ) +0.5*sqr(pT)/zFact; Energy2 dot1 = pj*pVect; Energy2 dot2 = pj*nVect; Energy2 dot3 = pj*qperp0; pipj = alpha0*dot1+beta0*dot2+dot3; // compute the constants for the phi dependent dot product pjk[0] = zFact*(alpha0*dot1+dot3-0.5*dot2/pn*(alpha0*m2-sqr(particle.showerParameters().pt)/alpha0)) +0.5*sqr(pT)*dot2/pn/zFact/alpha0; pjk[1] = (pj.x() - dot2/alpha0/pn*qperp0.x())*pT; pjk[2] = (pj.y() - dot2/alpha0/pn*qperp0.y())*pT; m12 = sqr(particle.dataPtr()->mass()); m22 = sqr(partner->dataPtr()->mass()); if(swapOrder) { pjk[1] *= -1.; pjk[2] *= -1.; } Ek[0] = zFact*(alpha0*pVect.t()-0.5*nVect.t()/pn*(alpha0*m2-sqr(particle.showerParameters().pt)/alpha0)) +0.5*sqr(pT)*nVect.t()/pn/zFact/alpha0; Ek[1] = -nVect.t()/alpha0/pn*qperp0.x()*pT; Ek[2] = -nVect.t()/alpha0/pn*qperp0.y()*pT; if(swapOrder) { Ek[1] *= -1.; Ek[2] *= -1.; } Energy mag2=sqrt(sqr(Ek[1])+sqr(Ek[2])); Ei = alpha0*pVect.t()+beta0*nVect.t(); Ej = pj.t(); double phi0 = atan2(-pjk[2],-pjk[1]); if(phi0<0.) phi0 += Constants::twopi; double phi1 = atan2(-Ek[2],-Ek[1]); if(phi1<0.) phi1 += Constants::twopi; double xi_min = pik/Ei/(Ek[0]+mag2), xi_max = pik/Ei/(Ek[0]-mag2), xi_ij = pipj/Ei/Ej; if(xi_min>xi_max) swap(xi_min,xi_max); if(xi_min>xi_ij) softAllowed = false; Energy2 mag = sqrt(sqr(pjk[1])+sqr(pjk[2])); if(dynamic_ptr_cast(ShowerHandler::currentHandler())->softCorrelations()==1) { aziMax = -m12/sqr(pik) -m22/sqr(pjk[0]+mag) +2.*pipj/pik/(pjk[0]-mag); } else if(dynamic_ptr_cast(ShowerHandler::currentHandler())->softCorrelations()==2) { double A = (pipj*Ek[0]- Ej*pik)/Ej/sqr(Ej); double B = -sqrt(sqr(pipj)*(sqr(Ek[1])+sqr(Ek[2])))/Ej/sqr(Ej); double C = pjk[0]/sqr(Ej); double D = -sqrt(sqr(pjk[1])+sqr(pjk[2]))/sqr(Ej); pair minima = softPhiMin(phi0,phi1,A,B,C,D); aziMax = 0.5/pik/(Ek[0]-mag2)*(Ei-m12*(Ek[0]-mag2)/pik + max(Ej*(A+B*cos(minima.first -phi1))/(C+D*cos(minima.first -phi0)), Ej*(A+B*cos(minima.second-phi1))/(C+D*cos(minima.second-phi0)))); } else assert(false); } // if spin correlations vector > wgts; if(dynamic_ptr_cast(ShowerHandler::currentHandler())->spinCorrelations()) { // calculate the weights wgts = splittingFn()->generatePhiForward(z,t,ids,rho); } else { wgts = {{ {0, 1.} }}; } // generate the azimuthal angle double phi,wgt; static const Complex ii(0.,1.); unsigned int ntry(0); double phiMax(0.),wgtMax(0.); do { phi = Constants::twopi*UseRandom::rnd(); // first the spin correlations bit (gives 1 if correlations off) Complex spinWgt = 0.; for(unsigned int ix=0;ix1e-10) { generator()->log() << "Forward spin weight problem " << wgt << " " << wgt-1. << " " << ids[0]->id() << " " << ids[1]->id() << " " << ids[2]->id() << " " << " " << phi << "\n"; generator()->log() << "Weights \n"; for(unsigned int ix=0;ixlog() << wgts[ix].first << " " << wgts[ix].second << "\n"; } // soft correlations bit double aziWgt = 1.; if(softAllowed) { Energy2 dot = pjk[0]+pjk[1]*cos(phi)+pjk[2]*sin(phi); Energy Eg = Ek[0]+Ek[1]*cos(phi)+Ek[2]*sin(phi); if(pipj*Eg>pik*Ej) { if(dynamic_ptr_cast(ShowerHandler::currentHandler())->softCorrelations()==1) { aziWgt = (-m12/sqr(pik) -m22/sqr(dot) +2.*pipj/pik/dot)/aziMax; } else if(dynamic_ptr_cast(ShowerHandler::currentHandler())->softCorrelations()==2) { aziWgt = max(ZERO,0.5/pik/Eg*(Ei-m12*Eg/pik + (pipj*Eg - Ej*pik)/dot)/aziMax); } if(aziWgt-1.>1e-10||aziWgt<-1e-10) { generator()->log() << "Forward soft weight problem " << aziWgt << " " << aziWgt-1. << " " << ids[0]->id() << " " << ids[1]->id() << " " << ids[2]->id() << " " << " " << phi << "\n"; } } else { aziWgt = 0.; } } wgt *= aziWgt; if(wgt>wgtMax) { phiMax = phi; wgtMax = wgt; } ++ntry; } while(wgtlog() << "Too many tries to generate phi in forward evolution\n"; phi = phiMax; } // return the azimuthal angle return phi; } double SudakovFormFactor::generatePhiBackward(ShowerParticle & particle, const IdList & ids, ShoKinPtr kinematics, const RhoDMatrix & rho) { // no correlations, return flat phi if(! dynamic_ptr_cast(ShowerHandler::currentHandler())->correlations()) return Constants::twopi*UseRandom::rnd(); // get the kinematic variables double z = kinematics->z(); Energy2 t = (1.-z)*sqr(kinematics->scale())/z; Energy pT = kinematics->pT(); // if soft correlations bool softAllowed = dynamic_ptr_cast(ShowerHandler::currentHandler())->softCorrelations() && (ids[2]->id()==ParticleID::g || ids[2]->id()==ParticleID::gamma); Energy2 pipj,pik,m12(ZERO),m22(ZERO); array pjk; Energy Ei,Ej,Ek; InvEnergy2 aziMax(ZERO); if(softAllowed) { // find the partner for the soft correlations tShowerParticlePtr partner=findCorrelationPartner(particle,false,splittingFn()->interactionType()); double zFact = (1.-z); // compute the transforms to the shower reference frame // first the boost Lorentz5Momentum pVect = particle.showerBasis()->pVector(); Lorentz5Momentum nVect = particle.showerBasis()->nVector(); assert(particle.showerBasis()->frame()==ShowerBasis::BackToBack); Boost beta_bb = -(pVect + nVect).boostVector(); pVect.boost(beta_bb); nVect.boost(beta_bb); Axis axis = pVect.vect().unit(); // and then the rotation LorentzRotation rot; if(axis.perp2()>0.) { double sinth(sqrt(sqr(axis.x())+sqr(axis.y()))); rot.rotate(acos(axis.z()),Axis(-axis.y()/sinth,axis.x()/sinth,0.)); } else if(axis.z()<0.) { rot.rotate(Constants::pi,Axis(1.,0.,0.)); } rot.invert(); pVect *= rot; nVect *= rot; // shower parameters Energy2 pn = pVect*nVect; Energy2 m2 = pVect.m2(); double alpha0 = particle.x(); double beta0 = -0.5/alpha0/pn*sqr(alpha0)*m2; Lorentz5Momentum pj = partner->momentum(); pj.boost(beta_bb); pj *= rot; double beta2 = 0.5*(1.-zFact)*(sqr(alpha0*zFact/(1.-zFact))*m2+sqr(pT))/alpha0/zFact/pn; // compute the two phi independent dot products Energy2 dot1 = pj*pVect; Energy2 dot2 = pj*nVect; pipj = alpha0*dot1+beta0*dot2; pik = alpha0*(alpha0*zFact/(1.-zFact)*m2+pn*(beta2+zFact/(1.-zFact)*beta0)); // compute the constants for the phi dependent dot product pjk[0] = alpha0*zFact/(1.-zFact)*dot1+beta2*dot2; pjk[1] = pj.x()*pT; pjk[2] = pj.y()*pT; m12 = ZERO; m22 = sqr(partner->dataPtr()->mass()); Energy2 mag = sqrt(sqr(pjk[1])+sqr(pjk[2])); if(dynamic_ptr_cast(ShowerHandler::currentHandler())->softCorrelations()==1) { aziMax = -m12/sqr(pik) -m22/sqr(pjk[0]+mag) +2.*pipj/pik/(pjk[0]-mag); } else if(dynamic_ptr_cast(ShowerHandler::currentHandler())->softCorrelations()==2) { Ek = alpha0*zFact/(1.-zFact)*pVect.t()+beta2*nVect.t(); Ei = alpha0*pVect.t()+beta0*nVect.t(); Ej = pj.t(); if(pipj*Ek> Ej*pik) { aziMax = 0.5/pik/Ek*(Ei-m12*Ek/pik + (pipj*Ek- Ej*pik)/(pjk[0]-mag)); } else { aziMax = 0.5/pik/Ek*(Ei-m12*Ek/pik); } } else { assert(dynamic_ptr_cast(ShowerHandler::currentHandler())->softCorrelations()==0); } } // if spin correlations vector > wgts; if(dynamic_ptr_cast(ShowerHandler::currentHandler())->spinCorrelations()) { // get the weights wgts = splittingFn()->generatePhiBackward(z,t,ids,rho); } else { wgts = {{ {0, 1.} }}; } // generate the azimuthal angle double phi,wgt; static const Complex ii(0.,1.); unsigned int ntry(0); double phiMax(0.),wgtMax(0.); do { phi = Constants::twopi*UseRandom::rnd(); Complex spinWgt = 0.; for(unsigned int ix=0;ix1e-10) { generator()->log() << "Backward weight problem " << wgt << " " << wgt-1. << " " << ids[0]->id() << " " << ids[1]->id() << " " << ids[2]->id() << " " << " " << z << " " << phi << "\n"; generator()->log() << "Weights \n"; for(unsigned int ix=0;ixlog() << wgts[ix].first << " " << wgts[ix].second << "\n"; } // soft correlations bit double aziWgt = 1.; if(softAllowed) { Energy2 dot = pjk[0]+pjk[1]*cos(phi)+pjk[2]*sin(phi); if(dynamic_ptr_cast(ShowerHandler::currentHandler())->softCorrelations()==1) { aziWgt = (-m12/sqr(pik) -m22/sqr(dot) +2.*pipj/pik/dot)/aziMax; } else if(dynamic_ptr_cast(ShowerHandler::currentHandler())->softCorrelations()==2) { aziWgt = max(ZERO,0.5/pik/Ek*(Ei-m12*Ek/pik + pipj*Ek/dot - Ej*pik/dot)/aziMax); } if(aziWgt-1.>1e-10||aziWgt<-1e-10) { generator()->log() << "Backward soft weight problem " << aziWgt << " " << aziWgt-1. << " " << ids[0]->id() << " " << ids[1]->id() << " " << ids[2]->id() << " " << " " << phi << "\n"; } } wgt *= aziWgt; if(wgt>wgtMax) { phiMax = phi; wgtMax = wgt; } ++ntry; } while(wgtlog() << "Too many tries to generate phi in backward evolution\n"; phi = phiMax; } // return the azimuthal angle return phi; } double SudakovFormFactor::generatePhiDecay(ShowerParticle & particle, const IdList & ids, ShoKinPtr kinematics, const RhoDMatrix &) { // only soft correlations in this case // no correlations, return flat phi if( !(dynamic_ptr_cast(ShowerHandler::currentHandler())->softCorrelations() && (ids[2]->id()==ParticleID::g || ids[2]->id()==ParticleID::gamma ))) return Constants::twopi*UseRandom::rnd(); // get the kinematic variables double z = kinematics->z(); Energy pT = kinematics->pT(); // if soft correlations // find the partner for the soft correlations tShowerParticlePtr partner = findCorrelationPartner(particle,true,splittingFn()->interactionType()); double zFact(1.-z); // compute the transforms to the shower reference frame // first the boost Lorentz5Momentum pVect = particle.showerBasis()->pVector(); Lorentz5Momentum nVect = particle.showerBasis()->nVector(); assert(particle.showerBasis()->frame()==ShowerBasis::Rest); Boost beta_bb = -pVect.boostVector(); pVect.boost(beta_bb); nVect.boost(beta_bb); Axis axis = nVect.vect().unit(); // and then the rotation LorentzRotation rot; if(axis.perp2()>0.) { double sinth(sqrt(sqr(axis.x())+sqr(axis.y()))); rot.rotate(acos(axis.z()),Axis(-axis.y()/sinth,axis.x()/sinth,0.)); } else if(axis.z()<0.) { rot.rotate(Constants::pi,Axis(1.,0.,0.)); } rot.invert(); pVect *= rot; nVect *= rot; // shower parameters Energy2 pn = pVect*nVect; Energy2 m2 = pVect.m2(); double alpha0 = particle.showerParameters().alpha; double beta0 = 0.5/alpha0/pn* (sqr(particle.dataPtr()->mass())-sqr(alpha0)*m2+sqr(particle.showerParameters().pt)); Lorentz5Momentum qperp0(particle.showerParameters().ptx, particle.showerParameters().pty,ZERO,ZERO); Lorentz5Momentum pj = partner->momentum(); pj.boost(beta_bb); pj *= rot; // compute the two phi independent dot products Energy2 pik = 0.5*zFact*(sqr(alpha0)*m2 - sqr(particle.showerParameters().pt) + 2.*alpha0*beta0*pn ) +0.5*sqr(pT)/zFact; Energy2 dot1 = pj*pVect; Energy2 dot2 = pj*nVect; Energy2 dot3 = pj*qperp0; Energy2 pipj = alpha0*dot1+beta0*dot2+dot3; // compute the constants for the phi dependent dot product array pjk; pjk[0] = zFact*(alpha0*dot1+dot3-0.5*dot2/pn*(alpha0*m2-sqr(particle.showerParameters().pt)/alpha0)) +0.5*sqr(pT)*dot2/pn/zFact/alpha0; pjk[1] = (pj.x() - dot2/alpha0/pn*qperp0.x())*pT; pjk[2] = (pj.y() - dot2/alpha0/pn*qperp0.y())*pT; Energy2 m12 = sqr(particle.dataPtr()->mass()); Energy2 m22 = sqr(partner->dataPtr()->mass()); Energy2 mag = sqrt(sqr(pjk[1])+sqr(pjk[2])); InvEnergy2 aziMax; array Ek; Energy Ei,Ej; if(dynamic_ptr_cast(ShowerHandler::currentHandler())->softCorrelations()==1) { aziMax = -m12/sqr(pik) -m22/sqr(pjk[0]+mag) +2.*pipj/pik/(pjk[0]-mag); } else if(dynamic_ptr_cast(ShowerHandler::currentHandler())->softCorrelations()==2) { Ek[0] = zFact*(alpha0*pVect.t()+-0.5*nVect.t()/pn*(alpha0*m2-sqr(particle.showerParameters().pt)/alpha0)) +0.5*sqr(pT)*nVect.t()/pn/zFact/alpha0; Ek[1] = -nVect.t()/alpha0/pn*qperp0.x()*pT; Ek[2] = -nVect.t()/alpha0/pn*qperp0.y()*pT; Energy mag2=sqrt(sqr(Ek[1])+sqr(Ek[2])); Ei = alpha0*pVect.t()+beta0*nVect.t(); Ej = pj.t(); aziMax = 0.5/pik/(Ek[0]-mag2)*(Ei-m12*(Ek[0]-mag2)/pik + pipj*(Ek[0]+mag2)/(pjk[0]-mag) - Ej*pik/(pjk[0]-mag) ); } else assert(dynamic_ptr_cast(ShowerHandler::currentHandler())->softCorrelations()==0); // generate the azimuthal angle double phi,wgt(0.); unsigned int ntry(0); double phiMax(0.),wgtMax(0.); do { phi = Constants::twopi*UseRandom::rnd(); Energy2 dot = pjk[0]+pjk[1]*cos(phi)+pjk[2]*sin(phi); if(dynamic_ptr_cast(ShowerHandler::currentHandler())->softCorrelations()==1) { wgt = (-m12/sqr(pik) -m22/sqr(dot) +2.*pipj/pik/dot)/aziMax; } else if(dynamic_ptr_cast(ShowerHandler::currentHandler())->softCorrelations()==2) { if(qperp0.m2()==ZERO) { wgt = 1.; } else { Energy Eg = Ek[0]+Ek[1]*cos(phi)+Ek[2]*sin(phi); wgt = max(ZERO,0.5/pik/Eg*(Ei-m12*Eg/pik + (pipj*Eg - Ej*pik)/dot)/aziMax); } } if(wgt-1.>1e-10||wgt<-1e-10) { generator()->log() << "Decay soft weight problem " << wgt << " " << wgt-1. << " " << ids[0]->id() << " " << ids[1]->id() << " " << ids[2]->id() << " " << " " << phi << "\n"; } if(wgt>wgtMax) { phiMax = phi; wgtMax = wgt; } ++ntry; } while(wgtlog() << "Too many tries to generate phi\n"; } // return the azimuthal angle return phi; } Energy SudakovFormFactor::calculateScale(double zin, Energy pt, IdList ids, unsigned int iopt) { Energy2 tmin; initialize(ids,tmin); // final-state branching if(iopt==0) { Energy2 scale=(sqr(pt)+masssquared_[1]*(1.-zin)+masssquared_[2]*zin); if(ids[0]->id()!=ParticleID::g) scale -= zin*(1.-zin)*masssquared_[0]; scale /= sqr(zin*(1-zin)); return scale<=ZERO ? sqrt(tmin) : sqrt(scale); } else if(iopt==1) { Energy2 scale=(sqr(pt)+zin*masssquared_[2])/sqr(1.-zin); return scale<=ZERO ? sqrt(tmin) : sqrt(scale); } else if(iopt==2) { Energy2 scale = (sqr(pt)+zin*masssquared_[2])/sqr(1.-zin)+masssquared_[0]; return scale<=ZERO ? sqrt(tmin) : sqrt(scale); } else { throw Exception() << "Unknown option in SudakovFormFactor::calculateScale() " << "iopt = " << iopt << Exception::runerror; } }