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diff --git a/MatrixElement/EW/ElectroWeakReweighter.cc b/MatrixElement/EW/ElectroWeakReweighter.cc
--- a/MatrixElement/EW/ElectroWeakReweighter.cc
+++ b/MatrixElement/EW/ElectroWeakReweighter.cc
@@ -1,1932 +1,1932 @@
// -*- C++ -*-
//
// This is the implementation of the non-inlined, non-templated member
// functions of the ElectroWeakReweighter class.
//
#include "ElectroWeakReweighter.h"
#include "ThePEG/Interface/ClassDocumentation.h"
#include "ThePEG/Interface/Reference.h"
#include "ThePEG/EventRecord/Particle.h"
#include "ThePEG/Repository/UseRandom.h"
#include "ThePEG/Repository/EventGenerator.h"
#include "ThePEG/Utilities/DescribeClass.h"
#include "ThePEG/Persistency/PersistentOStream.h"
#include "ThePEG/Persistency/PersistentIStream.h"
#include "boost/numeric/ublas/matrix.hpp"
#include "boost/numeric/ublas/operation.hpp"
#include "EWProcess.h"
#include "HighEnergyMatching.h"
#include "ElectroWeakMatching.h"
#include "ThePEG/Helicity/WaveFunction/SpinorWaveFunction.h"
#include "ThePEG/Helicity/WaveFunction/SpinorBarWaveFunction.h"
#include "ThePEG/Helicity/WaveFunction/VectorWaveFunction.h"
#include "ThePEG/Helicity/epsilon.h"
using namespace Herwig;
tEWCouplingsPtr ElectroWeakReweighter::staticEWCouplings_ = tEWCouplingsPtr();
ElectroWeakReweighter::ElectroWeakReweighter() {}
ElectroWeakReweighter::~ElectroWeakReweighter() {}
IBPtr ElectroWeakReweighter::clone() const {
return new_ptr(*this);
}
IBPtr ElectroWeakReweighter::fullclone() const {
return new_ptr(*this);
}
void ElectroWeakReweighter::persistentOutput(PersistentOStream & os) const {
os << EWCouplings_ << collinearSudakov_ << softSudakov_;
}
void ElectroWeakReweighter::persistentInput(PersistentIStream & is, int) {
is >> EWCouplings_ >> collinearSudakov_ >> softSudakov_;
}
// The following static variable is needed for the type
// description system in ThePEG.
DescribeClass<ElectroWeakReweighter,ReweightBase>
describeHerwigElectroWeakReweighter("Herwig::ElectroWeakReweighter", "HwMEEW.so");
void ElectroWeakReweighter::Init() {
static ClassDocumentation<ElectroWeakReweighter> documentation
("There is no documentation for the ElectroWeakReweighter class");
static Reference<ElectroWeakReweighter,EWCouplings> interfaceEWCouplings
("EWCouplings",
"The object to calculate the electroweak couplings",
&ElectroWeakReweighter::EWCouplings_, false, false, true, false, false);
static Reference<ElectroWeakReweighter,CollinearSudakov> interfaceCollinearSudakov
("CollinearSudakov",
"The collinear Sudakov",
&ElectroWeakReweighter::collinearSudakov_, false, false, true, false, false);
static Reference<ElectroWeakReweighter,SoftSudakov> interfaceSoftSudakov
("SoftSudakov",
"The soft Sudakov",
&ElectroWeakReweighter::softSudakov_, false, false, true, false, false);
}
namespace {
#ifdef ThePEG_HAS_UNITS_CHECKING
void axpy_prod_local(const boost::numeric::ublas::matrix<Complex> & A,
const boost::numeric::ublas::matrix<complex<InvEnergy2> > & B,
boost::numeric::ublas::matrix<complex<InvEnergy2> > & C) {
assert(A.size2()==B.size1());
C.resize(A.size1(),B.size2());
for(unsigned int ix=0;ix<A.size1();++ix) {
for(unsigned int iy=0;iy<B.size2();++iy) {
C(ix,iy) = ZERO;
for(unsigned int iz=0;iz<A.size2();++iz) {
C(ix,iy) += A(ix,iz)*B(iz,iy);
}
}
}
}
void axpy_prod_local(const boost::numeric::ublas::matrix<complex<InvEnergy2> > & A,
const boost::numeric::ublas::vector<complex<Energy2> > & B,
boost::numeric::ublas::vector<Complex > & C) {
assert(A.size2()==B.size());
C.resize(A.size1());
for(unsigned int ix=0;ix<A.size1();++ix) {
C(ix) = ZERO;
for(unsigned int iz=0;iz<A.size2();++iz) {
C(ix) += A(ix,iz)*B(iz);
}
}
}
void axpy_prod_local(const boost::numeric::ublas::matrix<complex<InvEnergy2> > & A,
const boost::numeric::ublas::matrix<Complex> & B,
boost::numeric::ublas::matrix<complex<InvEnergy2> > & C) {
assert(A.size2()==B.size1());
C.resize(A.size1(),B.size2());
for(unsigned int ix=0;ix<A.size1();++ix) {
for(unsigned int iy=0;iy<B.size2();++iy) {
C(ix,iy) = ZERO;
for(unsigned int iz=0;iz<A.size2();++iz) {
C(ix,iy) += A(ix,iz)*B(iz,iy);
}
}
}
}
#else
-void axpy_prod_local(const boost::numeric::ublas::matrix<Complex> > & A,
+void axpy_prod_local(const boost::numeric::ublas::matrix<Complex> & A,
const boost::numeric::ublas::matrix<Complex> & B,
- boost::numeric::ublas::matrix<Complex> > & C) {
+ boost::numeric::ublas::matrix<Complex> & C) {
axpy_prod(A,B,C);
}
#endif
}
double ElectroWeakReweighter::weight() const {
EWCouplings_->initialize();
staticEWCouplings_ = EWCouplings_;
// cerr << "aEM\n";
// for(Energy scale=10.*GeV; scale<10*TeV; scale *= 1.1) {
// cerr << scale/GeV << " "
// << EWCouplings_->aEM(scale) << "\n";
// }
// cerr << "aS\n";
// for(Energy scale=10.*GeV; scale<10*TeV; scale *= 1.4) {
// cerr << scale/GeV << " "
// << EWCouplings_->aS(scale) << "\n";
// }
// cerr << "y_t\n";
// for(Energy scale=10.*GeV; scale<10*TeV; scale *= 1.4) {
// cerr << scale/GeV << " "
// << EWCouplings_->y_t(scale) << "\n";
// }
// cerr << "lambda\n";
// for(Energy scale=91.2*GeV; scale<10*TeV; scale *= 1.4) {
// cerr << scale/GeV << " "
// << EWCouplings_->lambda(scale) << "\n";
// }
// cerr << "vev\n";
// for(Energy scale=91.2*GeV; scale<10*TeV; scale *= 1.4) {
// cerr << scale/GeV << " "
// << EWCouplings_->vev(scale)/GeV << "\n";
// }
// collinearSudakov_->makePlots();
// Energy2 s = sqr(5000.*GeV);
// Energy2 t = -0.25*s;
// Energy2 u = -0.75*s;
// testEvolution(s,t,u);
// cerr << subProcess() << "\n";
// cerr << *subProcess() << "\n";
// cerr << subProcess()->outgoing()[0] << *subProcess()->outgoing()[0] << "\n";
// cerr << subProcess()->outgoing()[0]->spinInfo() << "\n";
// cerr << subProcess()->outgoing()[0]->spinInfo()->productionVertex() << "\n";
if(subProcess()->outgoing().size()!=2)
return 1.;
// processes with gg initial-state
if(subProcess()->incoming().first->id()==ParticleID::g &&
subProcess()->incoming().second->id()==ParticleID::g) {
if(subProcess()->outgoing()[0]->id()==ParticleID::g &&
subProcess()->outgoing()[1]->id()==ParticleID::g)
return 1.;
else if(abs(subProcess()->outgoing()[0]->id())<=6 &&
subProcess()->outgoing()[0]->id()==-subProcess()->outgoing()[1]->id()) {
return reweightggqqbar();
}
else
assert(false);
}
// processes with q qbar initial-state
else if((subProcess()->incoming().first ->id() > 0 &&
subProcess()->incoming().first ->id()<= 5 &&
subProcess()->incoming().second->id() < 0 &&
subProcess()->incoming().second->id()>=-5) ||
(subProcess()->incoming().second->id() > 0 &&
subProcess()->incoming().second->id()<= 5 &&
subProcess()->incoming().first ->id() < 0 &&
subProcess()->incoming().first ->id()>=-5)) {
// identical flavour q qbar
if(subProcess()->incoming().first ->id() == -subProcess()->incoming().second->id()) {
// q qbar -> gg
if(subProcess()->outgoing()[0]->id()==ParticleID::g &&
subProcess()->outgoing()[1]->id()==ParticleID::g)
return reweightqqbargg();
// q qbar -> q' q'bar
else if(subProcess()->outgoing()[0]->id() == -subProcess()->outgoing()[1]->id() &&
abs(subProcess()->outgoing()[0]->id())<=6)
return reweightqqbarqqbarS();
}
// different flavour q qbar
else {
if((subProcess()->outgoing()[0]->id() > 0 &&
subProcess()->outgoing()[0]->id()<= 5 &&
subProcess()->outgoing()[1]->id() < 0 &&
subProcess()->outgoing()[1]->id()>=-5) ||
(subProcess()->outgoing()[1]->id() > 0 &&
subProcess()->outgoing()[1]->id()<= 5 &&
subProcess()->outgoing()[0]->id() < 0 &&
subProcess()->outgoing()[0]->id()>=-5)) {
return reweightqqbarqqbarT();
}
else
assert(false);
}
}
// processes with q g initial-state
else if((subProcess()->incoming().first ->id()> 0 &&
subProcess()->incoming().first ->id()<=5 &&
subProcess()->incoming().second->id()==ParticleID::g) ||
(subProcess()->incoming().second->id()> 0 &&
subProcess()->incoming().second->id()<=5 &&
subProcess()->incoming().first ->id()==ParticleID::g)) {
// qg -> qg
if((subProcess()->outgoing()[0]->id()> 0 &&
subProcess()->outgoing()[0]->id()<=5 &&
subProcess()->outgoing()[1]->id()==ParticleID::g) ||
(subProcess()->outgoing()[1]->id()> 0 &&
subProcess()->outgoing()[1]->id()<=5 &&
subProcess()->outgoing()[0]->id()==ParticleID::g))
return reweightqgqg();
// unknown
else
assert(false);
}
// processes with qbar g initial-state
else if((subProcess()->incoming().first ->id()>=-5 &&
subProcess()->incoming().first ->id()< 0 &&
subProcess()->incoming().second->id()==ParticleID::g) ||
(subProcess()->incoming().second->id()>=-5 &&
subProcess()->incoming().second->id()< 0 &&
subProcess()->incoming().first ->id()==ParticleID::g)) {
if((subProcess()->outgoing()[0]->id()>=-5 &&
subProcess()->outgoing()[0]->id()< 0 &&
subProcess()->outgoing()[1]->id()==ParticleID::g) ||
(subProcess()->outgoing()[1]->id()>=-5 &&
subProcess()->outgoing()[1]->id()< 0 &&
subProcess()->outgoing()[0]->id()==ParticleID::g))
return reweightqbargqbarg();
else
assert(false);
}
// processes with q q initial-state
else if( subProcess()->incoming().first ->id()> 0 &&
subProcess()->incoming().first ->id()<=5 &&
subProcess()->incoming().second->id()> 0 &&
subProcess()->incoming().second->id()<=5 ) {
if(subProcess()->outgoing()[0]->id()> 0 &&
subProcess()->outgoing()[0]->id()<=5 &&
subProcess()->outgoing()[1]->id()> 0 &&
subProcess()->outgoing()[1]->id()<=5)
return reweightqqqq();
else
assert(false);
}
// processes with qbar qbar initial-state
else if( subProcess()->incoming().first ->id()< 0 &&
subProcess()->incoming().first ->id()>= -5 &&
subProcess()->incoming().second->id()< 0 &&
subProcess()->incoming().second->id()>= -5 ) {
if(subProcess()->outgoing()[0]->id()< 0 &&
subProcess()->outgoing()[0]->id()>= -5 &&
subProcess()->outgoing()[1]->id()< 0 &&
subProcess()->outgoing()[1]->id()>= -5)
return reweightqbarqbarqbarqbar();
else
assert(false);
}
// unknown initial-state
else
assert(false);
assert(false);
staticEWCouplings_ = tEWCouplingsPtr();
}
void ElectroWeakReweighter::testEvolution(Energy2 s,Energy2 t, Energy2 u) const {
Energy highScale = sqrt(s);
Energy ewScale = coupling()->mZ();
Energy lowScale = 50.0*GeV;
for (unsigned int i=0; i<45;++i) {
EWProcess::Process process = (EWProcess::Process)i;
cerr << "process " << process << "\n";
// result for all EW and QCD SCET contributions:
boost::numeric::ublas::matrix<complex<InvEnergy2> > highMatch_val
= HighEnergyMatching::highEnergyMatching(highScale,s,t,u,process,true,true);
boost::numeric::ublas::matrix<Complex> highRunning_val
= softSudakov_->highEnergyRunning(highScale,ewScale,s,t,u,process,0);
boost::numeric::ublas::matrix<Complex> ewMatch_val =
ElectroWeakMatching::electroWeakMatching(ewScale,s,t,u,process,true,0);
boost::numeric::ublas::matrix<Complex> lowRunning_val =
softSudakov_->lowEnergyRunning(ewScale,lowScale,s,t,u,process,0);
boost::numeric::ublas::matrix<Complex> collinearHighRunning_val =
collinearSudakov_->highEnergyRunning(highScale,ewScale,s,process,false);
boost::numeric::ublas::matrix<Complex> collinearEWMatch_val =
collinearSudakov_->electroWeakMatching(ewScale,s,process,true);
boost::numeric::ublas::matrix<Complex> collinearLowRunning_val =
collinearSudakov_->lowEnergyRunning(ewScale,lowScale,s,process);
boost::numeric::ublas::matrix<Complex> lowMatchTemp_val =
boost::numeric::ublas::zero_matrix<Complex>(ewMatch_val.size1(),ewMatch_val.size2());
for (unsigned int ii=0; ii<ewMatch_val.size1(); ++ii) {
for (unsigned int jj=0; jj<ewMatch_val.size2(); ++jj) {
lowMatchTemp_val(ii,jj) = collinearEWMatch_val(ii,jj)*ewMatch_val(ii,jj);
}
}
boost::numeric::ublas::matrix<Complex> temp(highRunning_val.size1(),collinearHighRunning_val.size2());
boost::numeric::ublas::axpy_prod(highRunning_val,collinearHighRunning_val,temp);
boost::numeric::ublas::matrix<Complex> temp2(collinearLowRunning_val.size1(),lowRunning_val.size2());
boost::numeric::ublas::axpy_prod(collinearLowRunning_val,lowRunning_val,temp2);
boost::numeric::ublas::matrix<Complex> temp3(temp2.size1(),lowMatchTemp_val.size2());
boost::numeric::ublas::axpy_prod(temp2,lowMatchTemp_val,temp3);
temp2.resize(temp3.size1(),temp.size2());
boost::numeric::ublas::axpy_prod(temp3,temp,temp2);
boost::numeric::ublas::matrix<complex<InvEnergy2> > result(temp2.size1(),highMatch_val.size2());
axpy_prod_local(temp2,highMatch_val,result);
for(unsigned int ix=0;ix<result.size1();++ix) {
for(unsigned int iy=0;iy<result.size2();++iy) {
cerr << s*result(ix,iy) << " ";
}
cerr << "\n";
}
}
}
namespace {
void SackGluonPolarizations(Lorentz5Momentum &p1,
Lorentz5Momentum &p2,
Lorentz5Momentum &p3,
Lorentz5Momentum &p4,
Energy2 s, Energy2 t, Energy2 u, Energy2 m2,
vector<LorentzVector<Complex> > & eps3,
vector<LorentzVector<Complex> > & eps4,
unsigned int iopt) {
static const Complex I(0.,1.);
// p1 is p-, p2 is p+
// p3 is k-, p4 is k+
// both final-state
if(iopt==0) {
// swap t and u due Aneesh's defn
Energy3 den1 = sqrt((u*t-sqr(m2))*(s-4.*m2));
Energy3 den2 = sqrt(s*(u*t-sqr(m2)));
LorentzVector<Complex> eps3Para = (m2+t)/den1*p1 -(m2+u)/den1*p2 +(u-t)/den1*p3;
LorentzVector<Complex> eps3Perp = 2./den2*epsilon(p1,p2,p3);
LorentzVector<Complex> eps4Para = (m2+t)/den1*p2 -(m2+u)/den1*p1 +(u-t)/den1*p4;
LorentzVector<Complex> eps4Perp = 2./den2*epsilon(p1,p2,p4);
eps3.push_back(sqrt(0.5)*(eps3Para+I*eps3Perp));
eps3.push_back(sqrt(0.5)*(eps3Para-I*eps3Perp));
eps4.push_back(sqrt(0.5)*(eps4Para+I*eps4Perp));
eps4.push_back(sqrt(0.5)*(eps4Para-I*eps4Perp));
if(m2!=ZERO) assert(false);
}
// both initial-state
else if(iopt==1) {
if(m2!=ZERO) assert(false);
LorentzVector<Complex> eps3Para( 1., 0.,0.,0.);
LorentzVector<Complex> eps3Perp( 0.,-1.,0.,0.);
LorentzVector<Complex> eps4Para(-1.,0.,0., 0.);
LorentzVector<Complex> eps4Perp( 0., 1.,0.,0.);
eps3.push_back(sqrt(0.5)*(eps3Para+I*eps3Perp));
eps3.push_back(sqrt(0.5)*(eps3Para-I*eps3Perp));
eps4.push_back(sqrt(0.5)*(eps4Para+I*eps4Perp));
eps4.push_back(sqrt(0.5)*(eps4Para-I*eps4Perp));
}
else if(iopt==2) {
// rotation into the 2,3 Breit frame
Lorentz5Momentum pa = p3-p2;
Axis axis(pa.vect().unit());
LorentzRotation rot;
double sinth(sqrt(sqr(axis.x())+sqr(axis.y())));
if ( sinth > 1.e-9 )
rot.setRotate(-acos(axis.z()),Axis(-axis.y()/sinth,axis.x()/sinth,0.));
rot.rotateX(Constants::pi);
rot.boostZ( pa.e()/pa.vect().mag());
Lorentz5Momentum ptemp=rot*p2;
Boost trans = -1./ptemp.e()*ptemp.vect();
trans.setZ(0.);
rot.boost(trans);
LorentzVector<Complex> eps3Para( 1., 0.,0.,0.);
LorentzVector<Complex> eps3Perp( 0.,-1.,0.,0.);
LorentzVector<Complex> eps4Para(-1.,0.,0., 0.);
LorentzVector<Complex> eps4Perp( 0., 1.,0.,0.);
eps3.push_back(sqrt(0.5)*(eps3Para+I*eps3Perp));
eps3.push_back(sqrt(0.5)*(eps3Para-I*eps3Perp));
eps4.push_back(sqrt(0.5)*(eps4Para+I*eps4Perp));
eps4.push_back(sqrt(0.5)*(eps4Para-I*eps4Perp));
rot = rot.invert();
for(unsigned int ix=0;ix<2;++ix) {
eps3[ix] *=rot;
eps4[ix] *=rot;
}
}
else if(iopt==3) {
// rotation into the 1,4 Breit frame
Lorentz5Momentum pa = p4-p1;
Axis axis(pa.vect().unit());
LorentzRotation rot;
double sinth(sqrt(sqr(axis.x())+sqr(axis.y())));
if ( sinth > 1.e-9 )
rot.setRotate(-acos(axis.z()),Axis(-axis.y()/sinth,axis.x()/sinth,0.));
rot.rotateX(Constants::pi);
rot.boostZ( pa.e()/pa.vect().mag());
Lorentz5Momentum ptemp=rot*p1;
Boost trans = -1./ptemp.e()*ptemp.vect();
trans.setZ(0.);
rot.boost(trans);
LorentzVector<Complex> eps3Para( 1., 0.,0.,0.);
LorentzVector<Complex> eps3Perp( 0.,-1.,0.,0.);
LorentzVector<Complex> eps4Para(-1.,0.,0., 0.);
LorentzVector<Complex> eps4Perp( 0., 1.,0.,0.);
eps3.push_back(sqrt(0.5)*(eps3Para+I*eps3Perp));
eps3.push_back(sqrt(0.5)*(eps3Para-I*eps3Perp));
eps4.push_back(sqrt(0.5)*(eps4Para+I*eps4Perp));
eps4.push_back(sqrt(0.5)*(eps4Para-I*eps4Perp));
rot = rot.invert();
for(unsigned int ix=0;ix<2;++ix) {
eps3[ix] *=rot;
eps4[ix] *=rot;
}
}
else
assert(false);
}
}
double ElectroWeakReweighter::reweightqqbargg() const {
// momenta and invariants
Lorentz5Momentum p1 = subProcess()->incoming().first ->momentum();
tcPDPtr q = subProcess()->incoming().first ->dataPtr();
Lorentz5Momentum p2 = subProcess()->incoming().second->momentum();
tcPDPtr qbar = subProcess()->incoming().second->dataPtr();
if(subProcess()->incoming().first->id()<0) {
swap(p1,p2 );
swap(q ,qbar);
}
Lorentz5Momentum p3 = subProcess()->outgoing()[0]->momentum();
Lorentz5Momentum p4 = subProcess()->outgoing()[1]->momentum();
tcPDPtr g = subProcess()->outgoing()[1]->dataPtr();
Energy2 s = (p1+p2).m2();
Energy2 t = (p1-p4).m2();
Energy2 u = (p1-p3).m2();
// boost to partonci rest frame
Lorentz5Momentum psum=p1+p2;
LorentzRotation boost(-psum.boostVector());
p1 *= boost;
p2 *= boost;
p3 *= boost;
p4 *= boost;
// LO and EW corrected matrix element coefficients
boost::numeric::ublas::matrix<complex<InvEnergy2> >
bornQQGGweights,bornRRGGweights,EWQQGGweights,EWRRGGweights;
// quark left doublet
if(q->id()!=5) {
bornQQGGweights = evaluateRunning(EWProcess::QQGG,s,t,u,true ,0);
EWQQGGweights = evaluateRunning(EWProcess::QQGG,s,t,u,false,0);
}
else {
bornQQGGweights = evaluateRunning(EWProcess::QtQtGG,s,t,u,true ,0);
EWQQGGweights = evaluateRunning(EWProcess::QtQtGG,s,t,u,false,0);
}
// quark right singlet
if(abs(subProcess()->incoming().first->id())%2==0) {
bornRRGGweights = evaluateRunning(EWProcess::UUGG,s,t,u,true ,0);
EWRRGGweights = evaluateRunning(EWProcess::UUGG,s,t,u,false,0);
}
else {
bornRRGGweights = evaluateRunning(EWProcess::DDGG,s,t,u,true ,0);
EWRRGGweights = evaluateRunning(EWProcess::DDGG,s,t,u,false,0);
}
SpinorWaveFunction qw(p1,q ,incoming);
SpinorBarWaveFunction qbarw(p2,qbar,incoming);
vector<LorentzVector<Complex> > eps3,eps4;
SackGluonPolarizations(p1,p2,p3,p4,s,t,u,ZERO,eps3,eps4,0);
boost::numeric::ublas::matrix<Complex>
bornME = boost::numeric::ublas::zero_matrix<Complex>(3,3),
EWME = boost::numeric::ublas::zero_matrix<Complex>(3,3);
for(unsigned int iq=0;iq<2;++iq) {
if(iq==0) {
qw.reset (0);
qbarw.reset(1);
}
else {
qw.reset (1);
qbarw.reset(0);
}
LorentzVector<complex<Energy> > current = iq==0 ?
qw.dimensionedWave(). leftCurrent(qbarw.dimensionedWave()) :
qw.dimensionedWave().rightCurrent(qbarw.dimensionedWave());
for(unsigned int i1=0;i1<2;++i1) {
complex<Energy> d31 = eps3[i1].dot(p1);
for(unsigned int i2=0;i2<2;++i2) {
// g1w.reset(2*i1);
// g2w.reset(2*i2);
boost::numeric::ublas::vector<complex<Energy2> > M(5);
Complex d34 = eps3[i1].dot(eps4[i2]);
complex<Energy> d42 = eps4[i2].dot(p2);
// M0 in paper
M(0) = qw.dimensionedWave().slash(eps3[i1])
.slash(p4-p2).vectorCurrent(qbarw.dimensionedWave()).dot(eps4[i2]);
// M4 in paper
M(2) = current.dot(eps4[i2])*d31;
// M5 in paper
M(3) = -current.dot(eps3[i1])*d42;
// M1 in paper (missing factor)
M(1) = current.dot(p4);
// M6 in paper
M(4) = M(1)*d31*d42/GeV2;
// M1 final factor
M(1) *= d34;
// coefficient of different contributions
boost::numeric::ublas::vector<Complex> Cborn(3),CEW(3),Ctest(3);
// Ctest(0) = 1./6.*( MEU+MET);
// Ctest(1) = 0.5*( MEU+MET);
// Ctest(2) = 0.5*(MEU+MES-MET+MES);
if(iq==0) {
axpy_prod_local(bornQQGGweights,M,Cborn);
axpy_prod_local(EWQQGGweights ,M,CEW );
}
else {
axpy_prod_local(bornRRGGweights,M,Cborn);
axpy_prod_local(EWRRGGweights ,M,CEW );
}
unsigned int ioff = (Cborn.size()==6 && q->id()%2!=0) ? 3 : 0;
for(unsigned int ix=0;ix<3;++ix) {
for(unsigned int iy=0;iy<3;++iy) {
bornME(ix,iy) += Cborn(ix+ioff)*conj(Cborn(iy+ioff));
EWME (ix,iy) += CEW (ix+ioff)*conj(CEW (iy+ioff));
}
}
}
}
}
double born = 24.*real(bornME(0,0))+20./3.*real(bornME(1,1))+12.*real(bornME(2,2));
double EW = 24.*real(EWME(0,0))+20./3.*real(EWME(1,1))+12.*real(EWME(2,2));
return EW/born;
}
boost::numeric::ublas::matrix<complex<InvEnergy2> >
ElectroWeakReweighter::evaluateRunning(EWProcess::Process process, Energy2 s,
Energy2 t, Energy2 u, bool born,
unsigned int iswap) const {
using namespace boost::numeric::ublas;
bool SU3save = coupling()->SU3();
bool EWsave = coupling()-> EW();
Energy highScale = sqrt(s);
Energy ewScale = coupling()->mZ();
Energy lowScale = ewScale;
// result for all EW and QCD SCET contributions:
// MATCHING CONTRIBUTIONS
// high energy matching
matrix<complex<InvEnergy2> > highMatch_val;
if(iswap==0)
highMatch_val = HighEnergyMatching::highEnergyMatching(highScale,s,t,u,process,!born,false);
else if(iswap==1)
highMatch_val = HighEnergyMatching::highEnergyMatching(highScale,t,s,u,process,!born,false);
else if(iswap==2)
highMatch_val = HighEnergyMatching::highEnergyMatching(highScale,u,t,s,process,!born,false);
else
assert(false);
// low energy matching
matrix<Complex>
ewMatch_val = ElectroWeakMatching::electroWeakMatching(ewScale,s,t,u,process,!born,iswap);
matrix<Complex> collinearEWMatch_val =
collinearSudakov_->electroWeakMatching(ewScale,s,process,!born);
// EVOLUTION
matrix<Complex> highRunning_val,lowRunning_val,
collinearHighRunning_val,collinearLowRunning_val;
// born process
if(born) {
highRunning_val = identity_matrix<Complex>(softSudakov_->numberGauge(process));
lowRunning_val = identity_matrix<Complex>(softSudakov_->numberBrokenGauge(process));
collinearHighRunning_val = identity_matrix<Complex>(softSudakov_->numberGauge(process));
collinearLowRunning_val = identity_matrix<Complex>(softSudakov_->numberBrokenGauge(process));
}
// EW corrected
else {
coupling()->SU3(false);
coupling()-> EW( true);
highRunning_val = softSudakov_->highEnergyRunning(highScale, ewScale,s,t,u,process,iswap);
lowRunning_val = softSudakov_->lowEnergyRunning ( ewScale,lowScale,s,t,u,process,iswap);
collinearHighRunning_val = collinearSudakov_->highEnergyRunning(highScale,ewScale,s,process,false);
collinearLowRunning_val = collinearSudakov_->lowEnergyRunning(ewScale,lowScale,s,process);
};
matrix<Complex> lowMatchTemp_val =
zero_matrix<Complex>(ewMatch_val.size1(),ewMatch_val.size2());
for (unsigned int ii=0; ii<ewMatch_val.size1(); ++ii) {
for (unsigned int jj=0; jj<ewMatch_val.size2(); ++jj) {
lowMatchTemp_val(ii,jj) = collinearEWMatch_val(ii,jj)*ewMatch_val(ii,jj);
}
}
// perform all the multiplications
matrix<Complex> temp(highRunning_val.size1(),collinearHighRunning_val.size2());
axpy_prod(highRunning_val,collinearHighRunning_val,temp);
matrix<Complex> temp2(collinearLowRunning_val.size1(),lowRunning_val.size2());
axpy_prod(collinearLowRunning_val,lowRunning_val,temp2);
matrix<Complex> temp3(temp2.size1(),lowMatchTemp_val.size2());
axpy_prod(temp2,lowMatchTemp_val,temp3);
temp2.resize(temp3.size1(),temp.size2());
axpy_prod(temp3,temp,temp2);
matrix<complex<InvEnergy2> > result(temp2.size1(),highMatch_val.size2());
axpy_prod_local(temp2,highMatch_val,result);
// reset the couplings
coupling()->SU3(SU3save);
coupling()-> EW( EWsave);
// return the answer
return result;
}
double ElectroWeakReweighter::reweightggqqbar() const {
// momenta and invariants
Lorentz5Momentum p1 = subProcess()->incoming().first ->momentum();
Lorentz5Momentum p2 = subProcess()->incoming().second->momentum();
Lorentz5Momentum p3 = subProcess()->outgoing()[0]->momentum();
Lorentz5Momentum p4 = subProcess()->outgoing()[1]->momentum();
tcPDPtr qbar = subProcess()->outgoing()[0]->dataPtr();
tcPDPtr q = subProcess()->outgoing()[1]->dataPtr();
if(q->id()<0) {
swap(p3,p4 );
swap(q ,qbar);
}
Energy2 s = (p1+p2).m2();
Energy2 t = (p1-p4).m2();
Energy2 u = (p1-p3).m2();
// boost to partonic rest frame and rescale momenta of outgoing
// so zero mass
Lorentz5Momentum psum=p1+p2;
LorentzRotation boost(-psum.boostVector());
p1 *= boost;
p2 *= boost;
p3 *= boost;
p4 *= boost;
p3.setMass(ZERO);
p3.rescaleRho();
p4.setMass(ZERO);
p4.rescaleRho();
// LO and EW matrix element coefficents
boost::numeric::ublas::matrix<complex<InvEnergy2> >
bornQQGGweights,bornRRGGweights,EWQQGGweights,EWRRGGweights;
// quark left doublet
if(q->id()<5) {
bornQQGGweights = evaluateRunning(EWProcess::QQGG,s,t,u,true ,0);
EWQQGGweights = evaluateRunning(EWProcess::QQGG,s,t,u,false,0);
}
else {
bornQQGGweights = evaluateRunning(EWProcess::QtQtGG,s,t,u,true ,0);
EWQQGGweights = evaluateRunning(EWProcess::QtQtGG,s,t,u,false,0);
}
// quark right singlet
if(q->id()==0) {
if(q->id()==6) {
bornRRGGweights = evaluateRunning(EWProcess::tRtRGG,s,t,u,true ,0);
EWRRGGweights = evaluateRunning(EWProcess::tRtRGG,s,t,u,false,0);
}
else {
bornRRGGweights = evaluateRunning(EWProcess::UUGG,s,t,u,true ,0);
EWRRGGweights = evaluateRunning(EWProcess::UUGG,s,t,u,false,0);
}
}
else {
bornRRGGweights = evaluateRunning(EWProcess::DDGG,s,t,u,true ,0);
EWRRGGweights = evaluateRunning(EWProcess::DDGG,s,t,u,false,0);
}
SpinorWaveFunction qw(p4,qbar,incoming);
SpinorBarWaveFunction qbarw(p3,q ,incoming);
vector<LorentzVector<Complex> > eps1,eps2;
SackGluonPolarizations(p1,p2,p3,p4,s,t,u,ZERO,eps1,eps2,1);
boost::numeric::ublas::matrix<Complex>
bornME = boost::numeric::ublas::zero_matrix<Complex>(3,3),
EWME = boost::numeric::ublas::zero_matrix<Complex>(3,3);
// helicities of outgoing quarks
for(unsigned int iq=0;iq<2;++iq) {
if(iq==0) {
qw.reset (0);
qbarw.reset(1);
}
else {
qw.reset (1);
qbarw.reset(0);
}
LorentzVector<complex<Energy> > current = iq==0 ?
qw.dimensionedWave(). leftCurrent(qbarw.dimensionedWave()) :
qw.dimensionedWave().rightCurrent(qbarw.dimensionedWave());
for(unsigned int i1=0;i1<2;++i1) {
complex<Energy> d31 = eps1[i1].dot(p3);
for(unsigned int i2=0;i2<2;++i2) {
boost::numeric::ublas::vector<complex<Energy2> > M(5);
Complex d34 = eps1[i1].dot(eps2[i2]);
complex<Energy> d42 = eps2[i2].dot(p4);
// M0 in paper
M(0) = qw.dimensionedWave().slash(eps1[i1])
.slash(p2-p4).vectorCurrent(qbarw.dimensionedWave()).dot(eps2[i2]);
// M4 in paper
M(2) = current.dot(eps2[i2])*d31;
// M5 in paper
M(3) = -current.dot(eps1[i1])*d42;
// M1 in paper (missing factor)
M(1) = current.dot(p2);
// M6 in paper
M(4) = M(1)*d31*d42/GeV2;
// M1 final factor
M(1) *= d34;
// coefficient of different contributions
boost::numeric::ublas::vector<Complex> Cborn(3),CEW(3);
if(iq==0) {
axpy_prod_local(bornQQGGweights,M,Cborn);
axpy_prod_local(EWQQGGweights ,M,CEW );
}
else {
axpy_prod_local(bornRRGGweights,M,Cborn);
axpy_prod_local(EWRRGGweights ,M,CEW );
}
unsigned int ioff = (Cborn.size()==6 && q->id()%2!=0) ? 3 : 0;
for(unsigned int ix=0;ix<3;++ix) {
for(unsigned int iy=0;iy<3;++iy) {
bornME(ix,iy) += Cborn(ix+ioff)*conj(Cborn(iy+ioff));
EWME (ix,iy) += CEW (ix+ioff)*conj(CEW (iy+ioff));
}
}
}
}
}
double born = 24.*real(bornME(0,0))+20./3.*real(bornME(1,1))+12.*real(bornME(2,2));
double EW = 24.*real(EWME(0,0))+20./3.*real(EWME(1,1))+12.*real(EWME(2,2));
return EW/born;
}
double ElectroWeakReweighter::reweightqgqg() const {
// momenta and invariants
Lorentz5Momentum p1 = subProcess()->incoming().first ->momentum();
Lorentz5Momentum p2 = subProcess()->incoming().second->momentum();
tcPDPtr q;
if(subProcess()->incoming().first->id()!=ParticleID::g) {
q = subProcess()->incoming().first ->dataPtr();
}
else {
q = subProcess()->incoming().second->dataPtr();
swap(p1,p2);
}
Lorentz5Momentum p3 = subProcess()->outgoing()[0]->momentum();
Lorentz5Momentum p4 = subProcess()->outgoing()[1]->momentum();
if(subProcess()->outgoing()[0]->id()!=ParticleID::g)
swap(p3,p4);
Energy2 s = (p1+p2).m2();
Energy2 t = (p1-p4).m2();
Energy2 u = (p1-p3).m2();
// boost to partonic rest frame
Lorentz5Momentum psum=p1+p2;
LorentzRotation boost(-psum.boostVector());
p1 *= boost;
p2 *= boost;
p3 *= boost;
p4 *= boost;
// LO and EW corrected matrix element coefficients
boost::numeric::ublas::matrix<complex<InvEnergy2> >
bornQQGGweights,bornRRGGweights,EWQQGGweights,EWRRGGweights;
// quark left doublet
if(q->id()!=5) {
bornQQGGweights = evaluateRunning(EWProcess::QQGG,s,t,u,true ,1);
EWQQGGweights = evaluateRunning(EWProcess::QQGG,s,t,u,false,1);
}
else {
bornQQGGweights = evaluateRunning(EWProcess::QtQtGG,s,t,u,true ,1);
EWQQGGweights = evaluateRunning(EWProcess::QtQtGG,s,t,u,false,1);
}
// quark right singlet
if(abs(q->id())%2==0) {
bornRRGGweights = evaluateRunning(EWProcess::UUGG,s,t,u,true ,1);
EWRRGGweights = evaluateRunning(EWProcess::UUGG,s,t,u,false,1);
}
else {
bornRRGGweights = evaluateRunning(EWProcess::DDGG,s,t,u,true ,1);
EWRRGGweights = evaluateRunning(EWProcess::DDGG,s,t,u,false,1);
}
SpinorWaveFunction qw(p1,q,incoming);
SpinorBarWaveFunction qbarw(p4,q,outgoing);
vector<LorentzVector<Complex> > eps2,eps3;
SackGluonPolarizations(p1,p2,p3,p4,s,t,u,ZERO,eps2,eps3,2);
// compute the matrix elements
boost::numeric::ublas::matrix<Complex>
bornME = boost::numeric::ublas::zero_matrix<Complex>(3,3),
EWME = boost::numeric::ublas::zero_matrix<Complex>(3,3),
testME = boost::numeric::ublas::zero_matrix<Complex>(3,3);
for(unsigned int iq=0;iq<2;++iq) {
if(iq==0) {
qw.reset (0);
qbarw.reset(0);
}
else {
qw.reset (1);
qbarw.reset(1);
}
LorentzVector<complex<Energy> > current = iq==0 ?
qw.dimensionedWave(). leftCurrent(qbarw.dimensionedWave()) :
qw.dimensionedWave().rightCurrent(qbarw.dimensionedWave());
for(unsigned int i1=0;i1<2;++i1) {
complex<Energy> d31 = eps3[i1].dot(p1);
for(unsigned int i2=0;i2<2;++i2) {
boost::numeric::ublas::vector<complex<Energy2> > M(5);
Complex d34 = eps3[i1].dot(eps2[i2]);
complex<Energy> d42 = eps2[i2].dot(p4);
// M0 in paper
M(0) = qw.dimensionedWave().slash(eps3[i1])
.slash(p2-p4).vectorCurrent(qbarw.dimensionedWave()).dot(eps2[i2]);
// M4 in paper
M(2) = current.dot(eps2[i2])*d31;
// M5 in paper
M(3) = -current.dot(eps3[i1])*d42;
// M1 in paper (missing factor)
M(1) = current.dot(p2);
// M6 in paper
M(4) = M(1)*d31*d42/GeV2;
// M1 final factor
M(1) *= d34;
// coefficient of different contributions
boost::numeric::ublas::vector<Complex> Cborn(3),CEW(3);
if(iq==0) {
axpy_prod_local(bornQQGGweights,M,Cborn);
axpy_prod_local(EWQQGGweights ,M,CEW );
}
else {
axpy_prod_local(bornRRGGweights,M,Cborn);
axpy_prod_local(EWRRGGweights ,M,CEW );
}
unsigned int ioff = (Cborn.size()==6 && q->id()%2!=0) ? 3 : 0;
for(unsigned int ix=0;ix<3;++ix) {
for(unsigned int iy=0;iy<3;++iy) {
bornME(ix,iy) += Cborn(ix+ioff)*conj(Cborn(iy+ioff));
EWME (ix,iy) += CEW (ix+ioff)*conj(CEW (iy+ioff));
}
}
}
}
}
double born = 24.*real(bornME(0,0))+20./3.*real(bornME(1,1))+12.*real(bornME(2,2));
double EW = 24.*real(EWME(0,0))+20./3.*real(EWME(1,1))+12.*real(EWME(2,2));
return EW/born;
}
double ElectroWeakReweighter::reweightqbargqbarg() const {
// momenta and invariants
Lorentz5Momentum p1 = subProcess()->incoming().first ->momentum();
Lorentz5Momentum p2 = subProcess()->incoming().second->momentum();
tcPDPtr qbar;
if(subProcess()->incoming().first->id()==ParticleID::g) {
qbar = subProcess()->incoming().second->dataPtr();
}
else {
qbar = subProcess()->incoming().first ->dataPtr();
swap(p1,p2);
}
Lorentz5Momentum p3 = subProcess()->outgoing()[0]->momentum();
Lorentz5Momentum p4 = subProcess()->outgoing()[1]->momentum();
if(subProcess()->outgoing()[0]->id()==ParticleID::g)
swap(p3,p4);
Energy2 s = (p1+p2).m2();
Energy2 t = (p1-p4).m2();
Energy2 u = (p1-p3).m2();
// boost to partonci rest frame
Lorentz5Momentum psum=p1+p2;
LorentzRotation boost(-psum.boostVector());
p1 *= boost;
p2 *= boost;
p3 *= boost;
p4 *= boost;
// LO and EW corrected matrix element coefficients
boost::numeric::ublas::matrix<complex<InvEnergy2> >
bornQQGGweights,bornRRGGweights,EWQQGGweights,EWRRGGweights;
// quark left doublet
if(qbar->id()!=-5) {
bornQQGGweights = evaluateRunning(EWProcess::QQGG,s,t,u,true ,1);
EWQQGGweights = evaluateRunning(EWProcess::QQGG,s,t,u,false,1);
}
else {
bornQQGGweights = evaluateRunning(EWProcess::QtQtGG,s,t,u,true ,1);
EWQQGGweights = evaluateRunning(EWProcess::QtQtGG,s,t,u,false,1);
}
// quark right singlet
if(abs(qbar->id())%2==0) {
bornRRGGweights = evaluateRunning(EWProcess::UUGG,s,t,u,true ,1);
EWRRGGweights = evaluateRunning(EWProcess::UUGG,s,t,u,false,1);
}
else {
bornRRGGweights = evaluateRunning(EWProcess::DDGG,s,t,u,true ,1);
EWRRGGweights = evaluateRunning(EWProcess::DDGG,s,t,u,false,1);
}
SpinorWaveFunction qw(p3,qbar,outgoing);
SpinorBarWaveFunction qbarw(p2,qbar,incoming);
vector<LorentzVector<Complex> > eps1,eps4;
SackGluonPolarizations(p1,p2,p3,p4,s,t,u,ZERO,eps1,eps4,3);
boost::numeric::ublas::matrix<Complex>
bornME = boost::numeric::ublas::zero_matrix<Complex>(3,3),
EWME = boost::numeric::ublas::zero_matrix<Complex>(3,3);
for(unsigned int iq=0;iq<2;++iq) {
if(iq==0) {
qw.reset (1);
qbarw.reset(1);
}
else {
qw.reset (0);
qbarw.reset(0);
}
LorentzVector<complex<Energy> > current = iq==0 ?
qw.dimensionedWave(). leftCurrent(qbarw.dimensionedWave()) :
qw.dimensionedWave().rightCurrent(qbarw.dimensionedWave());
for(unsigned int i1=0;i1<2;++i1) {
complex<Energy> d31 = eps1[i1].dot(p3);
for(unsigned int i2=0;i2<2;++i2) {
boost::numeric::ublas::vector<complex<Energy2> > M(5);
Complex d34 = eps1[i1].dot(eps4[i2]);
complex<Energy> d42 = eps4[i2].dot(p2);
// M0 in paper
M(0) = qw.dimensionedWave().slash(eps1[i1])
.slash(p4-p2).vectorCurrent(qbarw.dimensionedWave()).dot(eps4[i2]);
// M4 in paper
M(2) = current.dot(eps4[i2])*d31;
// M5 in paper
M(3) = -current.dot(eps1[i1])*d42;
// M1 in paper (missing factor)
M(1) = current.dot(p4);
// M6 in paper
M(4) = M(1)*d31*d42/GeV2;
// M1 final factor
M(1) *= d34;
// coefficient of different contributions
boost::numeric::ublas::vector<Complex> Cborn(3),CEW(3);
if(iq==0) {
axpy_prod_local(bornQQGGweights,M,Cborn);
axpy_prod_local(EWQQGGweights ,M,CEW );
}
else {
axpy_prod_local(bornRRGGweights,M,Cborn);
axpy_prod_local(EWRRGGweights ,M,CEW );
}
unsigned int ioff = (Cborn.size()==6 && abs(qbar->id())%2!=0) ? 3 : 0;
for(unsigned int ix=0;ix<3;++ix) {
for(unsigned int iy=0;iy<3;++iy) {
bornME(ix,iy) += Cborn(ix+ioff)*conj(Cborn(iy+ioff));
EWME (ix,iy) += CEW (ix+ioff)*conj(CEW (iy+ioff));
}
}
}
}
}
double born = 24.*real(bornME(0,0))+20./3.*real(bornME(1,1))+12.*real(bornME(2,2));
double EW = 24.*real(EWME(0,0))+20./3.*real(EWME(1,1))+12.*real(EWME(2,2));
return EW/born;
}
double ElectroWeakReweighter::reweightqqbarqqbarS() const {
// momenta and invariants
Lorentz5Momentum p1 = subProcess()->incoming().first ->momentum();
tcPDPtr q1 = subProcess()->incoming().first ->dataPtr();
Lorentz5Momentum p2 = subProcess()->incoming().second->momentum();
tcPDPtr q1bar = subProcess()->incoming().second->dataPtr();
if(q1->id()<0) {
swap(p1,p2 );
swap(q1 ,q1bar);
}
Lorentz5Momentum p3 = subProcess()->outgoing()[0]->momentum();
tcPDPtr q2bar = subProcess()->outgoing()[0]->dataPtr();
Lorentz5Momentum p4 = subProcess()->outgoing()[1]->momentum();
tcPDPtr q2 = subProcess()->outgoing()[1]->dataPtr();
if(q2bar->id()>0) {
swap(p3,p4 );
swap(q2 ,q2bar);
}
Energy2 s = (p1+p2).m2();
Energy2 t = (p1-p4).m2();
Energy2 u = (p1-p3).m2();
// boost to partonci rest frame
Lorentz5Momentum psum=p1+p2;
LorentzRotation boost(-psum.boostVector());
p1 *= boost;
p2 *= boost;
p3 *= boost;
p4 *= boost;
p3.setMass(ZERO);
p3.rescaleRho();
p4.setMass(ZERO);
p4.rescaleRho();
// LO and EW corrected matrix element coefficients
boost::numeric::ublas::matrix<complex<InvEnergy2> >
bornLLLLWeights,bornLLRRWeights,bornRRLLWeights,bornRRRRWeights,
EWLLLLWeights,EWLLRRWeights,EWRRLLWeights,EWRRRRWeights;
bool ident = q1->id()==q2->id();
// LL -> LL
if((q1->id()<=4&& q2->id()<=4)|| (q1->id()==5 && q2->id()==5)) {
if(!ident) {
bornLLLLWeights = evaluateRunning(EWProcess::QQQQ,s,t,u,true ,0);
EWLLLLWeights = evaluateRunning(EWProcess::QQQQ,s,t,u,false,0);
}
else {
bornLLLLWeights = evaluateRunning(EWProcess::QQQQiden,s,t,u,true ,0);
EWLLLLWeights = evaluateRunning(EWProcess::QQQQiden,s,t,u,false,0);
}
}
else if(q1->id()==5 || q2->id()>=5) {
bornLLLLWeights = evaluateRunning(EWProcess::QtQtQQ,s,t,u,true ,0);
EWLLLLWeights = evaluateRunning(EWProcess::QtQtQQ,s,t,u,false,0);
}
else
assert(false);
// RR -> LL
if(q1->id()%2==0) {
if(q2->id()<5) {
bornRRLLWeights = evaluateRunning(EWProcess::QQUU,s,t,u,true ,0);
EWRRLLWeights = evaluateRunning(EWProcess::QQUU,s,t,u,false,0);
}
else {
bornRRLLWeights = evaluateRunning(EWProcess::QtQtUU,s,t,u,true ,0);
EWRRLLWeights = evaluateRunning(EWProcess::QtQtUU,s,t,u,false,0);
}
}
else {
if(q2->id()<5) {
bornRRLLWeights = evaluateRunning(EWProcess::QQDD,s,t,u,true ,0);
EWRRLLWeights = evaluateRunning(EWProcess::QQDD,s,t,u,false,0);
}
else {
bornRRLLWeights = evaluateRunning(EWProcess::QtQtDD,s,t,u,true ,0);
EWRRLLWeights = evaluateRunning(EWProcess::QtQtDD,s,t,u,false,0);
}
}
// LL -> RR
if(q1->id()<=4) {
if(q2->id()%2!=0) {
bornLLRRWeights = evaluateRunning(EWProcess::QQDD,s,t,u,true ,0);
EWLLRRWeights = evaluateRunning(EWProcess::QQDD,s,t,u,false,0);
}
else if (q2->id()==6) {
bornLLRRWeights = evaluateRunning(EWProcess::QQtRtR,s,t,u,true ,0);
EWLLRRWeights = evaluateRunning(EWProcess::QQtRtR,s,t,u,false,0);
}
else {
bornLLRRWeights = evaluateRunning(EWProcess::QQUU,s,t,u,true ,0);
EWLLRRWeights = evaluateRunning(EWProcess::QQUU,s,t,u,false,0);
}
}
else {
if(q2->id()%2!=0) {
bornLLRRWeights = evaluateRunning(EWProcess::QtQtDD,s,t,u,true ,0);
EWLLRRWeights = evaluateRunning(EWProcess::QtQtDD,s,t,u,false,0);
}
else {
bornLLRRWeights = evaluateRunning(EWProcess::QtQtUU,s,t,u,true ,0);
EWLLRRWeights = evaluateRunning(EWProcess::QtQtUU,s,t,u,false,0);
}
}
// RR -> RR
if(q1->id()%2==0) {
if(q2->id()==6) {
bornRRRRWeights = evaluateRunning(EWProcess::tRtRUU,s,t,u,true ,0);
EWRRRRWeights = evaluateRunning(EWProcess::tRtRUU,s,t,u,false,0);
}
else if(q2->id()%2==0) {
if(ident) {
bornRRRRWeights = evaluateRunning(EWProcess::UUUUiden,s,t,u,true ,0);
EWRRRRWeights = evaluateRunning(EWProcess::UUUUiden,s,t,u,false,0);
}
else {
bornRRRRWeights = evaluateRunning(EWProcess::UUUU,s,t,u,true ,0);
EWRRRRWeights = evaluateRunning(EWProcess::UUUU,s,t,u,false,0);
}
}
else {
bornRRRRWeights = evaluateRunning(EWProcess::UUDD,s,t,u,true ,0);
EWRRRRWeights = evaluateRunning(EWProcess::UUDD,s,t,u,false,0);
}
}
else {
if(q2->id()==6) {
bornRRRRWeights = evaluateRunning(EWProcess::tRtRDD,s,t,u,true ,0);
EWRRRRWeights = evaluateRunning(EWProcess::tRtRDD,s,t,u,false,0);
}
else if(q2->id()%2==0) {
bornRRRRWeights = evaluateRunning(EWProcess::UUDD,s,t,u,true ,0);
EWRRRRWeights = evaluateRunning(EWProcess::UUDD,s,t,u,false,0);
}
else {
if(ident) {
bornRRRRWeights = evaluateRunning(EWProcess::DDDDiden,s,t,u,true ,0);
EWRRRRWeights = evaluateRunning(EWProcess::DDDDiden,s,t,u,false,0);
}
else {
bornRRRRWeights = evaluateRunning(EWProcess::DDDD,s,t,u,true ,0);
EWRRRRWeights = evaluateRunning(EWProcess::DDDD,s,t,u,false,0);
}
}
}
// extra terms for identical particles
boost::numeric::ublas::matrix<complex<InvEnergy2> >
borntChannelWeights,EWtChannelWeights;
if(ident) {
if(q1->id()%2==0) {
borntChannelWeights = evaluateRunning(EWProcess::QQUU,s,t,u,true ,1);
EWtChannelWeights = evaluateRunning(EWProcess::QQUU,s,t,u,false,1);
}
else if(q1->id()==5) {
borntChannelWeights = evaluateRunning(EWProcess::QtQtDD,s,t,u,true ,1);
EWtChannelWeights = evaluateRunning(EWProcess::QtQtDD,s,t,u,false,1);
}
else {
borntChannelWeights = evaluateRunning(EWProcess::QQDD,s,t,u,true ,1);
EWtChannelWeights = evaluateRunning(EWProcess::QQDD,s,t,u,false,1);
}
}
SpinorWaveFunction q1w(p1,q1 ,incoming);
SpinorBarWaveFunction q1barw(p2,q1bar,incoming);
SpinorWaveFunction q2barw(p3,q2bar,outgoing);
SpinorBarWaveFunction q2w(p4,q2 ,outgoing);
boost::numeric::ublas::matrix<Complex>
bornME = boost::numeric::ublas::zero_matrix<Complex>(2,2),
EWME = boost::numeric::ublas::zero_matrix<Complex>(2,2);
for(unsigned int iq1=0;iq1<2;++iq1) {
if(iq1==0) {
q1w.reset (0);
q1barw.reset(1);
}
else {
q1w.reset (1);
q1barw.reset(0);
}
LorentzVector<complex<Energy> > current1 =
q1w.dimensionedWave().vectorCurrent(q1barw.dimensionedWave());
for(unsigned int iq2=0;iq2<2;++iq2) {
if(iq2==0) {
q2w.reset (0);
q2barw.reset(1);
}
else {
q2w.reset (1);
q2barw.reset(0);
}
LorentzVector<complex<Energy> > current2 =
q2barw.dimensionedWave().vectorCurrent(q2w.dimensionedWave());
complex<Energy2> amp = current1.dot(current2);
vector<Complex> Cborn(2),CEW(2);
// amplitudes
if(iq1==0) {
// LL
if(iq2==0) {
unsigned int ioff;
if(q1->id()%2==0) {
ioff = q2->id()%2==0 ? 0 : 2;
}
else {
ioff = q2->id()%2==0 ? 1 : 3;
}
for(unsigned int ix=0;ix<2;++ix) {
Cborn[ix] = amp*bornLLLLWeights(6*ix+ioff,0);
CEW [ix] = amp* EWLLLLWeights(6*ix+ioff,0);
}
}
// LR
else {
unsigned int ioff = q1->id()%2==0 ? 0 : 1;
for(unsigned int ix=0;ix<2;++ix) {
Cborn[ix] = amp*bornLLRRWeights(2*ix+ioff,0);
CEW [ix] = amp* EWLLRRWeights(2*ix+ioff,0);
}
}
}
else {
if(iq2==0) {
unsigned int ioff=q2->id()%2==0 ? 0 : 1;
for(unsigned int ix=0;ix<2;++ix) {
Cborn[ix] = amp*bornRRLLWeights(2*ix+ioff,0);
CEW [ix] = amp* EWRRLLWeights(2*ix+ioff,0);
}
}
else {
for(unsigned int ix=0;ix<2;++ix) {
Cborn[ix] = amp*bornRRRRWeights(ix,0);
CEW [ix] = amp* EWRRRRWeights(ix,0);
}
}
}
// square
for(unsigned int ix=0;ix<2;++ix) {
for(unsigned int iy=0;iy<2;++iy) {
bornME(ix,iy) += Cborn[ix]*conj(Cborn[iy]);
EWME (ix,iy) += CEW [ix]*conj(CEW [iy]);
}
}
}
}
// extra t-channel pieces if identical flavours
if(ident) {
for(unsigned int iq1=0;iq1<2;++iq1) {
q1w.reset(iq1);
q2w.reset(iq1);
LorentzVector<complex<Energy> > current1 =
q1w.dimensionedWave().vectorCurrent(q2w.dimensionedWave());
q1barw.reset(iq1);
q2barw.reset(iq1);
LorentzVector<complex<Energy> > current2 =
q2barw.dimensionedWave().vectorCurrent(q1barw.dimensionedWave());
complex<Energy2> amp = current1.dot(current2);
vector<Complex> Cborn(2),CEW(2);
unsigned int ioff = q1->id()%2==0 ? 0 : 1;
for(unsigned int ix=0;ix<2;++ix) {
Cborn[ix] = amp*borntChannelWeights(2*ix+ioff,0);
CEW [ix] = amp* EWtChannelWeights(2*ix+ioff,0);
}
// square
for(unsigned int ix=0;ix<2;++ix) {
for(unsigned int iy=0;iy<2;++iy) {
bornME(ix,iy) += Cborn[ix]*conj(Cborn[iy]);
EWME (ix,iy) += CEW [ix]*conj(CEW [iy]);
}
}
}
}
// colour factors
double born = 2.*real(bornME(0,0))+9.*real(bornME(1,1));
double EW = 2.*real( EWME(0,0))+9.*real( EWME(1,1));
return EW/born;
}
double ElectroWeakReweighter::reweightqqbarqqbarT() const {
// momenta and invariants
Lorentz5Momentum p1 = subProcess()->incoming().first ->momentum();
tcPDPtr q1 = subProcess()->incoming().first ->dataPtr();
Lorentz5Momentum p2 = subProcess()->incoming().second->momentum();
tcPDPtr q1bar = subProcess()->incoming().second->dataPtr();
if(q1->id()<0) {
swap(p1,p2 );
swap(q1 ,q1bar);
}
Lorentz5Momentum p3 = subProcess()->outgoing()[0]->momentum();
tcPDPtr q2bar = subProcess()->outgoing()[0]->dataPtr();
Lorentz5Momentum p4 = subProcess()->outgoing()[1]->momentum();
tcPDPtr q2 = subProcess()->outgoing()[1]->dataPtr();
if(q2bar->id()>0) {
swap(p3,p4 );
swap(q2 ,q2bar);
}
Energy2 s = (p1+p2).m2();
Energy2 t = (p1-p4).m2();
Energy2 u = (p1-p3).m2();
// boost to partonci rest frame
Lorentz5Momentum psum=p1+p2;
LorentzRotation boost(-psum.boostVector());
p1 *= boost;
p2 *= boost;
p3 *= boost;
p4 *= boost;
p3.setMass(ZERO);
p3.rescaleRho();
p4.setMass(ZERO);
p4.rescaleRho();
assert(q1==q2 && q1bar==q2bar);
assert( q1->id() != -q1bar->id() && q2->id() != -q2bar->id() );
// LO and EW corrected matrix element coefficients
boost::numeric::ublas::matrix<complex<InvEnergy2> >
bornLLLLWeights,bornLLRRWeights,bornRRLLWeights,bornRRRRWeights,
EWLLLLWeights,EWLLRRWeights,EWRRLLWeights,EWRRRRWeights;
// LL
if( q1->id() == ParticleID::b ||
q1bar->id() == ParticleID::bbar ) {
bornLLLLWeights = evaluateRunning(EWProcess::QtQtQQ,s,t,u,true ,1);
EWLLLLWeights = evaluateRunning(EWProcess::QtQtQQ,s,t,u,false,1);
}
else {
bornLLLLWeights = evaluateRunning(EWProcess::QQQQ,s,t,u,true ,1);
EWLLLLWeights = evaluateRunning(EWProcess::QQQQ,s,t,u,false,1);
}
// RR -> LL
if(q1->id()%2==0) {
if(q1bar->id()==ParticleID::bbar) {
bornRRLLWeights = evaluateRunning(EWProcess::QtQtUU,s,t,u,true ,1);
EWRRLLWeights = evaluateRunning(EWProcess::QtQtUU,s,t,u,false,1);
}
else {
bornRRLLWeights = evaluateRunning(EWProcess::QQUU,s,t,u,true ,1);
EWRRLLWeights = evaluateRunning(EWProcess::QQUU,s,t,u,false,1);
}
}
else {
if(q1bar->id()==ParticleID::bbar) {
bornRRLLWeights = evaluateRunning(EWProcess::QtQtDD,s,t,u,true ,1);
EWRRLLWeights = evaluateRunning(EWProcess::QtQtDD,s,t,u,false,1);
}
else {
bornRRLLWeights = evaluateRunning(EWProcess::QQDD,s,t,u,true ,1);
EWRRLLWeights = evaluateRunning(EWProcess::QQDD,s,t,u,false,1);
}
}
// LL -> RR
if(abs(q1bar->id())%2==0) {
if(q1->id()==ParticleID::b) {
bornLLRRWeights = evaluateRunning(EWProcess::QtQtUU,s,t,u,true ,1);
EWLLRRWeights = evaluateRunning(EWProcess::QtQtUU,s,t,u,false,1);
}
else {
bornLLRRWeights = evaluateRunning(EWProcess::QQUU,s,t,u,true ,1);
EWLLRRWeights = evaluateRunning(EWProcess::QQUU,s,t,u,false,1);
}
}
else {
if(q1->id()==ParticleID::b) {
bornLLRRWeights = evaluateRunning(EWProcess::QtQtDD,s,t,u,true ,1);
EWLLRRWeights = evaluateRunning(EWProcess::QtQtDD,s,t,u,false,1);
}
else {
bornLLRRWeights = evaluateRunning(EWProcess::QQDD,s,t,u,true ,1);
EWLLRRWeights = evaluateRunning(EWProcess::QQDD,s,t,u,false,1);
}
}
// RR -> RR
if(q1->id()%2==0) {
if(abs(q1bar->id())%2==0) {
bornRRRRWeights = evaluateRunning(EWProcess::UUUU,s,t,u,true ,1);
EWRRRRWeights = evaluateRunning(EWProcess::UUUU,s,t,u,false,1);
}
else {
bornRRRRWeights = evaluateRunning(EWProcess::UUDD,s,t,u,true ,1);
EWRRRRWeights = evaluateRunning(EWProcess::UUDD,s,t,u,false,1);
}
}
else {
if(abs(q1bar->id())%2==0) {
bornRRRRWeights = evaluateRunning(EWProcess::UUDD,s,t,u,true ,1);
EWRRRRWeights = evaluateRunning(EWProcess::UUDD,s,t,u,false,1);
}
else {
bornRRRRWeights = evaluateRunning(EWProcess::DDDD,s,t,u,true ,1);
EWRRRRWeights = evaluateRunning(EWProcess::DDDD,s,t,u,false,1);
}
}
// calculate the spinors
SpinorWaveFunction q1w(p1,q1 ,incoming);
SpinorBarWaveFunction q1barw(p2,q1bar,incoming);
SpinorWaveFunction q2barw(p3,q2bar,outgoing);
SpinorBarWaveFunction q2w(p4,q2 ,outgoing);
boost::numeric::ublas::matrix<Complex>
bornME = boost::numeric::ublas::zero_matrix<Complex>(2,2),
EWME = boost::numeric::ublas::zero_matrix<Complex>(2,2);
for(unsigned int iq1=0;iq1<2;++iq1) {
q1w.reset(iq1);
q2w.reset(iq1);
LorentzVector<complex<Energy> > current1 =
q1w.dimensionedWave().vectorCurrent(q2w.dimensionedWave());
for(unsigned int iq2=0;iq2<2;++iq2) {
q1barw.reset(iq2);
q2barw.reset(iq2);
LorentzVector<complex<Energy> > current2 =
q2barw.dimensionedWave().vectorCurrent(q1barw.dimensionedWave());
// calculate the amplitude
complex<Energy2> amp = current1.dot(current2);
vector<Complex> Cborn(2),CEW(2);
if(iq1==0) {
// LL RR
if(iq2==0) {
unsigned int ioff = q1->id()%2==0 ? 0 : 1;
for(unsigned int ix=0;ix<2;++ix) {
Cborn[ix] = amp*bornLLRRWeights(2*ix+ioff,0);
CEW [ix] = amp* EWLLRRWeights(2*ix+ioff,0);
}
}
// LL LL
else {
unsigned int ioff;
if(q1->id()%2==0) {
ioff = abs(q1bar->id())%2==0 ? 0 : 2;
}
else {
ioff = abs(q1bar->id())%2==0 ? 1 : 3;
}
for(unsigned int ix=0;ix<2;++ix) {
Cborn[ix] = amp*bornLLLLWeights(6*ix+ioff,0);
CEW [ix] = amp* EWLLLLWeights(6*ix+ioff,0);
}
}
}
else {
// RR RR
if(iq2==0) {
for(unsigned int ix=0;ix<2;++ix) {
Cborn[ix] = amp*bornRRRRWeights(ix,0);
CEW [ix] = amp* EWRRRRWeights(ix,0);
}
}
// RR LL
else {
unsigned int ioff=abs(q1bar->id())%2==0 ? 0 : 1;
for(unsigned int ix=0;ix<2;++ix) {
Cborn[ix] = amp*bornRRLLWeights(2*ix+ioff,0);
CEW [ix] = amp* EWRRLLWeights(2*ix+ioff,0);
}
}
}
// square
for(unsigned int ix=0;ix<2;++ix) {
for(unsigned int iy=0;iy<2;++iy) {
bornME(ix,iy) += Cborn[ix]*conj(Cborn[iy]);
EWME (ix,iy) += CEW [ix]*conj(CEW [iy]);
}
}
}
}
// colour factors
double born = 2.*real(bornME(0,0))+9.*real(bornME(1,1));
double EW = 2.*real( EWME(0,0))+9.*real( EWME(1,1));
return EW/born;
}
double ElectroWeakReweighter::reweightqqqq() const {
// momenta and invariants
Lorentz5Momentum p1 = subProcess()->incoming().first ->momentum();
tcPDPtr q1 = subProcess()->incoming().first ->dataPtr();
Lorentz5Momentum p2 = subProcess()->incoming().second->momentum();
tcPDPtr q2 = subProcess()->incoming().second->dataPtr();
Lorentz5Momentum p3 = subProcess()->outgoing()[0] ->momentum();
tcPDPtr q3 = subProcess()->outgoing()[0] ->dataPtr();
Lorentz5Momentum p4 = subProcess()->outgoing()[1] ->momentum();
tcPDPtr q4 = subProcess()->outgoing()[1] ->dataPtr();
if(q1->id()!=q3->id()) {
swap(q3,q4);
swap(p3,p4);
}
assert(q1->id()==q3->id());
assert(q2->id()==q4->id());
Energy2 s = (p1+p2).m2();
Energy2 t = (p1-p4).m2();
Energy2 u = (p1-p3).m2();
// boost to partonci rest frame
Lorentz5Momentum psum=p1+p2;
LorentzRotation boost(-psum.boostVector());
p1 *= boost;
p2 *= boost;
p3 *= boost;
p4 *= boost;
p3.setMass(ZERO);
p3.rescaleRho();
p4.setMass(ZERO);
p4.rescaleRho();
// LO and EW corrected matrix element coefficients
boost::numeric::ublas::matrix<complex<InvEnergy2> >
bornLLLLWeights,bornLLRRWeights,bornRRLLWeights,bornRRRRWeights,
EWLLLLWeights,EWLLRRWeights,EWRRLLWeights,EWRRRRWeights;
bool ident = q1->id()==q2->id();
// LL -> LL
if((q1->id()<=4&& q2->id()<=4)|| (q1->id()==5 && q2->id()==5)) {
if(!ident) {
bornLLLLWeights = evaluateRunning(EWProcess::QQQQ,s,t,u,true ,2);
EWLLLLWeights = evaluateRunning(EWProcess::QQQQ,s,t,u,false,2);
}
else {
bornLLLLWeights = evaluateRunning(EWProcess::QQQQiden,s,t,u,true ,2);
EWLLLLWeights = evaluateRunning(EWProcess::QQQQiden,s,t,u,false,2);
}
}
else if(q1->id()==5 || q2->id()==5) {
bornLLLLWeights = evaluateRunning(EWProcess::QtQtQQ,s,t,u,true ,2);
EWLLLLWeights = evaluateRunning(EWProcess::QtQtQQ,s,t,u,false,2);
}
else
assert(false);
// RR -> LL
if(q1->id()%2==0) {
if(q2->id()<5) {
bornRRLLWeights = evaluateRunning(EWProcess::QQUU,s,t,u,true ,2);
EWRRLLWeights = evaluateRunning(EWProcess::QQUU,s,t,u,false,2);
}
else {
bornRRLLWeights = evaluateRunning(EWProcess::QtQtUU,s,t,u,true ,2);
EWRRLLWeights = evaluateRunning(EWProcess::QtQtUU,s,t,u,false,2);
}
}
else {
if(q2->id()<5) {
bornRRLLWeights = evaluateRunning(EWProcess::QQDD,s,t,u,true ,2);
EWRRLLWeights = evaluateRunning(EWProcess::QQDD,s,t,u,false,2);
}
else {
bornRRLLWeights = evaluateRunning(EWProcess::QtQtDD,s,t,u,true ,2);
EWRRLLWeights = evaluateRunning(EWProcess::QtQtDD,s,t,u,false,2);
}
}
// LL -> RR
if(q1->id()<=4) {
if(q2->id()%2!=0) {
bornLLRRWeights = evaluateRunning(EWProcess::QQDD,s,t,u,true ,2);
EWLLRRWeights = evaluateRunning(EWProcess::QQDD,s,t,u,false,2);
}
else {
bornLLRRWeights = evaluateRunning(EWProcess::QQUU,s,t,u,true ,2);
EWLLRRWeights = evaluateRunning(EWProcess::QQUU,s,t,u,false,2);
}
}
else {
if(q2->id()%2!=0) {
bornLLRRWeights = evaluateRunning(EWProcess::QtQtDD,s,t,u,true ,2);
EWLLRRWeights = evaluateRunning(EWProcess::QtQtDD,s,t,u,false,2);
}
else {
bornLLRRWeights = evaluateRunning(EWProcess::QtQtUU,s,t,u,true ,2);
EWLLRRWeights = evaluateRunning(EWProcess::QtQtUU,s,t,u,false,2);
}
}
// RR -> RR
if(q1->id()%2==0) {
if(q2->id()%2==0) {
if(ident) {
bornRRRRWeights = evaluateRunning(EWProcess::UUUUiden,s,t,u,true ,2);
EWRRRRWeights = evaluateRunning(EWProcess::UUUUiden,s,t,u,false,2);
}
else {
bornRRRRWeights = evaluateRunning(EWProcess::UUUU,s,t,u,true ,2);
EWRRRRWeights = evaluateRunning(EWProcess::UUUU,s,t,u,false,2);
}
}
else {
bornRRRRWeights = evaluateRunning(EWProcess::UUDD,s,t,u,true ,2);
EWRRRRWeights = evaluateRunning(EWProcess::UUDD,s,t,u,false,2);
}
}
else {
if(q2->id()%2==0) {
bornRRRRWeights = evaluateRunning(EWProcess::UUDD,s,t,u,true ,2);
EWRRRRWeights = evaluateRunning(EWProcess::UUDD,s,t,u,false,2);
}
else {
if(ident) {
bornRRRRWeights = evaluateRunning(EWProcess::DDDDiden,s,t,u,true ,2);
EWRRRRWeights = evaluateRunning(EWProcess::DDDDiden,s,t,u,false,2);
}
else {
bornRRRRWeights = evaluateRunning(EWProcess::DDDD,s,t,u,true ,2);
EWRRRRWeights = evaluateRunning(EWProcess::DDDD,s,t,u,false,2);
}
}
}
// extra terms for identical particles
boost::numeric::ublas::matrix<complex<InvEnergy2> >
borntChannelWeights,EWtChannelWeights;
if(ident) {
if(q1->id()%2==0) {
borntChannelWeights = evaluateRunning(EWProcess::QQUU,s,u,t,true ,2);
EWtChannelWeights = evaluateRunning(EWProcess::QQUU,s,u,t,false,2);
}
else if(q1->id()==5) {
borntChannelWeights = evaluateRunning(EWProcess::QtQtDD,s,u,t,true ,2);
EWtChannelWeights = evaluateRunning(EWProcess::QtQtDD,s,u,t,false,2);
}
else {
borntChannelWeights = evaluateRunning(EWProcess::QQDD,s,u,t,true ,2);
EWtChannelWeights = evaluateRunning(EWProcess::QQDD,s,u,t,false,2);
}
}
SpinorWaveFunction q1w(p1,q1,incoming);
SpinorWaveFunction q2w(p2,q2,incoming);
SpinorBarWaveFunction q3w(p3,q3,outgoing);
SpinorBarWaveFunction q4w(p4,q4,outgoing);
boost::numeric::ublas::matrix<Complex>
bornME = boost::numeric::ublas::zero_matrix<Complex>(2,2),
EWME = boost::numeric::ublas::zero_matrix<Complex>(2,2);
for(unsigned int iq1=0;iq1<2;++iq1) {
q1w.reset(iq1);
q3w.reset(iq1);
LorentzVector<complex<Energy> > current1 =
q1w.dimensionedWave().vectorCurrent(q3w.dimensionedWave());
for(unsigned int iq2=0;iq2<2;++iq2) {
q2w.reset(iq2);
q4w.reset(iq2);
LorentzVector<complex<Energy> > current2 =
q2w.dimensionedWave().vectorCurrent(q4w.dimensionedWave());
complex<Energy2> amp = current1.dot(current2);
vector<Complex> Cborn(2),CEW(2);
// amplitudes
if(iq1==0) {
// LL
if(iq2==0) {
unsigned int ioff;
if(q1->id()%2==0) {
ioff = q2->id()%2==0 ? 0 : 2;
}
else {
ioff = q2->id()%2==0 ? 1 : 3;
}
for(unsigned int ix=0;ix<2;++ix) {
Cborn[ix] = amp*bornLLLLWeights(6*ix+ioff,0);
CEW [ix] = amp* EWLLLLWeights(6*ix+ioff,0);
}
}
// LR
else {
unsigned int ioff = q1->id()%2==0 ? 0 : 1;
for(unsigned int ix=0;ix<2;++ix) {
Cborn[ix] = amp*bornLLRRWeights(2*ix+ioff,0);
CEW [ix] = amp* EWLLRRWeights(2*ix+ioff,0);
}
}
}
else {
if(iq2==0) {
unsigned int ioff=q2->id()%2==0 ? 0 : 1;
for(unsigned int ix=0;ix<2;++ix) {
Cborn[ix] = amp*bornRRLLWeights(2*ix+ioff,0);
CEW [ix] = amp* EWRRLLWeights(2*ix+ioff,0);
}
}
else {
for(unsigned int ix=0;ix<2;++ix) {
Cborn[ix] = amp*bornRRRRWeights(ix,0);
CEW [ix] = amp* EWRRRRWeights(ix,0);
}
}
}
// square
for(unsigned int ix=0;ix<2;++ix) {
for(unsigned int iy=0;iy<2;++iy) {
bornME(ix,iy) += Cborn[ix]*conj(Cborn[iy]);
EWME (ix,iy) += CEW [ix]*conj(CEW [iy]);
}
}
}
}
// extra u-channel pieces if identical flavours
if(ident) {
for(unsigned int iq1=0;iq1<2;++iq1) {
q1w.reset(iq1);
q4w.reset(iq1);
LorentzVector<complex<Energy> > current1 =
q1w.dimensionedWave().vectorCurrent(q4w.dimensionedWave());
if(iq1==0) {
q2w.reset(1);
q3w.reset(1);
}
else {
q2w.reset(0);
q3w.reset(0);
}
LorentzVector<complex<Energy> > current2 =
q2w.dimensionedWave().vectorCurrent(q3w.dimensionedWave());
complex<Energy2> amp = current1.dot(current2);
vector<Complex> Cborn(2),CEW(2);
unsigned int ioff = q1->id()%2==0 ? 0 : 1;
for(unsigned int ix=0;ix<2;++ix) {
Cborn[ix] = amp*borntChannelWeights(2*ix+ioff,0);
CEW [ix] = amp* EWtChannelWeights(2*ix+ioff,0);
}
// square
for(unsigned int ix=0;ix<2;++ix) {
for(unsigned int iy=0;iy<2;++iy) {
bornME(ix,iy) += Cborn[ix]*conj(Cborn[iy]);
EWME (ix,iy) += CEW [ix]*conj(CEW [iy]);
}
}
}
}
// colour factors
double born = 2.*real(bornME(0,0))+9.*real(bornME(1,1));
double EW = 2.*real( EWME(0,0))+9.*real( EWME(1,1));
return EW/born;
}
double ElectroWeakReweighter::reweightqbarqbarqbarqbar() const {
// momenta and invariants
Lorentz5Momentum p1 = subProcess()->incoming().first ->momentum();
tcPDPtr qbar1 = subProcess()->incoming().first ->dataPtr();
Lorentz5Momentum p2 = subProcess()->incoming().second->momentum();
tcPDPtr qbar2 = subProcess()->incoming().second->dataPtr();
Lorentz5Momentum p3 = subProcess()->outgoing()[0] ->momentum();
tcPDPtr qbar3 = subProcess()->outgoing()[0] ->dataPtr();
Lorentz5Momentum p4 = subProcess()->outgoing()[1] ->momentum();
tcPDPtr qbar4 = subProcess()->outgoing()[1] ->dataPtr();
if(qbar1->id()!=qbar3->id()) {
swap(qbar3,qbar4);
swap(p3,p4);
}
assert(qbar1->id()==qbar3->id());
assert(qbar2->id()==qbar4->id());
Energy2 s = (p1+p2).m2();
Energy2 t = (p1-p4).m2();
Energy2 u = (p1-p3).m2();
// boost to partonic rest frame
Lorentz5Momentum psum=p1+p2;
LorentzRotation boost(-psum.boostVector());
p1 *= boost;
p2 *= boost;
p3 *= boost;
p4 *= boost;
p3.setMass(ZERO);
p3.rescaleRho();
p4.setMass(ZERO);
p4.rescaleRho();
// LO and EW corrected matrix element coefficients
boost::numeric::ublas::matrix<complex<InvEnergy2> >
bornLLLLWeights,bornLLRRWeights,bornRRLLWeights,bornRRRRWeights,
EWLLLLWeights,EWLLRRWeights,EWRRLLWeights,EWRRRRWeights;
bool ident = qbar1->id()==qbar2->id();
// LL -> LL
if((abs(qbar1->id())<=4 && abs(qbar2->id())<=4) ||
(abs(qbar1->id())==5 && abs(qbar2->id())==5)) {
if(!ident) {
bornLLLLWeights = evaluateRunning(EWProcess::QQQQ,s,t,u,true ,2);
EWLLLLWeights = evaluateRunning(EWProcess::QQQQ,s,t,u,false,2);
}
else {
bornLLLLWeights = evaluateRunning(EWProcess::QQQQiden,s,t,u,true ,2);
EWLLLLWeights = evaluateRunning(EWProcess::QQQQiden,s,t,u,false,2);
}
}
else if(abs(qbar1->id())==5 || abs(qbar2->id())==5) {
bornLLLLWeights = evaluateRunning(EWProcess::QtQtQQ,s,t,u,true ,2);
EWLLLLWeights = evaluateRunning(EWProcess::QtQtQQ,s,t,u,false,2);
}
else
assert(false);
// RR -> LL
if(abs(qbar1->id())%2==0) {
if(abs(qbar2->id())<5) {
bornRRLLWeights = evaluateRunning(EWProcess::QQUU,s,t,u,true ,2);
EWRRLLWeights = evaluateRunning(EWProcess::QQUU,s,t,u,false,2);
}
else {
bornRRLLWeights = evaluateRunning(EWProcess::QtQtUU,s,t,u,true ,2);
EWRRLLWeights = evaluateRunning(EWProcess::QtQtUU,s,t,u,false,2);
}
}
else {
if(abs(qbar2->id())<5) {
bornRRLLWeights = evaluateRunning(EWProcess::QQDD,s,t,u,true ,2);
EWRRLLWeights = evaluateRunning(EWProcess::QQDD,s,t,u,false,2);
}
else {
bornRRLLWeights = evaluateRunning(EWProcess::QtQtDD,s,t,u,true ,2);
EWRRLLWeights = evaluateRunning(EWProcess::QtQtDD,s,t,u,false,2);
}
}
// LL -> RR
if(abs(qbar1->id())<=4) {
if(abs(qbar2->id())%2!=0) {
bornLLRRWeights = evaluateRunning(EWProcess::QQDD,s,t,u,true ,2);
EWLLRRWeights = evaluateRunning(EWProcess::QQDD,s,t,u,false,2);
}
else {
bornLLRRWeights = evaluateRunning(EWProcess::QQUU,s,t,u,true ,2);
EWLLRRWeights = evaluateRunning(EWProcess::QQUU,s,t,u,false,2);
}
}
else {
if(abs(qbar2->id())%2!=0) {
bornLLRRWeights = evaluateRunning(EWProcess::QtQtDD,s,t,u,true ,2);
EWLLRRWeights = evaluateRunning(EWProcess::QtQtDD,s,t,u,false,2);
}
else {
bornLLRRWeights = evaluateRunning(EWProcess::QtQtUU,s,t,u,true ,2);
EWLLRRWeights = evaluateRunning(EWProcess::QtQtUU,s,t,u,false,2);
}
}
// RR -> RR
if(abs(qbar1->id())%2==0) {
if(abs(qbar2->id())%2==0) {
if(ident) {
bornRRRRWeights = evaluateRunning(EWProcess::UUUUiden,s,t,u,true ,2);
EWRRRRWeights = evaluateRunning(EWProcess::UUUUiden,s,t,u,false,2);
}
else {
bornRRRRWeights = evaluateRunning(EWProcess::UUUU,s,t,u,true ,2);
EWRRRRWeights = evaluateRunning(EWProcess::UUUU,s,t,u,false,2);
}
}
else {
bornRRRRWeights = evaluateRunning(EWProcess::UUDD,s,t,u,true ,2);
EWRRRRWeights = evaluateRunning(EWProcess::UUDD,s,t,u,false,2);
}
}
else {
if(abs(qbar2->id())%2==0) {
bornRRRRWeights = evaluateRunning(EWProcess::UUDD,s,t,u,true ,2);
EWRRRRWeights = evaluateRunning(EWProcess::UUDD,s,t,u,false,2);
}
else {
if(ident) {
bornRRRRWeights = evaluateRunning(EWProcess::DDDDiden,s,t,u,true ,2);
EWRRRRWeights = evaluateRunning(EWProcess::DDDDiden,s,t,u,false,2);
}
else {
bornRRRRWeights = evaluateRunning(EWProcess::DDDD,s,t,u,true ,2);
EWRRRRWeights = evaluateRunning(EWProcess::DDDD,s,t,u,false,2);
}
}
}
// extra terms for identical particles
boost::numeric::ublas::matrix<complex<InvEnergy2> >
borntChannelWeights,EWtChannelWeights;
if(ident) {
if(abs(qbar1->id())%2==0) {
borntChannelWeights = evaluateRunning(EWProcess::QQUU,s,u,t,true ,2);
EWtChannelWeights = evaluateRunning(EWProcess::QQUU,s,u,t,false,2);
}
else if(abs(qbar1->id())==5) {
borntChannelWeights = evaluateRunning(EWProcess::QtQtDD,s,u,t,true ,2);
EWtChannelWeights = evaluateRunning(EWProcess::QtQtDD,s,u,t,false,2);
}
else {
borntChannelWeights = evaluateRunning(EWProcess::QQDD,s,u,t,true ,2);
EWtChannelWeights = evaluateRunning(EWProcess::QQDD,s,u,t,false,2);
}
}
SpinorBarWaveFunction qbar1w(p1,qbar1,incoming);
SpinorBarWaveFunction qbar2w(p2,qbar2,incoming);
SpinorWaveFunction qbar3w(p3,qbar3,outgoing);
SpinorWaveFunction qbar4w(p4,qbar4,outgoing);
boost::numeric::ublas::matrix<Complex>
bornME = boost::numeric::ublas::zero_matrix<Complex>(2,2),
EWME = boost::numeric::ublas::zero_matrix<Complex>(2,2);
for(unsigned int iq1=0;iq1<2;++iq1) {
qbar1w.reset(iq1);
qbar3w.reset(iq1);
LorentzVector<complex<Energy> > current1 =
qbar3w.dimensionedWave().vectorCurrent(qbar1w.dimensionedWave());
for(unsigned int iq2=0;iq2<2;++iq2) {
qbar2w.reset(iq2);
qbar4w.reset(iq2);
LorentzVector<complex<Energy> > current2 =
qbar4w.dimensionedWave().vectorCurrent(qbar2w.dimensionedWave());
complex<Energy2> amp = current1.dot(current2);
vector<Complex> Cborn(2),CEW(2);
// amplitudes
if(iq1==1) {
// LL
if(iq2==1) {
unsigned int ioff;
if(abs(qbar1->id())%2==0) {
ioff = abs(qbar2->id())%2==0 ? 0 : 2;
}
else {
ioff = abs(qbar2->id())%2==0 ? 1 : 3;
}
for(unsigned int ix=0;ix<2;++ix) {
Cborn[ix] = amp*bornLLLLWeights(6*ix+ioff,0);
CEW [ix] = amp* EWLLLLWeights(6*ix+ioff,0);
}
}
// LR
else {
unsigned int ioff = abs(qbar1->id())%2==0 ? 0 : 1;
for(unsigned int ix=0;ix<2;++ix) {
Cborn[ix] = amp*bornLLRRWeights(2*ix+ioff,0);
CEW [ix] = amp* EWLLRRWeights(2*ix+ioff,0);
}
}
}
else {
if(iq2==1) {
unsigned int ioff=abs(qbar2->id())%2==0 ? 0 : 1;
for(unsigned int ix=0;ix<2;++ix) {
Cborn[ix] = amp*bornRRLLWeights(2*ix+ioff,0);
CEW [ix] = amp* EWRRLLWeights(2*ix+ioff,0);
}
}
else {
for(unsigned int ix=0;ix<2;++ix) {
Cborn[ix] = amp*bornRRRRWeights(ix,0);
CEW [ix] = amp* EWRRRRWeights(ix,0);
}
}
}
// square
for(unsigned int ix=0;ix<2;++ix) {
for(unsigned int iy=0;iy<2;++iy) {
bornME(ix,iy) += Cborn[ix]*conj(Cborn[iy]);
EWME (ix,iy) += CEW [ix]*conj(CEW [iy]);
}
}
}
}
// extra u-channel pieces if identical flavours
if(ident) {
for(unsigned int iq1=0;iq1<2;++iq1) {
qbar1w.reset(iq1);
qbar4w.reset(iq1);
LorentzVector<complex<Energy> > current1 =
qbar4w.dimensionedWave().vectorCurrent(qbar1w.dimensionedWave());
if(iq1==0) {
qbar2w.reset(1);
qbar3w.reset(1);
}
else {
qbar2w.reset(0);
qbar3w.reset(0);
}
LorentzVector<complex<Energy> > current2 =
qbar3w.dimensionedWave().vectorCurrent(qbar2w.dimensionedWave());
complex<Energy2> amp = current1.dot(current2);
vector<Complex> Cborn(2),CEW(2);
unsigned int ioff = abs(qbar1->id())%2==0 ? 0 : 1;
for(unsigned int ix=0;ix<2;++ix) {
Cborn[ix] = amp*borntChannelWeights(2*ix+ioff,0);
CEW [ix] = amp* EWtChannelWeights(2*ix+ioff,0);
}
// square
for(unsigned int ix=0;ix<2;++ix) {
for(unsigned int iy=0;iy<2;++iy) {
bornME(ix,iy) += Cborn[ix]*conj(Cborn[iy]);
EWME (ix,iy) += CEW [ix]*conj(CEW [iy]);
}
}
}
}
// colour factors
double born = 2.*real(bornME(0,0))+9.*real(bornME(1,1));
double EW = 2.*real( EWME(0,0))+9.*real( EWME(1,1));
return EW/born;
}
diff --git a/MatrixElement/EW/HighEnergyMatching.cc b/MatrixElement/EW/HighEnergyMatching.cc
--- a/MatrixElement/EW/HighEnergyMatching.cc
+++ b/MatrixElement/EW/HighEnergyMatching.cc
@@ -1,1171 +1,1179 @@
// -*- C++ -*-
//
// HighEnergyMatching.cc is a part of Herwig - A multi-purpose Monte Carlo event generator
//
// Herwig is licenced under version 2 of the GPL, see COPYING for details.
// Please respect the MCnet academic guidelines, see GUIDELINES for details.
//
//
//
#include "HighEnergyMatching.h"
#include "ElectroWeakReweighter.h"
#include "GroupInvariants.h"
#include <boost/numeric/ublas/operation.hpp>
#include <boost/numeric/ublas/vector.hpp>
using namespace Herwig;
using namespace HighEnergyMatching;
using namespace GroupInvariants;
using namespace EWProcess;
namespace {
/**
* \f$M_N\f$, this matrix is used for identical particle scattering
*/
boost::numeric::ublas::matrix<Complex> M_N(unsigned int suN) {
double N(suN);
boost::numeric::ublas::matrix<Complex> M(2,2);
M(0,0) = -1.0/N;
M(0,1) = 2.0;
M(1,0) = 0.5 - 1.0/(2.0*N*N);
M(1,1) = 1.0/N;
return M;
}
+#ifdef ThePEG_HAS_UNITS_CHECKING
void axpy_prod_local(const boost::numeric::ublas::matrix<Complex> & A,
const boost::numeric::ublas::matrix<complex<InvEnergy2> > & B,
boost::numeric::ublas::matrix<complex<InvEnergy2> > & C) {
assert(A.size2()==B.size1());
C.resize(A.size1(),B.size2());
for(unsigned int ix=0;ix<A.size1();++ix) {
for(unsigned int iy=0;iy<B.size2();++iy) {
C(ix,iy) = ZERO;
for(unsigned int iz=0;iz<A.size2();++iz) {
C(ix,iy) += A(ix,iz)*B(iz,iy);
}
}
}
}
void axpy_prod_local(const boost::numeric::ublas::matrix<complex<InvEnergy2> > & A,
const boost::numeric::ublas::matrix<Complex> & B,
boost::numeric::ublas::matrix<complex<InvEnergy2> > & C) {
assert(A.size2()==B.size1());
C.resize(A.size1(),B.size2());
for(unsigned int ix=0;ix<A.size1();++ix) {
for(unsigned int iy=0;iy<B.size2();++iy) {
C(ix,iy) = ZERO;
for(unsigned int iz=0;iz<A.size2();++iz) {
C(ix,iy) += A(ix,iz)*B(iz,iy);
}
}
}
}
+#else
+void axpy_prod_local(const boost::numeric::ublas::matrix<Complex> & A,
+ const boost::numeric::ublas::matrix<Complex> & B,
+ boost::numeric::ublas::matrix<Complex> & C) {
+ axpy_prod(A,B,C);
+}
+#endif
}
boost::numeric::ublas::matrix<complex<InvEnergy2> >
HighEnergyMatching::highEnergyMatching(Energy highScale,
Energy2 s, Energy2 t, Energy2 u,
EWProcess::Process process,
bool oneLoop, bool includeAlphaS2) {
switch (process) {
case QQQQ: case QQQQiden:
case QtQtQQ: case QQUU:
case QtQtUU: case QQtRtR:
case QQDD: case QtQtDD:
case QQLL: case QQEE:
case UUUU: case UUUUiden:
case tRtRUU: case UUDD:
case tRtRDD: case UULL:
case UUEE: case DDDD:
case DDDDiden: case DDLL:
case DDEE: case LLLL:
case LLLLiden: case LLEE:
case EEEE: case EEEEiden:
return SpinHalfMatching(highScale,s,t,u,process,oneLoop,includeAlphaS2);
break;
case QQWW:
case QQWG:
case QQBG:
case QQGG:
case QtQtGG:
case LLWW:
case UUBB:
case UUBG:
case UUGG:
case tRtRGG:
case DDBB:
case DDBG:
case DDGG:
case EEBB:
return Spin1HighMatching(highScale,s,t,u,process,oneLoop,includeAlphaS2);
break;
case QQPhiPhi:
case LLPhiPhi:
case UUPhiPhi:
case DDPhiPhi:
case EEPhiPhi:
return Spin0HighMatching(highScale,s,t,u,process,oneLoop,includeAlphaS2);
break;
default:
assert(false);
break;
}
}
boost::numeric::ublas::matrix<complex<InvEnergy2> >
HighEnergyMatching::SpinHalfMatching(Energy highScale,
Energy2 s, Energy2 t, Energy2 u,
EWProcess::Process process,
bool oneLoop, bool includeAlphaS2) {
using Constants::pi;
boost::numeric::ublas::matrix<complex<InvEnergy2> > highC;
Energy Q = highScale;
double a1 = ElectroWeakReweighter::coupling()->a1(Q);
double a2 = ElectroWeakReweighter::coupling()->a2(Q);
double a3 = ElectroWeakReweighter::coupling()->a3(Q);
double y_t = ElectroWeakReweighter::coupling()->y_t(Q);
unsigned int order = !oneLoop ? 0 : 1;
double Yi(0.),Yf(0.);
Complex Ls = MinusLog(-s/(Q*Q));
double C_A_2 = C_A(2);
double C_A_3 = C_A(3);
double C_F_2 = C_F(2);
double C_F_3 = C_F(3);
double C_d_2 = C_d(2);
double C_d_3 = C_d(3);
double C_1_2 = C_1(2);
double C_1_3 = C_1(3);
Complex W = WFunction(Q,s);
Complex X_2_st = XNFunction(2,Q,s,t);
//Complex X_2_su = XNFunction(2,Q,s,u);
Complex X_3_st = XNFunction(3,Q,s,t);
Complex X_3_su = XNFunction(3,Q,s,u);
Complex PI1 = PI1_function(Q,s);
Complex fTilde_st = fTildeFunction(Q,s,t);
Complex fTilde_su = fTildeFunction(Q,s,u);
switch (process) {
case QQQQ:
// NOTE this 4x1 column vector highC is given by (C_11,C_21,C_12,C_22),
// where C_12 is the coeff. for the term that transforms under SU(2) but not SU(3)
Yi = Yf = 1./6.;
highC.resize(4,1);
highC(0,0) = ZERO;
highC(2,0) = 4.0*pi*a2 / s;
highC(1,0) = 4.0*pi*a3 / s;
highC(3,0) = 4.0*pi*a1*Yi*Yf / s;
if (order >= 1) {
highC(0,0) += (1.0/s)*(-2.0*a2*a3*fTilde_st);
highC(2,0) += (1.0/s)*(a2*a2*(X_2_st-(C_d_2+C_A_2)/4.0*fTilde_st) +
2.0*(a1*a2*Yi*Yf+a2*a3*C_F_3)*W -
2.0*a1*a2*Yi*Yf*fTilde_st);
highC(1,0) += (1.0/s)*(2.0*(a1*a3*Yi*Yf+a2*a3*C_F_2)*W -
2.0*a1*a3*Yi*Yf*fTilde_st);
highC(3,0) += (1.0/s)*(-1.0*(a2*a2*C_1_2+a1*a1*Yi*Yi*Yf*Yf)*fTilde_st +
a1*a1*Yi*Yf*PI1 +
2.0*(a1*a3*Yi*Yf*C_F_3+a1*a2*Yi*Yf*C_F_2+a1*a1*Yi*Yi*Yf*Yf)*W);
if (includeAlphaS2) {
highC(1,0) += (1.0/s)*(a3*a3*(X_3_st-(C_d_3+C_A_3)/4.0*fTilde_st));
highC(3,0) += (1.0/s)*(-1.0*(a3*a3*C_1_3)*fTilde_st);
}
}
break;
case QQQQiden:
{
Process parentCase = QQQQ;
boost::numeric::ublas::matrix<complex<InvEnergy2> >
highCs_st = highEnergyMatching(Q,s,t,u,parentCase,oneLoop,includeAlphaS2);
boost::numeric::ublas::matrix<complex<InvEnergy2> >
highCs_ts = highEnergyMatching(Q,t,s,u,parentCase,oneLoop,includeAlphaS2);
boost::numeric::ublas::matrix<complex<InvEnergy2> > highCt_st(4,1);
boost::numeric::ublas::matrix<complex<InvEnergy2> > highCs_ts_2x2(2,2);
highCs_ts_2x2(0,0) = highCs_ts(0,0);
highCs_ts_2x2(1,0) = highCs_ts(1,0);
highCs_ts_2x2(0,1) = highCs_ts(2,0);
highCs_ts_2x2(1,1) = highCs_ts(3,0);
boost::numeric::ublas::matrix<Complex> temp(2,2);
temp = boost::numeric::ublas::trans(M_N(3));
boost::numeric::ublas::matrix<complex<InvEnergy2> > highCt_st_2x2(2,2),temp2(2,2);
axpy_prod_local(highCs_ts_2x2,temp,temp2);
axpy_prod_local(M_N(2),temp2,highCt_st_2x2);
highCt_st(0,0) = highCt_st_2x2(0,0);
highCt_st(1,0) = highCt_st_2x2(1,0);
highCt_st(2,0) = highCt_st_2x2(0,1);
highCt_st(3,0) = highCt_st_2x2(1,1);
highC = highCs_st + highCt_st;
}
break;
case QtQtQQ:
{
highC.resize(4,1);
Process parentCase = QQQQ;
highC = highEnergyMatching(Q,s,t,u,parentCase,oneLoop,includeAlphaS2);
double Y = 1.0/6.0; // Hypercharge of the non-3rd-gen doublet (still a quark doublet).
if (order >= 1) {
highC(2,0) += y_t*y_t*a2/(4.0*pi*s)*(3.0/2.0-0.5*Ls);
highC(1,0) += y_t*y_t*a3/(4.0*pi*s)*(1.0/2.0-0.5*Ls);
highC(3,0) += y_t*y_t*a1*Y/(4.0*pi*s)*(-5.0/12.0-1.0/12.0*Ls);
}
}
break;
case QQUU:
Yi = 1./6.; Yf = 2./3.;
highC.resize(2,1);
highC(0,0) = 4.0*pi*a3 / s;
highC(1,0) = 4.0*pi*a1*Yi*Yf / s;
if (order >= 1) {
highC(0,0) += (1.0/s)*((a1*a3*(Yi*Yi+Yf*Yf)+a2*a3*C_F_2)*W +
2.0*a1*a3*Yi*Yf*fTilde_su);
highC(1,0) += (1.0/s)*(a1*a1*Yi*Yf*PI1 +
(a1*a2*Yi*Yf*C_F_2+2.0*a1*a3*Yi*Yf*C_F_3+
a1*a1*(Yi*Yi*Yi*Yf+Yf*Yf*Yf*Yi))*W);
if (includeAlphaS2) {
highC(0,0) += (1.0/s)*(a3*a3*(X_3_su+(C_d_3-C_A_3)/4.0*fTilde_su));
highC(1,0) += (1.0/s)*((a3*a3*C_1_3+a1*a1*Yi*Yi*Yf*Yf)*fTilde_su);
}
}
break;
case QtQtUU:
{
highC.resize(2,1);
Process parentCase = QQUU;
highC = highEnergyMatching(Q,s,t,u,parentCase,oneLoop,includeAlphaS2);
double Y = 2./3.;
if (order >= 1) {
highC(0,0) += y_t*y_t*a3/(4.0*pi*s)*(1.0/2.0-0.5*Ls);
highC(1,0) += y_t*y_t*a1*Y/(4.0*pi*s)*(-5.0/12.0-1.0/12.0*Ls);
}
}
break;
case QQtRtR:
{
highC.resize(2,1);
Process parentCase = QQUU;
highC = highEnergyMatching(Q,s,t,u,parentCase,oneLoop,includeAlphaS2);
double Y = 1.0/6.0;
if (order >= 1) {
highC(0,0) += y_t*y_t*a3/(4.0*pi*s)*(1.0-Ls);
highC(1,0) += y_t*y_t*a1*Y/(4.0*pi*s)*(5.0/3.0-2.0/3.0*Ls);
}
}
break;
case QQDD:
Yi = 1./6.; Yf = -1./3.;
highC.resize(2,1);
highC(0,0) = 4.0*pi*a3 / s;
highC(1,0) = 4.0*pi*a1*Yi*Yf / s;
if (order >= 1) {
highC(0,0) += (1.0/s)*((a1*a3*(Yi*Yi+Yf*Yf)+a2*a3*C_F_2)*W +
2.0*a1*a3*Yi*Yf*fTilde_su);
highC(1,0) += (1.0/s)*(a1*a1*Yi*Yf*PI1 +
(a1*a2*Yi*Yf*C_F_2+2.0*a1*a3*Yi*Yf*C_F_3+
a1*a1*(Yi*Yi*Yi*Yf+Yf*Yf*Yf*Yi))*W);
if (includeAlphaS2) {
highC(0,0) += (1.0/s)*(a3*a3*(X_3_su+(C_d_3-C_A_3)/4.0*fTilde_su));
highC(1,0) += (1.0/s)*((a3*a3*C_1_3+a1*a1*Yi*Yi*Yf*Yf)*fTilde_su);
}
}
break;
case QtQtDD:
{
highC.resize(2,1);
Process parentCase = QQDD;
highC = highEnergyMatching(Q,s,t,u,parentCase,oneLoop,includeAlphaS2);
double Y = -1./3.;
if (order >= 1) {
highC(0,0) += y_t*y_t*a3/(4.0*pi*s)*(1.0/2.0-0.5*Ls);
highC(1,0) += y_t*y_t*a1*Y/(4.0*pi*s)*(-5.0/12.0-1.0/12.0*Ls);
}
}
break;
case QQLL:
Yi = 1./6.; Yf = -1./2.;
highC.resize(2,1);
highC(0,0) = 4.0*pi*a2 / s;
highC(1,0) = 4.0*pi*a1*Yi*Yf / s;
if (order >= 1) {
highC(0,0) += (1.0/s)*(a2*a2*(X_2_st-(C_d_2+C_A_2)/4.0*fTilde_st) +
(a2*a3*C_F_3 + a1*a2*(Yi*Yi+Yf*Yf))*W -
2.0*a1*a2*Yi*Yf*fTilde_st);
highC(1,0) += (1.0/s)*(-1.0*(a2*a2*C_1_2+a1*a1*Yi*Yi*Yf*Yf)*fTilde_st +
a1*a1*Yi*Yf*PI1 +
(a1*a3*Yi*Yf*C_F_3+2.0*a1*a2*Yi*Yf*C_F_2+
a1*a1*(Yi*Yi*Yi*Yf+Yf*Yf*Yf*Yi))*W);
}
break;
case QQEE:
Yi = 1./6.; Yf = -1.;
highC.resize(1,1);
highC(0,0) = 4.0*pi*a1*Yi*Yf / s;
if (order >= 1) {
highC(0,0) += (1.0/s)*(a1*a1*Yi*Yi*Yf*Yf*fTilde_su + a1*a1*Yi*Yf*PI1 +
(a1*a3*Yi*Yf*C_F_3 + a1*a2*Yi*Yf*C_F_2 +
a1*a1*(Yi*Yi*Yi*Yf+Yf*Yf*Yf*Yi))*W);
}
break;
case UUUU:
Yi = Yf = 2./3.;
highC.resize(2,1);
highC(0,0) = 4.0*pi*a3 / s;
highC(1,0) = 4.0*pi*a1*Yi*Yf / s;
if (order >= 1) {
highC(0,0) += (1.0/s)*(-2.0*a1*a3*Yi*Yf*fTilde_st +
a1*a3*(Yi*Yi+Yf*Yf)*W);
highC(1,0) += (1.0/s)*(-1.0*(a1*a1*Yi*Yi*Yf*Yf)*fTilde_st +
a1*a1*Yi*Yf*PI1 +
(2.0*a1*a3*Yi*Yf*C_F_3+a1*a1*(Yi*Yi*Yi*Yf+Yf*Yf*Yf*Yi))*W);
if (includeAlphaS2) {
highC(0,0) += (1.0/s)*(a3*a3*(X_3_st-(C_d_3+C_A_3)/4.0*fTilde_st));
highC(1,0) += (1.0/s)*(-1.0*(a3*a3*C_1_3)*fTilde_st);
}
}
break;
case UUUUiden:
{
Process parentCase = UUUU;
boost::numeric::ublas::matrix<complex<InvEnergy2> >
highCs_st = highEnergyMatching(Q,s,t,u,parentCase,oneLoop,includeAlphaS2);
boost::numeric::ublas::matrix<complex<InvEnergy2> >
highCs_ts = highEnergyMatching(Q,t,s,u,parentCase,oneLoop,includeAlphaS2);
boost::numeric::ublas::matrix<complex<InvEnergy2> > highCt_st;
axpy_prod_local(M_N(3),highCs_ts,highCt_st);
highC = highCs_st + highCt_st;
}
break;
case tRtRUU:
{
highC.resize(2,1);
Process parentCase = UUUU;
highC = highEnergyMatching(Q,s,t,u,parentCase,oneLoop,includeAlphaS2);
double Y = 2./3.;
if (order >= 1) {
highC(0,0) += y_t*y_t*a3/(4.0*pi*s)*(1.0-Ls);
highC(1,0) += y_t*y_t*a1*Y/(4.0*pi*s)*(5.0/3.0-2.0/3.0*Ls);
}
}
break;
case UUDD:
Yi = 2./3.; Yf = -1./3.;
highC.resize(2,1);
highC(0,0) = 4.0*pi*a3 / s;
highC(1,0) = 4.0*pi*a1*Yi*Yf / s;
if (order >= 1) {
highC(0,0) += (1.0/s)*(-2.0*a1*a3*Yi*Yf*fTilde_st +
a1*a3*(Yi*Yi+Yf*Yf)*W);
highC(1,0) += (1.0/s)*(-1.0*(a1*a1*Yi*Yi*Yf*Yf)*fTilde_st +
a1*a1*Yi*Yf*PI1 +
(2.0*a1*a3*Yi*Yf*C_F_3+a1*a1*(Yi*Yi*Yi*Yf+Yf*Yf*Yf*Yi))*W);
if (includeAlphaS2) {
highC(0,0) += (1.0/s)*(a3*a3*(X_3_st-(C_d_3+C_A_3)/4.0*fTilde_st));
highC(1,0) += (1.0/s)*(-1.0*(a3*a3*C_1_3)*fTilde_st);
}
}
break;
case tRtRDD:
{
highC.resize(2,1);
Process parentCase = UUDD;
highC = highEnergyMatching(Q,s,t,u,parentCase,oneLoop,includeAlphaS2);
double Y = -1./3.;
if (order >= 1) {
highC(0,0) += y_t*y_t*a3/(4.0*pi*s)*(1.0-Ls);
highC(1,0) += y_t*y_t*a1*Y/(4.0*pi*s)*(5.0/3.0-2.0/3.0*Ls);
}
}
break;
case UULL:
Yi = 2./3.; Yf = -0.5;
highC.resize(1,1);
highC(0,0) = 4.0*pi*a1*Yi*Yf / s;
if (order >= 1) {
highC(0,0) += (1.0/s)*(a1*a1*Yi*Yi*Yf*Yf*fTilde_su + a1*a1*Yi*Yf*PI1 +
(a1*a3*Yi*Yf*C_F_3 + a1*a2*Yi*Yf*C_F_2 +
a1*a1*(Yi*Yi*Yi*Yf+Yf*Yf*Yf*Yi))*W);
}
break;
case UUEE:
Yi = 2./3.; Yf = -1.;
highC.resize(1,1);
highC(0,0) = 4.0*pi*a1*Yi*Yf / s;
if (order >= 1) {
highC(0,0) += (1.0/s)*(-1.0*a1*a1*Yi*Yi*Yf*Yf*fTilde_st + a1*a1*Yi*Yf*PI1 +
(a1*a3*Yi*Yf*C_F_3 +
a1*a1*(Yi*Yi*Yi*Yf+Yf*Yf*Yf*Yi))*W);
}
break;
case DDDD:
Yi = Yf = -1./3.;
highC.resize(2,1);
highC(0,0) = 4.0*pi*a3 / s;
highC(1,0) = 4.0*pi*a1*Yi*Yf / s;
if (order >= 1) {
highC(0,0) += (1.0/s)*(-2.0*a1*a3*Yi*Yf*fTilde_st +
a1*a3*(Yi*Yi+Yf*Yf)*W);
highC(1,0) += (1.0/s)*(-1.0*(a1*a1*Yi*Yi*Yf*Yf)*fTilde_st +
a1*a1*Yi*Yf*PI1 +
(2.0*a1*a3*Yi*Yf*C_F_3+a1*a1*(Yi*Yi*Yi*Yf+Yf*Yf*Yf*Yi))*W);
if (includeAlphaS2) {
highC(0,0) += (1.0/s)*(a3*a3*(X_3_st-(C_d_3+C_A_3)/4.0*fTilde_st));
highC(1,0) += (1.0/s)*(-1.0*(a3*a3*C_1_3)*fTilde_st);
}
}
break;
case DDDDiden:
{
Process parentCase = DDDD;
boost::numeric::ublas::matrix<complex<InvEnergy2> >
highCs_st = highEnergyMatching(Q,s,t,u,parentCase,oneLoop,includeAlphaS2);
boost::numeric::ublas::matrix<complex<InvEnergy2> >
highCs_ts = highEnergyMatching(Q,t,s,u,parentCase,oneLoop,includeAlphaS2);
boost::numeric::ublas::matrix<complex<InvEnergy2> > highCt_st;
axpy_prod_local(M_N(3),highCs_ts,highCt_st);
highC = highCs_st + highCt_st;
}
break;
case DDLL:
Yi = -1./3.; Yf = -0.5;
highC.resize(1,1);
highC(0,0) = 4.0*pi*a1*Yi*Yf / s;
if (order >= 1) {
highC(0,0) += (1.0/s)*(a1*a1*Yi*Yi*Yf*Yf*fTilde_su + a1*a1*Yi*Yf*PI1 +
(a1*a3*Yi*Yf*C_F_3 + a1*a2*Yi*Yf*C_F_2 +
a1*a1*(Yi*Yi*Yi*Yf+Yf*Yf*Yf*Yi))*W);
}
break;
case DDEE:
Yi = -1./3.; Yf = -1.;
highC.resize(1,1);
highC(0,0) = 4.0*pi*a1*Yi*Yf / s;
if (order >= 1) {
highC(0,0) += (1.0/s)*(-1.0*a1*a1*Yi*Yi*Yf*Yf*fTilde_st + a1*a1*Yi*Yf*PI1 +
(a1*a3*Yi*Yf*C_F_3 +
a1*a1*(Yi*Yi*Yi*Yf+Yf*Yf*Yf*Yi))*W);
}
break;
case LLLL:
Yi = Yf = -0.5;
highC.resize(2,1);
highC(0,0) = 4.0*pi*a2 / s;
highC(1,0) = 4.0*pi*a1*Yi*Yf / s;
if (order >= 1) {
highC(0,0) += (1.0/s)*(a2*a2*(X_2_st-(C_d_2+C_A_2)/4.0*fTilde_st) +
2.0*a1*a2*Yi*Yf*W -
2.0*a1*a2*Yi*Yf*fTilde_st);
highC(1,0) += (1.0/s)*(-1.0*(a2*a2*C_1_2+a1*a1*Yi*Yi*Yf*Yf)*fTilde_st +
a1*a1*Yi*Yf*PI1 +
2.0*(a1*a2*Yi*Yf*C_F_2+a1*a1*Yi*Yi*Yf*Yf)*W);
}
break;
case LLLLiden:
{
Process parentCase = LLLL;
boost::numeric::ublas::matrix<complex<InvEnergy2> >
highCs_st = highEnergyMatching(Q,s,t,u,parentCase,oneLoop,includeAlphaS2);
boost::numeric::ublas::matrix<complex<InvEnergy2> >
highCs_ts = highEnergyMatching(Q,t,s,u,parentCase,oneLoop,includeAlphaS2);
boost::numeric::ublas::matrix<complex<InvEnergy2> > highCt_st;
axpy_prod_local(M_N(2), highCs_ts, highCt_st);
highC = highCs_st + highCt_st;
}
break;
case LLEE:
Yi = -0.5; Yf = -1.;
highC.resize(1,1);
highC(0,0) = 4.0*pi*a1*Yi*Yf / s;
if (order >= 1) {
highC(0,0) += (1.0/s)*(a1*a1*Yi*Yi*Yf*Yf*fTilde_su + a1*a1*Yi*Yf*PI1 +
(a1*a2*Yi*Yf*C_F_2 +
a1*a1*(Yi*Yi*Yi*Yf+Yf*Yf*Yf*Yi))*W);
}
break;
case EEEE:
Yi = Yf = -1.;
highC.resize(1,1);
highC(0,0) = 4.0*pi*a1*Yi*Yf / s;
if (order >= 1) {
highC(0,0) += (1.0/s)*(-1.0*a1*a1*Yi*Yi*Yf*Yf*fTilde_st + a1*a1*Yi*Yf*PI1 +
2.0*a1*a1*Yi*Yi*Yf*Yf*W);
}
break;
case EEEEiden:
{
Process parentCase = EEEE;
boost::numeric::ublas::matrix<complex<InvEnergy2> >
highCs_st = highEnergyMatching(Q,s,t,u,parentCase,oneLoop,includeAlphaS2);
boost::numeric::ublas::matrix<complex<InvEnergy2> >
highCs_ts = highEnergyMatching(Q,t,s,u,parentCase,oneLoop,includeAlphaS2);
boost::numeric::ublas::matrix<complex<InvEnergy2> >
highCt_st = highCs_ts;
highC = highCs_st + highCt_st;
}
break;
default:
assert(false);
}
return highC;
}
boost::numeric::ublas::matrix<complex<InvEnergy2> >
HighEnergyMatching::Spin1HighMatching(Energy highScale,
Energy2 s, Energy2 t, Energy2 u,
EWProcess::Process process,
bool oneLoop, bool includeAlphaS2) {
using Constants::pi;
unsigned int order = !oneLoop ? 0 : 1;
// (If crossed graphs, swap s and t here)
Complex L_s = MinusLog(-s/(highScale*highScale));
Complex L_t = MinusLog(-t/(highScale*highScale));
Complex L_u = MinusLog(-u/(highScale*highScale));
Complex L_s2 = L_s*L_s;
Complex L_t2 = L_t*L_t;
Complex L_u2 = L_u*L_u;
// Tree-Level:
// Topology types defined. Note each of these is a vector of 5 entries. They are the coefficients
// for the dirac structures M_0, M_1, M_4, M_5, and M_6 for vector boson production.
boost::numeric::ublas::vector<complex<InvEnergy2> > R1(5);
for(unsigned int ix=0;ix<5;++ix) R1[ix] = ZERO;
R1[0] = -1.0/t;
R1[1] = -2.0/t;
R1[2] = ZERO;
R1[3] = ZERO;
R1[4] = ZERO;
boost::numeric::ublas::vector<complex<InvEnergy2> > R1_bar(5);
for(unsigned int ix=0;ix<5;++ix) R1_bar[ix] = ZERO;
R1_bar[0] = -1.0/u;
boost::numeric::ublas::vector<complex<InvEnergy2> > R2(5);
for(unsigned int ix=0;ix<5;++ix) R2[ix] = ZERO;
R2[1] = -1.0/s*2.0;
// Topologies T1:
boost::numeric::ublas::vector<complex<InvEnergy2> > T1a(5);
for(unsigned int ix=0;ix<5;++ix) T1a[ix] = ZERO;
T1a[0] = 1.0/(t*u)*(-3.0*t*L_s2-(s+4.0*t)*L_t2+2.0*(s+4.0*t)*L_s*L_t+2.0*u*L_t-
pi*pi*(7.0/6.0*s+25.0/6.0*t)-4.0*u);
T1a[1] = 1.0/(u*u*t*s)*(0.5*t*(9.0*s*s+14.0*s*t+7.0*t*t)*L_s2+s*(2.0*s+t)*(s+2.0*t)*L_t2-
2.0*(2.0*s*s*s+9.0*s*s*t+10.0*s*t*t+4.0*t*t*t)*L_s*L_t-
2.0*t*t*u*L_s-2.0*u*s*(2.0*s+3.0*t)*L_t+
pi*pi*(7.0/3.0*s*s*s+125.0/12.0*s*s*t+71.0/6.0*s*t*t+
19.0/4.0*t*t*t)-
8.0*s*s*s-20.0*s*s*t-16.0*s*t*t-4.0*t*t*t);
T1a[2] = 1.0/(t*u*u)*(-t*(3.0*s+4.0*t)*L_s2-(s*s+5.0*s*t+5.0*t*t)*L_t2+
2.0*t*(3.0*s+4.0*t)*L_s*L_t+2.0*u*t*(2.0*s+t)*L_s/s-
2.0*u*t*L_t+pi*pi*(s*s/6.0-8.0/3.0*s*t-23.0/6.0*t*t)+
4.0*t*t*t/s+4.0*s*t+8.0*t*t);
T1a[3] = T1a[2];
T1a[4] = GeV2/(t*u*u*u)*(-4.0*t*(s+2.0*t)*(L_s-L_t)*(L_s-L_t)+
4.0*u*(3.0*s+5.0*t)*(L_s-L_t)-4.0*pi*pi*t*(s+2.0*t)-4.0*u*u);
boost::numeric::ublas::vector<complex<InvEnergy2> > T1b(5);
for(unsigned int ix=0;ix<5;++ix) T1b[ix] = ZERO;
T1b[0] = 1.0/(t*u*s*s)*(-s*t*(2.0*s+3.0*t)*L_u2+s*u*(s+3.0*t)*L_t2+
2.0*s*(s*s+3.0*s*t+3.0*t*t)*L_u*L_t+s*s*t*L_u+s*s*u*L_t-
pi*pi*(7.0/6.0*s*s*s+3.0*s*s*t+3.0*s*t*t)+2.0*s*s*s);
T1b[1] = 1.0/(t*s*s*u)*(3.0*s*t*u*L_u2+s*u*(2.0*s+3.0*t)*L_t2-
2.0*s*u*(2.0*s+3.0*t)*L_u*L_t+2.0*s*s*u*L_t-
pi*pi*(7.0/3.0*s*s*s+16.0/3.0*s*s*t+3.0*s*t*t)+
4.0*s*s*s+4.0*s*s*t);
T1b[2] = 1.0/(t*u*s*s)*(-3.0*s*t*u*(L_u-L_t)*(L_u-L_t)+4.0*s*s*t*L_u+4.0*s*s*u*L_t+
pi*pi*(3.0*s*s*t+3.0*s*t*t)+8.0*s*s*s);
T1b[3] = 1.0/(t*u*s*s)*(s*t*(2.0*s+3.0*t)*L_u2-s*u*(s+3.0*t)*L_t2+6.0*s*t*u*L_u*L_t+
pi*pi*(-1.0/6.0*s*s*s+3.0*s*s*t+3.0*s*t*t));
T1b[4] = 12.0*GeV2/(t*u)*(L_t-L_u);
boost::numeric::ublas::vector<complex<InvEnergy2> > T1c(5);
for(unsigned int ix=0;ix<5;++ix) T1c[ix] = ZERO;
T1c[0] = 1.0/t*(2.0*L_s*L_t-7.0*pi*pi/6.0-L_t2);
T1c[1] = 1.0/(t*u*u)*(s*t*L_s2-(2.0*s*s+3.0*s*t+2.0*t*t)*L_t2+
2.0*(2.0*s*s+3.0*s*t+2.0*t*t)*L_s*L_t+2.0*t*u*(L_s-L_t)-
pi*pi*(7.0/3.0*s*s+11.0/3.0*s*t+7.0/3.0*t*t));
T1c[2] = 1.0/(t*u*u)*(t*(3.0*s+2.0*t)*(L_s-L_t)*(L_s-L_t)+2.0*u*t*L_s+
2.0*u*(2.0*s+t)*L_t+pi*pi*t*(3.0*s+2.0*t)+8.0*u*u);
T1c[3] = T1c[2];
T1c[4] = GeV2/(t*u*u*u)*(4.0*t*(2.0*s+t)*(L_s-L_t)*(L_s-L_t)-4.0*u*(3.0*s+t)*(L_s-L_t)+
4.0*pi*pi*t*(2.0*s+t)-4.0*u*u);
boost::numeric::ublas::vector<complex<InvEnergy2> > T1d(5);
for(unsigned int ix=0;ix<5;++ix) T1d[ix] = ZERO;
T1d[2] = 1.0/s*(-2.0*L_s+4.0);
T1d[3] = T1d[2];
boost::numeric::ublas::vector<complex<InvEnergy2> > T1a_bar(5);
for(unsigned int ix=0;ix<5;++ix) T1a_bar[ix] = ZERO;
T1a_bar[0] = 1.0/(u*t)*(-3.0*u*L_s2-(s+4.0*u)*L_u2+2.0*(s+4.0*u)*L_s*L_u+2.0*t*L_u-
pi*pi*(7.0/6.0*s+25.0/6.0*u)-4.0*t);
T1a_bar[1] = 2.0*T1a_bar[0] -
1.0/(t*t*u*s)*(0.5*u*(9.0*s*s+14.0*s*u+7.0*u*u)*L_s2+s*(2.0*s+u)*(s+2.0*u)*L_u2-
2.0*(2.0*s*s*s+9.0*s*s*u+10.0*s*u*u+4.0*u*u*u)*L_s*L_u-
2.0*u*u*t*L_s-2.0*t*s*(2.0*s+3.0*u)*L_u+
pi*pi*(7.0/3.0*s*s*s+125.0/12.0*s*s*u+71.0/6.0*s*u*u+
19.0/4.0*u*u*u)-
8.0*s*s*s-20.0*s*s*u-16.0*s*u*u-4.0*u*u*u);
T1a_bar[2] = 1.0/(u*t*t)*(-u*(3.0*s+4.0*u)*L_s2-(s*s+5.0*s*u+5.0*u*u)*L_u2+
2.0*u*(3.0*s+4.0*u)*L_s*L_u+2.0*t*u*(2.0*s+u)*L_s/s-
2.0*t*u*L_u+pi*pi*(s*s/6.0-8.0/3.0*s*u-23.0/6.0*u*u)+
4.0*u*u*u/s+4.0*s*u+8.0*u*u);
T1a_bar[3] = T1a_bar[2];
T1a_bar[4] = -GeV2/(u*t*t*t)*(-4.0*u*(s+2.0*u)*(L_s-L_u)*(L_s-L_u)+
4.0*t*(3.0*s+5.0*u)*(L_s-L_u)-4.0*pi*pi*u*(s+2.0*u)-4.0*t*t);
boost::numeric::ublas::vector<complex<InvEnergy2> > T1b_bar(5);
for(unsigned int ix=0;ix<5;++ix) T1b_bar[ix] = ZERO;
T1b_bar[0] = 1.0/(u*t*s*s)*(-s*u*(2.0*s+3.0*u)*L_t2+s*t*(s+3.0*u)*L_u2+
2.0*s*(s*s+3.0*s*u+3.0*u*u)*L_t*L_u+
s*s*u*L_t+s*s*t*L_u-
pi*pi*(7.0/6.0*s*s*s+3.0*s*s*u+3.0*s*u*u)+2.0*s*s*s);
T1b_bar[1] = 2.0*T1b_bar[0] -
1.0/(u*s*s*t)*(3.0*s*u*t*L_t2+s*t*(2.0*s+3.0*u)*L_u2-
2.0*s*t*(2.0*s+3.0*u)*L_t*L_u+2.0*s*s*t*L_u-
pi*pi*(7.0/3.0*s*s*s+16.0/3.0*s*s*u+3.0*s*u*u)+
4.0*s*s*s+4.0*s*s*u);
T1b_bar[3] = 1.0/(u*t*s*s)*(-3.0*s*u*t*(L_t-L_u)*(L_t-L_u)+4.0*s*s*u*L_t+4.0*s*s*t*L_u+
pi*pi*(3.0*s*s*u+3.0*s*u*u)+8.0*s*s*s);
T1b_bar[2] = 1.0/(u*t*s*s)*(s*u*(2.0*s+3.0*u)*L_t2-s*t*(s+3.0*u)*L_u2+6.0*s*u*t*L_t*L_u+
pi*pi*(-1.0/6.0*s*s*s+3.0*s*s*u+3.0*s*u*u));
T1b_bar[4] = -12.0*GeV2/(u*t)*(L_u-L_t);
boost::numeric::ublas::vector<complex<InvEnergy2> > T1c_bar(5);
for(unsigned int ix=0;ix<5;++ix) T1c_bar[ix] = ZERO;
T1c_bar[0] = 1.0/u*(2.0*L_s*L_u-7.0*pi*pi/6.0-L_u2);
T1c_bar[1] = 2.0*T1c_bar[0] -
1.0/(u*t*t)*(s*u*L_s2-(2.0*s*s+3.0*s*u+2.0*u*u)*L_u2+
2.0*(2.0*s*s+3.0*s*u+2.0*u*u)*L_s*L_u+2.0*u*t*(L_s-L_u)-
pi*pi*(7.0/3.0*s*s+11.0/3.0*s*u+7.0/3.0*u*u));
T1c_bar[2] = 1.0/(u*t*t)*(u*(3.0*s+2.0*u)*(L_s-L_u)*(L_s-L_u)+2.0*t*u*L_s+
2.0*t*(2.0*s+u)*L_u+pi*pi*u*(3.0*s+2.0*u)+8.0*t*t);
T1c_bar[3] = T1c_bar[2];
T1c_bar[4] = -GeV2/(u*t*t*t)*(4.0*u*(2.0*s+u)*(L_s-L_u)*(L_s-L_u)-4.0*t*(3.0*s+u)*(L_s-L_u)+
4.0*pi*pi*u*(2.0*s+u)-4.0*t*t);
// Topologies T2:
boost::numeric::ublas::vector<complex<InvEnergy2> > T2a(5);
for(unsigned int ix=0;ix<5;++ix) T2a[ix] = ZERO;
T2a[1] = 1.0/s*(L_s/6.0-11.0/18.0);
boost::numeric::ublas::vector<complex<InvEnergy2> > T2b(5);
for(unsigned int ix=0;ix<5;++ix) T2b[ix] = ZERO;
T2b[1] = 1.0/s*(-2.0/3.0*L_s+22.0/9.0);
boost::numeric::ublas::vector<complex<InvEnergy2> > T2c(5);
for(unsigned int ix=0;ix<5;++ix) T2c[ix] = ZERO;
T2c[1] = 1.0/s*(3.0/2.0*L_s2-17.0/2.0*L_s-pi*pi/4.0+95.0/6.0);
boost::numeric::ublas::vector<complex<InvEnergy2> > T2d(5);
for(unsigned int ix=0;ix<5;++ix) T2d[ix] = ZERO;
T2d[1] = 1.0/s*(-4.0/3.0*L_s+14.0/9.0);
// Topologies T3:
boost::numeric::ublas::vector<complex<InvEnergy2> > T3a(5);
for(unsigned int ix=0;ix<5;++ix) T3a[ix] = ZERO;
T3a[0] = 1.0/t*(L_t2-pi*pi/6.0);
T3a[1] = 2.0*T3a[0];
T3a[3] = 1.0/t*(-L_t2+pi*pi/6.0+2.0);
boost::numeric::ublas::vector<complex<InvEnergy2> > T3b(5);
for(unsigned int ix=0;ix<5;++ix) T3b[ix] = ZERO;
T3b[0] = 1.0/t*(-L_t+4.0);
T3b[1] = 2.0*T3b[0];
T3b[3] = 1.0/t*(4.0*L_t-10.0);
boost::numeric::ublas::vector<complex<InvEnergy2> > T3a_bar(5);
for(unsigned int ix=0;ix<5;++ix) T3a_bar[ix] = ZERO;
T3a_bar[0] = 1.0/u*(L_u2-pi*pi/6.0);
T3a_bar[2] = 1.0/u*(-L_u2+pi*pi/6.0+2.0);
boost::numeric::ublas::vector<complex<InvEnergy2> > T3b_bar(5);
for(unsigned int ix=0;ix<5;++ix) T3b_bar[ix] = ZERO;
T3b_bar[0] = 1.0/u*(-L_u+4.0);
T3b_bar[2] = 1.0/u*(4.0*L_u-10.0);
// Topologies T4:
boost::numeric::ublas::vector<complex<InvEnergy2> > T4a(5);
for(unsigned int ix=0;ix<5;++ix) T4a[ix] = ZERO;
T4a[0] = 1.0/t*(L_t2-pi*pi/6.0);
T4a[1] = 2.0*T4a[0];
T4a[2] = 1.0/t*(-L_t2+pi*pi/6.0+2.0);
boost::numeric::ublas::vector<complex<InvEnergy2> > T4b(5);
for(unsigned int ix=0;ix<5;++ix) T4b[ix] = ZERO;
T4b[0] = 1.0/t*(-L_t+4.0);
T4b[1] = 2.0*T4b[0];
T4b[2] = 1.0/t*(4.0*L_t-10.0);
boost::numeric::ublas::vector<complex<InvEnergy2> > T4a_bar(5);
for(unsigned int ix=0;ix<5;++ix) T4a_bar[ix] = ZERO;
T4a_bar[0] = 1.0/u*(L_u2-pi*pi/6.0);
T4a_bar[3] = 1.0/u*(-L_u2+pi*pi/6.0+2.0);
boost::numeric::ublas::vector<complex<InvEnergy2> > T4b_bar(5);
for(unsigned int ix=0;ix<5;++ix) T4b_bar[ix] = ZERO;
T4b_bar[0] = 1.0/u*(-L_u+4.0);
T4b_bar[3] = 1.0/u*(4.0*L_u-10.0);
// Topologies T5:
boost::numeric::ublas::vector<complex<InvEnergy2> > T5a(5);
for(unsigned int ix=0;ix<5;++ix) T5a[ix] = ZERO;
T5a[1] = 1.0/s*(2.0*L_s-4.0);
boost::numeric::ublas::vector<complex<InvEnergy2> > T5b(5);
for(unsigned int ix=0;ix<5;++ix) T5b[ix] = ZERO;
T5b[1] = 1.0/s*(-2.0*L_s2+6.0*L_s-16.0+pi*pi/3.0);
// Topologies T6:
boost::numeric::ublas::vector<complex<InvEnergy2> > T6a(5);
for(unsigned int ix=0;ix<5;++ix) T6a[ix] = ZERO;
T6a[1] = 1.0/s*(-19.0/6.0*L_s+58.0/9.0);
boost::numeric::ublas::vector<complex<InvEnergy2> > T6b(5);
for(unsigned int ix=0;ix<5;++ix) T6b[ix] = ZERO;
T6b[1] = 1.0/s*(-1.0/6.0*L_s+4.0/9.0);
boost::numeric::ublas::vector<complex<InvEnergy2> > T6c(5);
for(unsigned int ix=0;ix<5;++ix) T6c[ix] = ZERO;
T6c[1] = 1.0/s*(2.0/3.0*L_s-16.0/9.0);
boost::numeric::ublas::vector<complex<InvEnergy2> > T6d(5);
for(unsigned int ix=0;ix<5;++ix) T6d[ix] = ZERO;
T6d[1] = 1.0/s*(4.0/3.0*L_s-20.0/9.0);
// Topology T7:
boost::numeric::ublas::vector<complex<InvEnergy2> > T7(5);
for(unsigned int ix=0;ix<5;++ix) T7[ix] = ZERO;
T7[0] = 1.0/t*(-L_t+1.0);
T7[1] = 2.0*T7[0];
boost::numeric::ublas::vector<complex<InvEnergy2> > T7_bar(5);
for(unsigned int ix=0;ix<5;++ix) T7_bar[ix] = ZERO;
T7_bar[0] = 1.0/u*(-L_u+1.0);
// Group Theory Factors / SM parameters needed for matrix elements:
double a1 = ElectroWeakReweighter::coupling()->a1(highScale);
double a2 = ElectroWeakReweighter::coupling()->a2(highScale);
double a3 = ElectroWeakReweighter::coupling()->a3(highScale);
double y_t = ElectroWeakReweighter::coupling()->y_t(highScale);
// Traces over complex scalars and weyl fermions.
double T_CS_3 = 0.0;
double T_CS_2 = 0.5;
//double T_CS_1 = 0.5;
double T_WF_3 = 2.0*3.0;
double T_WF_2 = 2.0*3.0;
//double T_WF_1 = 10.0/3.0*3.0;
double C_A_3 = 3.0;
double C_A_2 = 2.0;
double C_A_1 = 0.0;
double C_F_3 = 4.0/3.0;
double C_F_2 = 3.0/4.0;
double C_F_1 = 1.0;
// This is the coefficient of the delta term in G_TT
double G_TT = 0.5;
// This is the coeffidient of d^ABC in G_TT (non-zero for SU(3))
double G_TT_3_D = 0.25*C_A_3;
double G_f = 1.0;
// Factors TBD after fermion helicity is specified:
double Y_Q(0.), G_Plus_U1(0.);
double G_Plus_SU2 = 0.25;
double G_Plus_SU3 = 1./6.;
double G_Plus_SU3_D = 0.5;
double Lambda_Q(0.);
// the _s and _ew are the alpha3 and alpha1/2 parts of Lambda_Q
double Lambda_Q_s(0.);
double Lambda_Q_ew(0.);
double rho12(0.), rho13(0.);
double rho23 = sqrt(a2*a3);
double tRorQ = 1.0;
boost::numeric::ublas::matrix<complex<InvEnergy2> > highC(1,1);
switch (process) {
case QQWW: case LLWW:
{
// Finish Group Theory Factors:
if (process==QQWW) {
Y_Q = 1.0/6.0;
G_Plus_U1 = Y_Q*Y_Q;
Lambda_Q = C_F_3*a3 + C_F_2*a2 + Y_Q*Y_Q*C_F_1*a1;
rho12 = Y_Q*sqrt(a1*a2);
}
else if (process==LLWW) {
Y_Q = -1.0/2.0;
G_Plus_U1 = Y_Q*Y_Q;
Lambda_Q = C_F_2*a2 + Y_Q*Y_Q*C_F_1*a1;
rho12 = Y_Q*sqrt(a1*a2);
}
highC.resize(5,5);
for (int i=0; i<5; i++) {
highC(0,i) = G_Plus_SU2*(4.0*pi*a2)*(R1[i]+R1_bar[i]);
highC(1,i) = G_f*4.0*pi*a2*(-0.5*R1[i]+0.5*R1_bar[i]-R2[i]);
highC(2,i) = rho12*4.0*pi*(R1[i]+R1_bar[i]);
highC(3,i) = rho12*4.0*pi*(R1[i]+R1_bar[i]);
highC(4,i) = G_Plus_U1*(4.0*pi*a1)*(R1[i]+R1_bar[i]);
if (order>=1) {
highC(0,i) += G_Plus_SU2*((-0.5*a2*a2*C_A_2)*(T1b[i]+T1b_bar[i])+
a2*(Lambda_Q-a2*C_A_2)*(T1c[i]+T1c_bar[i])+
0.5*a2*a2*C_A_2*(T3a[i]+T3a_bar[i])+
a2*(Lambda_Q-0.5*a2*C_A_2)*(T3b[i]+T3b_bar[i])+
0.5*a2*a2*C_A_2*(T4a[i]+T4a_bar[i])+
a2*(Lambda_Q-0.5*a2*C_A_2)*(T4b[i]+T4b_bar[i])+
a2*Lambda_Q*(T7[i]+T7_bar[i])) +
G_TT*(-a2*a2*(T1a[i]+T1a_bar[i])+a2*a2*(T1b[i]+T1b_bar[i])+
a2*a2*(T1c[i]+T1c_bar[i])+2.0*a2*a2*T1d[i]);
highC(1,i) += G_f*(0.25*a2*a2*C_A_2*(T1a[i]-T1a_bar[i])+
a2*(0.25*a2*C_A_2-0.5*Lambda_Q)*(T1c[i]-T1c_bar[i])+
0.5*a2*a2*C_A_2*T2a[i]+a2*a2*T_CS_2*T2b[i]-
0.5*a2*a2*C_A_2*T2c[i]+a2*a2*T_WF_2*T2d[i]-
0.25*a2*a2*C_A_2*(T3a[i]-T3a_bar[i])-
0.5*a2*(Lambda_Q-0.5*a2*C_A_2)*(T3b[i]-T3b_bar[i])-
0.25*a2*a2*C_A_2*(T4a[i]-T4a_bar[i])-
0.5*a2*(Lambda_Q-0.5*a2*C_A_2)*(T4b[i]-T4b_bar[i])+
0.5*a2*a2*C_A_2*T5a[i]+a2*(Lambda_Q-0.5*a2*C_A_2)*T5b[i]+
a2*a2*C_A_2*T6a[i]+a2*a2*C_A_2*T6b[i]+
a2*a2*T_CS_2*T6c[i]+a2*a2*T_WF_2*T6d[i]-
0.5*a2*Lambda_Q*(T7[i]-T7_bar[i]));
highC(2,i) += rho12*(-0.5*a1*C_A_1*T1b[i]-0.5*a2*C_A_2*T1b_bar[i]+
(Lambda_Q-0.5*a1*C_A_1-0.5*a2*C_A_2)*(T1c[i]+T1c_bar[i])+
0.5*a1*C_A_1*T3a[i]+0.5*a2*C_A_2*T3a_bar[i]+
(Lambda_Q-0.5*a1*C_A_1)*T3b[i]+(Lambda_Q-0.5*a2*C_A_2)*T3b_bar[i]+
0.5*a2*C_A_2*T4a[i]+0.5*a1*C_A_1*T4a_bar[i]+
(Lambda_Q-0.5*a2*C_A_2)*T4b[i]+(Lambda_Q-0.5*a1*C_A_1)*T4b_bar[i]+
Lambda_Q*(T7[i]+T7_bar[i]));
highC(3,i) += rho12*(-0.5*a2*C_A_2*T1b[i]-0.5*a1*C_A_1*T1b_bar[i]+
(Lambda_Q-0.5*a2*C_A_2-0.5*a1*C_A_1)*(T1c[i]+T1c_bar[i])+
0.5*a2*C_A_2*T3a[i]+0.5*a1*C_A_1*T3a_bar[i]+
(Lambda_Q-0.5*a2*C_A_2)*T3b[i]+(Lambda_Q-0.5*a1*C_A_1)*T3b_bar[i]+
0.5*a1*C_A_1*T4a[i]+0.5*a2*C_A_2*T4a_bar[i]+
(Lambda_Q-0.5*a1*C_A_1)*T4b[i]+(Lambda_Q-0.5*a2*C_A_2)*T4b_bar[i]+
Lambda_Q*(T7[i]+T7_bar[i]));
highC(4,i) += G_Plus_U1*((-0.5*a1*a1*C_A_1)*(T1b[i]+T1b_bar[i])+
a1*(Lambda_Q-a1*C_A_1)*(T1c[i]+T1c_bar[i])+
0.5*a1*a1*C_A_1*(T3a[i]+T3a_bar[i])+
a1*(Lambda_Q-0.5*a1*C_A_1)*(T3b[i]+T3b_bar[i])+
0.5*a1*a1*C_A_1*(T4a[i]+T4a_bar[i])+
a1*(Lambda_Q-0.5*a1*C_A_1)*(T4b[i]+T4b_bar[i])+
a1*Lambda_Q*(T7[i]+T7_bar[i]));
}
}
}
break;
case UUBB: case DDBB: case EEBB:
{
// Finish Group Theory Factors:
if (process==UUBB) {
Y_Q = 2.0/3.0;
G_Plus_U1 = Y_Q*Y_Q;
Lambda_Q = C_F_3*a3 + Y_Q*Y_Q*C_F_1*a1;
}
else if (process==DDBB) {
Y_Q = -1.0/3.0;
G_Plus_U1 = Y_Q*Y_Q;
Lambda_Q = C_F_3*a3 + Y_Q*Y_Q*C_F_1*a1;
}
else if (process==EEBB) {
Y_Q = -1.0;
G_Plus_U1 = Y_Q*Y_Q;
Lambda_Q = Y_Q*Y_Q*C_F_1*a1;
}
highC.resize(1,5);
for (int i=0; i<5; i++) {
highC(0,i) = G_Plus_U1*(4.0*pi*a1)*(R1[i]+R1_bar[i]);
if (order>=1) {
highC(0,i) += G_Plus_U1*((-0.5*a1*a1*C_A_1)*(T1b[i]+T1b_bar[i])+
a1*(Lambda_Q-a1*C_A_1)*(T1c[i]+T1c_bar[i])+
0.5*a1*a1*C_A_1*(T3a[i]+T3a_bar[i])+
a1*(Lambda_Q-0.5*a1*C_A_1)*(T3b[i]+T3b_bar[i])+
0.5*a1*a1*C_A_1*(T4a[i]+T4a_bar[i])+
a1*(Lambda_Q-0.5*a1*C_A_1)*(T4b[i]+T4b_bar[i])+
a1*Lambda_Q*(T7[i]+T7_bar[i]));
}
}
}
break;
case QQWG:
{
// Finish Group Theory Factors:
Y_Q = 1./6.;
Lambda_Q = C_F_3*a3 + C_F_2*a2 + Y_Q*Y_Q*C_F_1*a1;
highC.resize(1,5);
for (int i=0; i<5; i++) {
highC(0,i) = rho23*4.0*pi*(R1[i]+R1_bar[i]);
if (order>=1) {
highC(0,i) += rho23*(-0.5*a3*C_A_3*T1b[i]-0.5*a2*C_A_2*T1b_bar[i]+
(Lambda_Q-0.5*a3*C_A_3-0.5*a2*C_A_2)*(T1c[i]+T1c_bar[i])+
0.5*a3*C_A_3*T3a[i]+0.5*a2*C_A_2*T3a_bar[i]+
(Lambda_Q-0.5*a3*C_A_3)*T3b[i]+(Lambda_Q-0.5*a2*C_A_2)*T3b_bar[i]+
0.5*a2*C_A_2*T4a[i]+0.5*a3*C_A_3*T4a_bar[i]+
(Lambda_Q-0.5*a2*C_A_2)*T4b[i]+(Lambda_Q-0.5*a3*C_A_3)*T4b_bar[i]+
Lambda_Q*(T7[i]+T7_bar[i]));
}
}
}
break;
case QQBG:
{
// Finish Group Theory Factors:
Y_Q = 1.0/6.0;
Lambda_Q = C_F_3*a3 + C_F_2*a2 + Y_Q*Y_Q*C_F_1*a1;
rho13 = Y_Q*sqrt(a1*a3);
highC.resize(1,5);
for (int i=0; i<5; i++) {
highC(0,i) = rho13*4.0*pi*(R1[i]+R1_bar[i]);
if (order>=1) {
highC(0,i) += rho13*(-0.5*a3*C_A_3*T1b[i]-0.5*a1*C_A_1*T1b_bar[i]+
(Lambda_Q-0.5*a3*C_A_3-0.5*a1*C_A_1)*(T1c[i]+T1c_bar[i])+
0.5*a3*C_A_3*T3a[i]+0.5*a1*C_A_1*T3a_bar[i]+
(Lambda_Q-0.5*a3*C_A_3)*T3b[i]+(Lambda_Q-0.5*a1*C_A_1)*T3b_bar[i]+
0.5*a1*C_A_1*T4a[i]+0.5*a3*C_A_3*T4a_bar[i]+
(Lambda_Q-0.5*a1*C_A_1)*T4b[i]+(Lambda_Q-0.5*a3*C_A_3)*T4b_bar[i]+
Lambda_Q*(T7[i]+T7_bar[i]));
}
}
}
break;
case UUBG: case DDBG:
{
// Finish Group Theory Factors:
if (process==UUBG) {
Y_Q = 2.0/3.0;
Lambda_Q = C_F_3*a3 + Y_Q*Y_Q*C_F_1*a1;
rho13 = Y_Q*sqrt(a1*a3);
}
else if (process==DDBG) {
Y_Q = -1.0/3.0;
Lambda_Q = C_F_3*a3 + Y_Q*Y_Q*C_F_1*a1;
rho13 = Y_Q*sqrt(a1*a3);
}
highC.resize(1,5);
for (int i=0; i<5; i++) {
highC(0,i) = rho13*4.0*pi*(R1[i]+R1_bar[i]);
if (order>=1) {
highC(0,i) += rho13*(-0.5*a3*C_A_3*T1b[i]-0.5*a1*C_A_1*T1b_bar[i]+
(Lambda_Q-0.5*a3*C_A_3-0.5*a1*C_A_1)*(T1c[i]+T1c_bar[i])+
0.5*a3*C_A_3*T3a[i]+0.5*a1*C_A_1*T3a_bar[i]+
(Lambda_Q-0.5*a3*C_A_3)*T3b[i]+(Lambda_Q-0.5*a1*C_A_1)*T3b_bar[i]+
0.5*a1*C_A_1*T4a[i]+0.5*a3*C_A_3*T4a_bar[i]+
(Lambda_Q-0.5*a1*C_A_1)*T4b[i]+(Lambda_Q-0.5*a3*C_A_3)*T4b_bar[i]+
Lambda_Q*(T7[i]+T7_bar[i]));
}
}
}
break;
case QQGG: case QtQtGG: case UUGG:
case tRtRGG: case DDGG:
{
// Finish Group Theory Factors:
if (process==QQGG || process==QtQtGG) {
Y_Q = 1.0/6.0;
Lambda_Q = C_F_3*a3 + C_F_2*a2 + Y_Q*Y_Q*C_F_1*a1;
Lambda_Q_s = C_F_3*a3;
Lambda_Q_ew = C_F_2*a2 + Y_Q*Y_Q*C_F_1*a1;
}
else if (process==UUGG || process==tRtRGG) {
Y_Q = 2.0/3.0;
Lambda_Q = C_F_3*a3 + Y_Q*Y_Q*C_F_1*a1;
Lambda_Q_s = C_F_3*a3;
Lambda_Q_ew = Y_Q*Y_Q*C_F_1*a1;
}
else if (process==DDGG || process==tRtRGG) {
Y_Q = -1.0/3.0;
Lambda_Q = C_F_3*a3 + Y_Q*Y_Q*C_F_1*a1;
Lambda_Q_s = C_F_3*a3;
Lambda_Q_ew = Y_Q*Y_Q*C_F_1*a1;
}
highC.resize(3,5);
for (int i=0; i<5; i++) {
highC(0,i) = G_Plus_SU3*(4.0*pi*a3)*(R1[i]+R1_bar[i]);
highC(1,i) = G_Plus_SU3_D*(4.0*pi*a3)*(R1[i]+R1_bar[i]);
highC(2,i) = G_f*4.0*pi*a3*(-0.5*R1[i]+0.5*R1_bar[i]-R2[i]);
if (order>=1) {
highC(0,i) += G_Plus_SU3*(a3*(Lambda_Q_ew)*(T1c[i]+T1c_bar[i])+
a3*(Lambda_Q_ew)*(T3b[i]+T3b_bar[i])+
a3*(Lambda_Q_ew)*(T4b[i]+T4b_bar[i])+
a3*Lambda_Q_ew*(T7[i]+T7_bar[i]));
highC(1,i) += G_Plus_SU3_D*(a3*(Lambda_Q_ew)*(T1c[i]+T1c_bar[i])+
a3*(Lambda_Q_ew)*(T3b[i]+T3b_bar[i])+
a3*(Lambda_Q_ew)*(T4b[i]+T4b_bar[i])+
a3*Lambda_Q_ew*(T7[i]+T7_bar[i]));
highC(2,i) += G_f*(a3*(-0.5*Lambda_Q_ew)*(T1c[i]-T1c_bar[i])-
0.5*a3*(Lambda_Q_ew)*(T3b[i]-T3b_bar[i])-
0.5*a3*(Lambda_Q_ew)*(T4b[i]-T4b_bar[i])+
a3*(Lambda_Q_ew)*T5b[i]-
0.5*a3*Lambda_Q_ew*(T7[i]-T7_bar[i]));
if (includeAlphaS2) {
highC(0,i) += G_Plus_SU3*((-0.5*a3*a3*C_A_3)*(T1b[i]+T1b_bar[i])+
a3*(Lambda_Q_s-a3*C_A_3)*(T1c[i]+T1c_bar[i])+
0.5*a3*a3*C_A_3*(T3a[i]+T3a_bar[i])+
a3*(Lambda_Q_s-0.5*a3*C_A_3)*(T3b[i]+T3b_bar[i])+
0.5*a3*a3*C_A_3*(T4a[i]+T4a_bar[i])+
a3*(Lambda_Q_s-0.5*a3*C_A_3)*(T4b[i]+T4b_bar[i])+
a3*Lambda_Q_s*(T7[i]+T7_bar[i])) +
G_TT*(-a3*a3*(T1a[i]+T1a_bar[i])+a3*a3*(T1b[i]+T1b_bar[i])+
a3*a3*(T1c[i]+T1c_bar[i])+2.0*a3*a3*T1d[i]);
highC(1,i) += G_Plus_SU3_D*((-0.5*a3*a3*C_A_3)*(T1b[i]+T1b_bar[i])+
a3*(Lambda_Q_s-a3*C_A_3)*(T1c[i]+T1c_bar[i])+
0.5*a3*a3*C_A_3*(T3a[i]+T3a_bar[i])+
a3*(Lambda_Q_s-0.5*a3*C_A_3)*(T3b[i]+T3b_bar[i])+
0.5*a3*a3*C_A_3*(T4a[i]+T4a_bar[i])+
a3*(Lambda_Q_s-0.5*a3*C_A_3)*(T4b[i]+T4b_bar[i])+
a3*Lambda_Q_s*(T7[i]+T7_bar[i])) +
G_TT_3_D*(-a3*a3*(T1a[i]+T1a_bar[i])+a3*a3*(T1b[i]+T1b_bar[i])+
a3*a3*(T1c[i]+T1c_bar[i])+2.0*a3*a3*T1d[i]);
highC(2,i) += G_f*(0.25*a3*a3*C_A_3*(T1a[i]-T1a_bar[i])+
a3*(0.25*a3*C_A_3-0.5*Lambda_Q_s)*(T1c[i]-T1c_bar[i])+
0.5*a3*a3*C_A_3*T2a[i]+a3*a3*T_CS_3*T2b[i]-
0.5*a3*a3*C_A_3*T2c[i]+a3*a3*T_WF_3*T2d[i]-
0.25*a3*a3*C_A_3*(T3a[i]-T3a_bar[i])-
0.5*a3*(Lambda_Q_s-0.5*a3*C_A_3)*(T3b[i]-T3b_bar[i])-
0.25*a3*a3*C_A_3*(T4a[i]-T4a_bar[i])-
0.5*a3*(Lambda_Q_s-0.5*a3*C_A_3)*(T4b[i]-T4b_bar[i])+
0.5*a3*a3*C_A_3*T5a[i]+a3*(Lambda_Q_s-0.5*a3*C_A_3)*T5b[i]+
a3*a3*C_A_3*T6a[i]+a3*a3*C_A_3*T6b[i]+
a3*a3*T_CS_3*T6c[i]+a3*a3*T_WF_3*T6d[i]-
0.5*a3*Lambda_Q_s*(T7[i]-T7_bar[i]));
}
}
}
if ( (process==QtQtGG||process==tRtRGG) && order>=1) {
if (process==tRtRGG) {
tRorQ = 2.0;
}
else {
tRorQ = 1.0;
}
highC(0,0) += tRorQ*(-1.0*(s*((s+t)*L_t - t*L_u)*y_t*y_t*a3)/(48.*pi*t*u*s));
highC(0,1) += tRorQ*((s*L_t*y_t*y_t*a3)/(24.*pi*t*s));
highC(0,2) += tRorQ*(-(s*s*y_t*y_t*a3)/((24.*pi*s*t+24.*pi*t*t)*s));
highC(0,3) += tRorQ*(-(s*s*y_t*y_t*a3)/((24.*pi*s*t+24.*pi*t*t)*s));
highC(1,0) += tRorQ*(-1.0*(s*((s+t)*L_t - t*L_u)*y_t*y_t*a3)/(16.*pi*t*u*s));
highC(1,1) += tRorQ*((s*L_t*y_t*y_t*a3)/(8.*pi*t*s));
highC(1,2) += tRorQ*(-(s*s*y_t*y_t*a3)/((8.*pi*s*t+8.*pi*t*t)*s));
highC(1,3) += tRorQ*(-(s*s*y_t*y_t*a3)/((8.*pi*s*t+8.*pi*t*t)*s));
highC(2,0) += tRorQ*((s*((s+t)*L_t + t*L_u)*y_t*y_t*a3)/(16.*pi*t*u*s));
highC(2,1) += tRorQ*(((2.*t-2.*t*L_s-s*L_t)*y_t*y_t*a3)/(8.*pi*t*s));
highC(2,2) += tRorQ*(-1.0*(s*(s+2.*t)*y_t*y_t*a3)/(8.*pi*t*u*s));
highC(2,3) += tRorQ*(-1.0*(s*(s+2.*t)*y_t*y_t*a3)/(8.*pi*t*u*s));
}
}
break;
default:
assert(false);
}
return highC;
}
boost::numeric::ublas::matrix<complex<InvEnergy2> >
HighEnergyMatching::Spin0HighMatching(Energy highScale,
Energy2 s, Energy2 t, Energy2 u,
EWProcess::Process process,
bool oneLoop, bool ) {
using Constants::pi;
unsigned int order = !oneLoop? 0 : 1;
// (If crossed graphs, swap s and t here)
Complex L_s = MinusLog(-s/(highScale*highScale));
Complex L_t = MinusLog(-t/(highScale*highScale));
Complex L_u = MinusLog(-u/(highScale*highScale));
Complex L_s2 = L_s*L_s;
Complex L_t2 = L_t*L_t;
Complex L_u2 = L_u*L_u;
// Tree-Level:
complex<InvEnergy2> S1 = 2.0/s;
// Topology T1:
complex<InvEnergy2> T1b = (-L_s2/(2.0*u)*(7.0*t/s+3.0)+2.0/u*L_t2+L_s*L_t*4.0/u*(t-u)/s+
L_s*2.0/s-4.0/s-pi*pi/(4.0*u)*(11.0+19.0*t/s));
complex<InvEnergy2> T1b_bar = -1.0*(-L_s2/(2.0*t)*(7.0*u/s+3.0)+2.0/t*L_u2+L_s*L_u*4.0/t*(u-t)/s+
L_s*2.0/s-4.0/s-pi*pi/(4.0*t)*(11.0+19.0*u/s));
// Topologies T2:
complex<InvEnergy2> T2a = 1.0/s*(-2.0*L_s2+8.0*L_s-16.0+pi*pi/3.0);
complex<InvEnergy2> T2b = 1.0/s*(0.5*L_s2+2.0*L_s-4.0-pi*pi/12.0);
// Topologies T5:
complex<InvEnergy2> T5a = 1.0/s*(-2.0*L_s2+6.0*L_s+pi*pi/3.0-16.0);
complex<InvEnergy2> T5b = 1.0/s*(2.0*L_s-4.0);
// Topologies T6:
complex<InvEnergy2> T6a = 1.0/s*(-19.0/6.0*L_s+58.0/9.0);
complex<InvEnergy2> T6b = 1.0/s*(-1.0/6.0*L_s+4.0/9.0);
complex<InvEnergy2> T6c = 1.0/s*(2.0/3.0*L_s-16.0/9.0);
complex<InvEnergy2> T6d = 1.0/s*(4.0/3.0*L_s-20.0/9.0);
// Group Theory Factors / SM parameters needed for matrix elements:
double a1 = ElectroWeakReweighter::coupling()->a1(highScale);
double a2 = ElectroWeakReweighter::coupling()->a2(highScale);
double a3 = ElectroWeakReweighter::coupling()->a3(highScale);
double y_t = ElectroWeakReweighter::coupling()->y_t(highScale);
double Y_phi = 1.0/2.0;
double C_F_3 = 4.0/3.0;
double C_F_2 = 3.0/4.0;
double C_F_1 = 1.0;
double n_g = 3.0;
double n_S = 1.0;
// Factors TBD after fermion helicity is specified:
double Y_Q(0.), Lambda_Q(0.), Lambda_phi(0.);
boost::numeric::ublas::matrix<complex<InvEnergy2> > highC(1,1);
switch (process) {
case QQPhiPhi: case LLPhiPhi:
// Finish Group Theory Factors:
if (process==QQPhiPhi) {
Y_Q = 1.0/6.0;
Lambda_Q = C_F_3*a3 + C_F_2*a2 + Y_Q*Y_Q*C_F_1*a1;
Lambda_phi = C_F_2*a2+Y_phi*Y_phi*a1;
}
else if (process==LLPhiPhi) {
Y_Q = -1.0/2.0;
Lambda_Q = C_F_2*a2 + Y_Q*Y_Q*C_F_1*a1;
Lambda_phi = C_F_2*a2+Y_phi*Y_phi*a1;
}
highC.resize(2,1);
highC(0,0) = S1*(4.0*pi*a2);
highC(1,0) = S1*(4.0*pi*a1*Y_Q*Y_phi);
if (order>=1) {
highC(0,0) += T1b*(0.5*a2*a2+2.0*a1*a2*Y_Q*Y_phi) +
T1b_bar*(-0.5*a2*a2+2.0*a1*a2*Y_Q*Y_phi) +
T2a*(-a2*a2+Lambda_phi*a2) + T2b*a2*a2 +
T5a*(-a2*a2+Lambda_Q*a2) + T5b*a2*a2 +
T6a*2.0*a2*a2 + T6b*2.0*a2*a2 +
T6c*0.5*a2*a2*n_S + T6d*2.0*a2*a2*n_g;
highC(1,0) += T1b*(3.0/16.0*a2*a2+a1*a1*Y_Q*Y_Q*Y_phi*Y_phi) +
T1b_bar*(3.0/16.0*a2*a2+a1*a1*Y_Q*Y_Q*Y_phi*Y_phi) +
T2a*(Lambda_phi*a1*Y_Q*Y_phi) + T5a*(Lambda_Q*a1*Y_Q*Y_phi) +
T6c*(2.0*a1*a1*n_S*Y_Q*Y_phi*Y_phi*Y_phi) +
T6d*(10.0/3.0*a1*a1*n_g*Y_Q*Y_phi);
// Top Quark contributions:
highC(0,0) += -3.0*y_t*y_t*a2/(4.0*pi)/s*(2.0*L_s-4.0);
highC(1,0) += -3.0*y_t*y_t*a1/(4.0*pi)*(Y_Q*Y_phi)/s*(2.0*L_s-4.0);
}
break;
case UUPhiPhi: case DDPhiPhi: case EEPhiPhi:
// Finish Group Theory Factors:
if (process==UUPhiPhi) {
Y_Q = 2.0/3.0;
Lambda_Q = C_F_3*a3 + Y_Q*Y_Q*C_F_1*a1;
Lambda_phi = C_F_2*a2 + Y_phi*Y_phi*a1;
}
else if (process==DDPhiPhi) {
Y_Q = -1.0/3.0;
Lambda_Q = C_F_3*a3 + Y_Q*Y_Q*C_F_1*a1;
Lambda_phi = C_F_2*a2 + Y_phi*Y_phi*a1;
}
else if (process==EEPhiPhi) {
Y_Q = -1.0;
Lambda_Q = Y_Q*Y_Q*C_F_1*a1;
Lambda_phi = C_F_2*a2 + Y_phi*Y_phi*a1;
}
highC.resize(1,1);
highC(0,0) = ZERO;
highC(0,0) = S1*(4.0*pi*a1*Y_Q*Y_phi);
if (order>=1) {
highC(0,0) += T1b*(a1*a1*Y_Q*Y_Q*Y_phi*Y_phi) +
T1b_bar*(a1*a1*Y_Q*Y_Q*Y_phi*Y_phi) +
T2a*(Lambda_phi*a1*Y_Q*Y_phi) + T5a*(Lambda_Q*a1*Y_Q*Y_phi) +
T6c*(2.0*a1*a1*n_S*Y_Q*Y_phi*Y_phi*Y_phi) +
T6d*(10.0/3.0*a1*a1*n_g*Y_Q*Y_phi);
// Top Quark Contribution:
highC(0,0) += -3.0*y_t*y_t*a1/(4.0*pi)*(Y_Q*Y_phi)/s*(2.0*L_s-4.0);
}
break;
default:
assert(false);
}
return highC;
}

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