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diff --git a/Shower/Default/QTildeSudakov.cc b/Shower/Default/QTildeSudakov.cc
--- a/Shower/Default/QTildeSudakov.cc
+++ b/Shower/Default/QTildeSudakov.cc
@@ -1,982 +1,977 @@
// -*- C++ -*-
//
// QTildeSudakov.cc is a part of Herwig++ - A multi-purpose Monte Carlo event generator
// Copyright (C) 2002-2011 The Herwig Collaboration
//
// Herwig++ is licenced under version 2 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 QTildeSudakov class.
//
#include "QTildeSudakov.h"
#include "ThePEG/Interface/ClassDocumentation.h"
#include "ThePEG/Interface/Parameter.h"
#include "ThePEG/Interface/Switch.h"
#include "ThePEG/PDT/ParticleData.h"
#include "ThePEG/EventRecord/Event.h"
#include "ThePEG/Repository/EventGenerator.h"
#include "ThePEG/Repository/CurrentGenerator.h"
#include "ThePEG/PDT/EnumParticles.h"
#include "Herwig++/Shower/Default/FS_QTildeShowerKinematics1to2.h"
#include "Herwig++/Shower/Default/IS_QTildeShowerKinematics1to2.h"
#include "Herwig++/Shower/Default/Decay_QTildeShowerKinematics1to2.h"
#include "ThePEG/Utilities/DescribeClass.h"
#include "Herwig++/Shower/Base/ShowerVertex.h"
#include "Herwig++/Shower/Base/ShowerParticle.h"
#include "Herwig++/Shower/ShowerHandler.h"
#include "Herwig++/Shower/Base/Evolver.h"
#include "Herwig++/Shower/Base/PartnerFinder.h"
#include "Herwig++/Shower/Base/ShowerModel.h"
#include "Herwig++/Shower/Base/KinematicsReconstructor.h"
using namespace Herwig;
DescribeNoPIOClass<QTildeSudakov,Herwig::SudakovFormFactor>
describeQTildeSudakov ("Herwig::QTildeSudakov","HwShower.so");
void QTildeSudakov::Init() {
static ClassDocumentation<QTildeSudakov> documentation
("The QTildeSudakov class implements the Sudakov form factor for ordering it"
" qtilde");
}
bool QTildeSudakov::guessTimeLike(Energy2 &t,Energy2 tmin,double enhance) {
Energy2 told = t;
// calculate limits on z and if lower>upper return
if(!computeTimeLikeLimits(t)) return false;
// guess values of t and z
t = guesst(told,0,ids_,enhance,ids_[1]==ids_[2]);
z(guessz(0,ids_));
// actual values for z-limits
if(!computeTimeLikeLimits(t)) return false;
if(t<tmin) {
t=-1.0*GeV2;
return false;
}
else
return true;
}
bool QTildeSudakov::guessSpaceLike(Energy2 &t, Energy2 tmin, const double x,
double enhance) {
Energy2 told = t;
// calculate limits on z if lower>upper return
if(!computeSpaceLikeLimits(t,x)) return false;
// guess values of t and z
t = guesst(told,1,ids_,enhance,ids_[1]==ids_[2]);
z(guessz(1,ids_));
// actual values for z-limits
if(!computeSpaceLikeLimits(t,x)) return false;
if(t<tmin) {
t=-1.0*GeV2;
return false;
}
else
return true;
}
bool QTildeSudakov::PSVeto(const Energy2 t) {
// still inside PS, return true if outside
// check vs overestimated limits
if(z() < zLimits().first || z() > zLimits().second) return true;
// compute the pts
Energy2 pt2=sqr(z()*(1.-z()))*t-masssquared_[1]*(1.-z())-masssquared_[2]*z();
if(ids_[0]!=ParticleID::g) pt2+=z()*(1.-z())*masssquared_[0];
// if pt2<0 veto
if(pt2<pT2min()) return true;
// otherwise calculate pt and return
pT(sqrt(pt2));
return false;
}
ShoKinPtr QTildeSudakov::generateNextTimeBranching(const Energy startingScale,
const IdList &ids,const bool cc,
double enhance) {
// 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,cc);
// check max > min
if(tmax<=tmin) return ShoKinPtr();
// calculate next value of t using veto algorithm
Energy2 t(tmax);
do {
if(!guessTimeLike(t,tmin,enhance)) break;
}
while(PSVeto(t) || SplittingFnVeto(z()*(1.-z())*t,ids,true) ||
alphaSVeto(sqr(z()*(1.-z()))*t));
q_ = t > ZERO ? Energy(sqrt(t)) : -1.*MeV;
if(q_ < ZERO) return ShoKinPtr();
// return the ShowerKinematics object
return createFinalStateBranching(q_,z(),phi(),pT());
}
ShoKinPtr QTildeSudakov::
generateNextSpaceBranching(const Energy startingQ,
const IdList &ids,
double x,bool cc,
double enhance,
Ptr<BeamParticleData>::transient_const_pointer beam) {
// 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,cc);
// check max > min
if(tmax<=tmin) return ShoKinPtr();
// extract the partons which are needed for the PDF veto
// Different order, incoming parton is id = 1, outgoing are id=0,2
tcPDPtr parton0 = getParticleData(ids[0]);
tcPDPtr parton1 = getParticleData(ids[1]);
if(cc) {
if(parton0->CC()) parton0 = parton0->CC();
if(parton1->CC()) parton1 = parton1->CC();
}
// calculate next value of t using veto algorithm
Energy2 t(tmax),pt2(ZERO);
do {
if(!guessSpaceLike(t,tmin,x,enhance)) break;
pt2=sqr(1.-z())*t-z()*masssquared_[2];
}
while(z() > zLimits().second ||
SplittingFnVeto((1.-z())*t/z(),ids,true) ||
alphaSVeto(sqr(1.-z())*t) ||
PDFVeto(t,x,parton0,parton1,beam) || pt2 < pT2min() );
if(t > ZERO && zLimits().first < zLimits().second) q_ = sqrt(t);
else return ShoKinPtr();
pT(sqrt(pt2));
// create the ShowerKinematics and return it
return createInitialStateBranching(q_,z(),phi(),pT());
}
void QTildeSudakov::initialize(const IdList & ids, Energy2 & tmin,const bool cc) {
ids_=ids;
if(cc) {
for(unsigned int ix=0;ix<ids.size();++ix) {
if(getParticleData(ids[ix])->CC()) ids_[ix]*=-1;
}
}
tmin = cutOffOption() != 2 ? ZERO : 4.*pT2min();
masses_ = virtualMasses(ids);
masssquared_.clear();
for(unsigned int ix=0;ix<masses_.size();++ix) {
masssquared_.push_back(sqr(masses_[ix]));
if(ix>0) tmin=max(masssquared_[ix],tmin);
}
}
ShoKinPtr QTildeSudakov::generateNextDecayBranching(const Energy startingScale,
const Energy stoppingScale,
const Energy minmass,
const IdList &ids,
const bool cc,
double enhance) {
// 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,cc);
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)) break;
pt2 = sqr(1.-z())*(t-masssquared_[0])-z()*masssquared_[2];
}
while(SplittingFnVeto((1.-z())*t/z(),ids,true)||
alphaSVeto(sqr(1.-z())*t) ||
pt2<pT2min() ||
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 createDecayBranching(q_,z(),phi(),pT());
}
bool QTildeSudakov::guessDecay(Energy2 &t,Energy2 tmax, Energy minmass,
double enhance) {
// previous scale
Energy2 told = t;
// overestimated limits on z
if(tmax<masssquared_[0]) {
t=-1.0*GeV2;
return false;
}
Energy2 tm2 = tmax-masssquared_[0];
Energy tm = sqrt(tm2);
pair<double,double> limits=make_pair(sqr(minmass/masses_[0]),
1.-sqrt(masssquared_[2]+pT2min()+
0.25*sqr(masssquared_[2])/tm2)/tm
+0.5*masssquared_[2]/tm2);
zLimits(limits);
if(zLimits().second<zLimits().first) {
t=-1.0*GeV2;
return false;
}
// guess values of t and z
t = guesst(told,2,ids_,enhance,ids_[1]==ids_[2]);
z(guessz(2,ids_));
// actual values for z-limits
if(t<masssquared_[0]) {
t=-1.0*GeV2;
return false;
}
tm2 = t-masssquared_[0];
tm = sqrt(tm2);
limits=make_pair(sqr(minmass/masses_[0]),
1.-sqrt(masssquared_[2]+pT2min()+
0.25*sqr(masssquared_[2])/tm2)/tm
+0.5*masssquared_[2]/tm2);
zLimits(limits);
if(t>tmax||zLimits().second<zLimits().first) {
t=-1.0*GeV2;
return false;
}
else
return true;
}
bool QTildeSudakov::computeTimeLikeLimits(Energy2 & t) {
if (t < 1e-20 * GeV2) {
t=-1.*GeV2;
return false;
}
// special case for gluon radiating
pair<double,double> limits;
if(ids_[0]==ParticleID::g||ids_[0]==ParticleID::gamma) {
// no emission possible
if(t<16.*(masssquared_[1]+pT2min())) {
t=-1.*GeV2;
return false;
}
// overestimate of the limits
limits.first = 0.5*(1.-sqrt(1.-4.*sqrt((masssquared_[1]+pT2min())/t)));
limits.second = 1.-limits.first;
}
// special case for radiated particle is gluon
else if(ids_[2]==ParticleID::g||ids_[2]==ParticleID::gamma) {
limits.first = sqrt((masssquared_[1]+pT2min())/t);
limits.second = 1.-sqrt((masssquared_[2]+pT2min())/t);
}
else if(ids_[1]==ParticleID::g||ids_[1]==ParticleID::gamma) {
limits.second = sqrt((masssquared_[2]+pT2min())/t);
limits.first = 1.-sqrt((masssquared_[1]+pT2min())/t);
}
else {
limits.first = (masssquared_[1]+pT2min())/t;
limits.second = 1.-(masssquared_[2]+pT2min())/t;
}
if(limits.first>=limits.second) {
t=-1.*GeV2;
return false;
}
zLimits(limits);
return true;
}
bool QTildeSudakov::computeSpaceLikeLimits(Energy2 & t, double x) {
if (t < 1e-20 * GeV2) {
t=-1.*GeV2;
return false;
}
pair<double,double> limits;
// compute the limits
limits.first = x;
double yy = 1.+0.5*masssquared_[2]/t;
limits.second = yy - sqrt(sqr(yy)-1.+pT2min()/t);
// return false if lower>upper
zLimits(limits);
if(limits.second<limits.first) {
t=-1.*GeV2;
return false;
}
else
return true;
}
namespace {
tShowerParticlePtr findCorrelationPartner(ShowerParticle & particle,
bool forward,
ShowerInteraction::Type inter) {
tPPtr child = &particle;
tShowerParticlePtr mother;
if(forward) {
mother = !particle.parents().empty() ?
dynamic_ptr_cast<tShowerParticlePtr>(particle.parents()[0]) : tShowerParticlePtr();
}
else {
mother = particle.children().size()==2 ?
dynamic_ptr_cast<tShowerParticlePtr>(&particle) : tShowerParticlePtr();
}
tShowerParticlePtr partner;
while(mother) {
tPPtr otherChild;
if(forward) {
for (unsigned int ix=0;ix<mother->children().size();++ix) {
if(mother->children()[ix]!=child) {
otherChild = mother->children()[ix];
break;
}
}
}
else {
otherChild = mother->children()[1];
}
tShowerParticlePtr other = dynamic_ptr_cast<tShowerParticlePtr>(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<tShowerParticlePtr>(mother);
break;
}
child = mother;
if(forward) {
mother = ! mother->parents().empty() ?
dynamic_ptr_cast<tShowerParticlePtr>(mother->parents()[0]) : tShowerParticlePtr();
}
else {
if(mother->children()[0]->children().size()!=2)
break;
tShowerParticlePtr mtemp =
dynamic_ptr_cast<tShowerParticlePtr>(mother->children()[0]);
if(!mtemp)
break;
else
mother=mtemp;
}
}
if(!partner) {
if(forward) {
partner = dynamic_ptr_cast<tShowerParticlePtr>( child)->partner();
}
else {
if(mother) {
tShowerParticlePtr parent;
if(!mother->children().empty()) {
parent = dynamic_ptr_cast<tShowerParticlePtr>(mother->children()[0]);
}
if(!parent) {
parent = dynamic_ptr_cast<tShowerParticlePtr>(mother);
}
partner = parent->partner();
}
else {
partner = dynamic_ptr_cast<tShowerParticlePtr>(&particle)->partner();
}
}
}
return partner;
}
pair<double,double> 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;
return make_pair(atan2(B*s01*(-C*(num + root) / denom + D) / denom2, -(num + root ) / denom) + phi0,
atan2(B*s01*(-C*(num - root) / denom + D) / denom2, -(num - root ) / denom) + phi0);
}
}
double QTildeSudakov::generatePhiForward(ShowerParticle & particle,
const IdList & ids,
ShoKinPtr kinematics) {
// no correlations, return flat phi
if(! ShowerHandler::currentHandler()->evolver()->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]==ParticleID::g || ids[1]==ParticleID::gamma,
ids[2]==ParticleID::g || ids[2]==ParticleID::gamma };
vector<Energy2> pjk(3,ZERO);
vector<Energy> Ek(3,ZERO);
Energy Ei,Ej;
Energy2 m12(ZERO),m22(ZERO);
InvEnergy2 aziMax(ZERO);
bool softAllowed = ShowerHandler::currentHandler()->evolver()->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
vector<Lorentz5Momentum> basis = kinematics->getBasis();
Lorentz5Momentum pVect = basis[0], nVect = basis[1];
Boost beta_bb;
if(kinematics->frame()==ShowerKinematics::BackToBack) {
beta_bb = -(pVect + nVect).boostVector();
}
else if(kinematics->frame()==ShowerKinematics::Rest) {
beta_bb = -pVect.boostVector();
}
else
assert(false);
pVect.boost(beta_bb);
nVect.boost(beta_bb);
Axis axis;
if(kinematics->frame()==ShowerKinematics::BackToBack) {
axis = pVect.vect().unit();
}
else if(kinematics->frame()==ShowerKinematics::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(ShowerHandler::currentHandler()->evolver()->softCorrelations()==1) {
aziMax = -m12/sqr(pik) -m22/sqr(pjk[0]+mag) +2.*pipj/pik/(pjk[0]-mag);
}
else if(ShowerHandler::currentHandler()->evolver()->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<double,double> 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<pair<int,Complex> > wgts;
if(ShowerHandler::currentHandler()->evolver()->spinCorrelations()) {
// get the spin density matrix and the mapping
RhoDMatrix mapping;
SpinPtr inspin;
bool needMapping = getMapping(inspin,mapping,particle,kinematics);
// set the decayed flag
inspin->decay();
// get the spin density matrix
RhoDMatrix rho=inspin->rhoMatrix();
// map to the shower basis if needed
if(needMapping) {
RhoDMatrix rhop(rho.iSpin(),false);
for(int ixa=0;ixa<rho.iSpin();++ixa) {
for(int ixb=0;ixb<rho.iSpin();++ixb) {
for(int iya=0;iya<rho.iSpin();++iya) {
for(int iyb=0;iyb<rho.iSpin();++iyb) {
rhop(ixa,ixb) += rho(iya,iyb)*mapping(iya,ixa)*conj(mapping(iyb,ixb));
}
}
}
}
rhop.normalize();
rho = rhop;
}
// calculate the weights
wgts = splittingFn()->generatePhiForward(z,t,ids,rho);
}
else {
wgts = vector<pair<int,Complex> >(1,make_pair(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;ix<wgts.size();++ix) {
if(wgts[ix].first==0)
spinWgt += wgts[ix].second;
else
spinWgt += exp(double(wgts[ix].first)*ii*phi)*wgts[ix].second;
}
wgt = spinWgt.real();
if(wgt-1.>1e-10) {
generator()->log() << "Forward spin weight problem " << wgt << " " << wgt-1.
<< " " << ids[0] << " " << ids[1] << " " << ids[2] << " " << " " << phi << "\n";
generator()->log() << "Weights \n";
for(unsigned int ix=0;ix<wgts.size();++ix)
generator()->log() << 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/Ei/Ej>pik/Ei/Eg) {
if(ShowerHandler::currentHandler()->evolver()->softCorrelations()==1) {
aziWgt = (-m12/sqr(pik) -m22/sqr(dot) +2.*pipj/pik/dot)/aziMax;
}
else if(ShowerHandler::currentHandler()->evolver()->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] << " " << ids[1] << " " << ids[2] << " " << " " << phi << "\n";
}
}
else {
aziWgt = 0.;
}
}
wgt *= aziWgt;
if(wgt>wgtMax) {
phiMax = phi;
wgtMax = wgt;
}
++ntry;
}
while(wgt<UseRandom::rnd()&&ntry<10000);
if(ntry==10000) {
generator()->log() << "Too many tries to generate phi in forward evolution\n";
phi = phiMax;
}
// return the azimuthal angle
return phi;
}
double QTildeSudakov::generatePhiBackward(ShowerParticle & particle,
const IdList & ids,
ShoKinPtr kinematics) {
// no correlations, return flat phi
if(! ShowerHandler::currentHandler()->evolver()->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 = ShowerHandler::currentHandler()->evolver()->softCorrelations() &&
(ids[2]==ParticleID::g || ids[2]==ParticleID::gamma);
Energy2 pipj,pik,m12(ZERO),m22(ZERO);
vector<Energy2> pjk(3,ZERO);
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
vector<Lorentz5Momentum> basis = kinematics->getBasis();
Lorentz5Momentum pVect = basis[0];
Lorentz5Momentum nVect = basis[1];
assert(kinematics->frame()==ShowerKinematics::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(ShowerHandler::currentHandler()->evolver()->softCorrelations()==1) {
aziMax = -m12/sqr(pik) -m22/sqr(pjk[0]+mag) +2.*pipj/pik/(pjk[0]-mag);
}
else if(ShowerHandler::currentHandler()->evolver()->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(ShowerHandler::currentHandler()->evolver()->softCorrelations()==0);
}
}
// if spin correlations
vector<pair<int,Complex> > wgts;
if(ShowerHandler::currentHandler()->evolver()->spinCorrelations()) {
// get the spin density matrix and the mapping
RhoDMatrix mapping;
SpinPtr inspin;
bool needMapping = getMapping(inspin,mapping,particle,kinematics);
// set the decayed flag (counterintuitive but going backward)
inspin->decay();
// get the spin density matrix
RhoDMatrix rho=inspin->DMatrix();
// map to the shower basis if needed
if(needMapping) {
RhoDMatrix rhop(rho.iSpin(),false);
for(int ixa=0;ixa<rho.iSpin();++ixa) {
for(int ixb=0;ixb<rho.iSpin();++ixb) {
for(int iya=0;iya<rho.iSpin();++iya) {
for(int iyb=0;iyb<rho.iSpin();++iyb) {
rhop(ixa,ixb) += rho(iya,iyb)*mapping(iya,ixa)*conj(mapping(iyb,ixb));
}
}
}
}
rhop.normalize();
rho = rhop;
}
wgts = splittingFn()->generatePhiBackward(z,t,ids,rho);
}
else {
wgts = vector<pair<int,Complex> >(1,make_pair(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;ix<wgts.size();++ix) {
if(wgts[ix].first==0)
spinWgt += wgts[ix].second;
else
spinWgt += exp(double(wgts[ix].first)*ii*phi)*wgts[ix].second;
}
wgt = spinWgt.real();
if(wgt-1.>1e-10) {
generator()->log() << "Backward weight problem " << wgt << " " << wgt-1.
<< " " << ids[0] << " " << ids[1] << " " << ids[2] << " " << " " << z << " " << phi << "\n";
generator()->log() << "Weights \n";
for(unsigned int ix=0;ix<wgts.size();++ix)
generator()->log() << 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(ShowerHandler::currentHandler()->evolver()->softCorrelations()==1) {
aziWgt = (-m12/sqr(pik) -m22/sqr(dot) +2.*pipj/pik/dot)/aziMax;
}
else if(ShowerHandler::currentHandler()->evolver()->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] << " " << ids[1] << " " << ids[2] << " " << " " << phi << "\n";
}
}
wgt *= aziWgt;
if(wgt>wgtMax) {
phiMax = phi;
wgtMax = wgt;
}
++ntry;
}
while(wgt<UseRandom::rnd()&&ntry<10000);
if(ntry==10000) {
generator()->log() << "Too many tries to generate phi in backward evolution\n";
phi = phiMax;
}
// return the azimuthal angle
return phi;
}
double QTildeSudakov::generatePhiDecay(ShowerParticle & particle,
const IdList & ids,
ShoKinPtr kinematics) {
// only soft correlations in this case
// no correlations, return flat phi
if( !(ShowerHandler::currentHandler()->evolver()->softCorrelations() &&
(ids[2]==ParticleID::g || ids[2]==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);
vector<Lorentz5Momentum> basis = kinematics->getBasis();
// compute the transforms to the shower reference frame
// first the boost
Lorentz5Momentum pVect = basis[0];
Lorentz5Momentum nVect = basis[1];
assert(kinematics->frame()==ShowerKinematics::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
vector<Energy2> pjk(3,ZERO);
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;
vector<Energy> Ek(3,ZERO);
Energy Ei,Ej;
if(ShowerHandler::currentHandler()->evolver()->softCorrelations()==1) {
aziMax = -m12/sqr(pik) -m22/sqr(pjk[0]+mag) +2.*pipj/pik/(pjk[0]-mag);
}
else if(ShowerHandler::currentHandler()->evolver()->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(ShowerHandler::currentHandler()->evolver()->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(ShowerHandler::currentHandler()->evolver()->softCorrelations()==1) {
wgt = (-m12/sqr(pik) -m22/sqr(dot) +2.*pipj/pik/dot)/aziMax;
}
else if(ShowerHandler::currentHandler()->evolver()->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] << " " << ids[1] << " " << ids[2] << " " << " " << phi << "\n";
}
if(wgt>wgtMax) {
phiMax = phi;
wgtMax = wgt;
}
++ntry;
}
while(wgt<UseRandom::rnd()&&ntry<10000);
if(ntry==10000) {
phi = phiMax;
generator()->log() << "Too many tries to generate phi\n";
}
// return the azimuthal angle
return phi;
}
Energy QTildeSudakov::calculateScale(double zin, Energy pt, IdList ids,
unsigned int iopt) {
Energy2 tmin;
initialize(ids,tmin,false);
// final-state branching
if(iopt==0) {
Energy2 scale=(sqr(pt)+masssquared_[1]*(1.-zin)+masssquared_[2]*zin);
if(ids[0]!=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 QTildeSudakov::calculateScale() "
<< "iopt = " << iopt << Exception::runerror;
}
}
ShoKinPtr QTildeSudakov::createFinalStateBranching(Energy scale,double z,
double phi, Energy pt) {
ShoKinPtr showerKin = new_ptr(FS_QTildeShowerKinematics1to2());
showerKin->scale(scale);
showerKin->z(z);
showerKin->phi(phi);
showerKin->pT(pt);
showerKin->SudakovFormFactor(this);
return showerKin;
}
ShoKinPtr QTildeSudakov::createInitialStateBranching(Energy scale,double z,
double phi, Energy pt) {
ShoKinPtr showerKin = new_ptr(IS_QTildeShowerKinematics1to2());
showerKin->scale(scale);
showerKin->z(z);
showerKin->phi(phi);
showerKin->pT(pt);
showerKin->SudakovFormFactor(this);
return showerKin;
}
ShoKinPtr QTildeSudakov::createDecayBranching(Energy scale,double z,
double phi, Energy pt) {
ShoKinPtr showerKin = new_ptr(Decay_QTildeShowerKinematics1to2());
showerKin->scale(scale);
showerKin->z(z);
showerKin->phi(phi);
showerKin->pT(pt);
showerKin->SudakovFormFactor(this);
return showerKin;
}

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