diff --git a/src/MatrixElement.cc b/src/MatrixElement.cc
index 629ab4a..ab353ec 100644
--- a/src/MatrixElement.cc
+++ b/src/MatrixElement.cc
@@ -1,1747 +1,1747 @@
/**
* \authors The HEJ collaboration (see AUTHORS for details)
* \date 2019
* \copyright GPLv2 or later
*/
#include "HEJ/MatrixElement.hh"
#include <algorithm>
#include <assert.h>
#include <limits>
#include <math.h>
#include <stddef.h>
#include <unordered_map>
#include <utility>
#include "CLHEP/Vector/LorentzVector.h"
#include "fastjet/ClusterSequence.hh"
#include "HEJ/Constants.hh"
#include "HEJ/currents.hh"
#include "HEJ/PDG_codes.hh"
#include "HEJ/event_types.hh"
#include "HEJ/Event.hh"
#include "HEJ/exceptions.hh"
#include "HEJ/Particle.hh"
#include "HEJ/utility.hh"
namespace HEJ{
double MatrixElement::omega0(
double alpha_s, double mur,
fastjet::PseudoJet const & q_j
) const {
const double lambda = param_.regulator_lambda;
const double result = - alpha_s*N_C/M_PI*log(q_j.perp2()/(lambda*lambda));
if(! param_.log_correction) return result;
// use alpha_s(sqrt(q_j*lambda)), evolved to mur
return (
1. + alpha_s/(4.*M_PI)*beta0*log(mur*mur/(q_j.perp()*lambda))
)*result;
}
Weights MatrixElement::operator()(
Event const & event
) const {
return tree(event)*virtual_corrections(event);
}
Weights MatrixElement::tree(
Event const & event
) const {
return tree_param(event)*tree_kin(event);
}
Weights MatrixElement::tree_param(
Event const & event
) const {
if(! is_HEJ(event.type())) {
return Weights{0., std::vector<double>(event.variations().size(), 0.)};
}
Weights result;
// only compute once for each renormalisation scale
std::unordered_map<double, double> known;
result.central = tree_param(event, event.central().mur);
known.emplace(event.central().mur, result.central);
for(auto const & var: event.variations()) {
const auto ME_it = known.find(var.mur);
if(ME_it == end(known)) {
const double wt = tree_param(event, var.mur);
result.variations.emplace_back(wt);
known.emplace(var.mur, wt);
}
else {
result.variations.emplace_back(ME_it->second);
}
}
return result;
}
Weights MatrixElement::virtual_corrections(
Event const & event
) const {
if(! is_HEJ(event.type())) {
return Weights{0., std::vector<double>(event.variations().size(), 0.)};
}
Weights result;
// only compute once for each renormalisation scale
std::unordered_map<double, double> known;
result.central = virtual_corrections(event, event.central().mur);
known.emplace(event.central().mur, result.central);
for(auto const & var: event.variations()) {
const auto ME_it = known.find(var.mur);
if(ME_it == end(known)) {
const double wt = virtual_corrections(event, var.mur);
result.variations.emplace_back(wt);
known.emplace(var.mur, wt);
}
else {
result.variations.emplace_back(ME_it->second);
}
}
return result;
}
double MatrixElement::virtual_corrections_W(
Event const & event,
double mur,
Particle const & WBoson
) const{
auto const & in = event.incoming();
const auto partons = filter_partons(event.outgoing());
fastjet::PseudoJet const & pa = in.front().p;
#ifndef NDEBUG
fastjet::PseudoJet const & pb = in.back().p;
double const norm = (in.front().p + in.back().p).E();
#endif
assert(std::is_sorted(partons.begin(), partons.end(), rapidity_less{}));
assert(partons.size() >= 2);
assert(pa.pz() < pb.pz());
fastjet::PseudoJet q = pa - partons[0].p;
size_t first_idx = 0;
size_t last_idx = partons.size() - 1;
bool wc = true;
bool wqq = false;
// With extremal qqx or unordered gluon outside the extremal
// partons then it is not part of the FKL ladder and does not
// contribute to the virtual corrections. W emitted from the
// most backward leg must be taken into account in t-channel
if (event.type() == event_type::FKL) {
if (in[0].type != partons[0].type ){
q -= WBoson.p;
wc = false;
}
}
else if (event.type() == event_type::unob) {
q -= partons[1].p;
++first_idx;
if (in[0].type != partons[1].type ){
q -= WBoson.p;
wc = false;
}
}
else if (event.type() == event_type::qqxexb) {
q -= partons[1].p;
++first_idx;
if (abs(partons[0].type) != abs(partons[1].type)){
q -= WBoson.p;
wc = false;
}
}
if(event.type() == event_type::unof
|| event.type() == event_type::qqxexf){
--last_idx;
}
size_t first_idx_qqx = last_idx;
size_t last_idx_qqx = last_idx;
//if qqxMid event, virtual correction do not occur between
//qqx pair.
if(event.type() == event_type::qqxmid){
const auto backquark = std::find_if(
begin(partons) + 1, end(partons) - 1 ,
[](Particle const & s){ return (s.type != pid::gluon); }
);
if(backquark == end(partons) || (backquark+1)->type==pid::gluon) return 0;
if(abs(backquark->type) != abs((backquark+1)->type)) {
wqq=true;
wc=false;
}
last_idx = std::distance(begin(partons), backquark);
first_idx_qqx = last_idx+1;
}
double exponent = 0;
const double alpha_s = alpha_s_(mur);
for(size_t j = first_idx; j < last_idx; ++j){
exponent += omega0(alpha_s, mur, q)*(
partons[j+1].rapidity() - partons[j].rapidity()
);
q -=partons[j+1].p;
} // End Loop one
if (last_idx != first_idx_qqx) q -= partons[last_idx+1].p;
if (wqq) q -= WBoson.p;
for(size_t j = first_idx_qqx; j < last_idx_qqx; ++j){
exponent += omega0(alpha_s, mur, q)*(
partons[j+1].rapidity() - partons[j].rapidity()
);
q -= partons[j+1].p;
}
if (wc) q -= WBoson.p;
assert(
nearby(q, -1*pb, norm)
|| is_AWZH_boson(partons.back().type)
|| event.type() == event_type::unof
|| event.type() == event_type::qqxexf
);
return exp(exponent);
}
double MatrixElement::virtual_corrections(
Event const & event,
double mur
) const{
auto const & in = event.incoming();
auto const & out = event.outgoing();
fastjet::PseudoJet const & pa = in.front().p;
#ifndef NDEBUG
fastjet::PseudoJet const & pb = in.back().p;
double const norm = (in.front().p + in.back().p).E();
#endif
const auto AWZH_boson = std::find_if(
begin(out), end(out),
[](Particle const & p){ return is_AWZH_boson(p); }
);
if(AWZH_boson != end(out) && abs(AWZH_boson->type) == pid::Wp){
return virtual_corrections_W(event, mur, *AWZH_boson);
}
assert(std::is_sorted(out.begin(), out.end(), rapidity_less{}));
assert(out.size() >= 2);
assert(pa.pz() < pb.pz());
fastjet::PseudoJet q = pa - out[0].p;
size_t first_idx = 0;
size_t last_idx = out.size() - 1;
// if there is a Higgs boson, extremal qqx or unordered gluon
// outside the extremal partons then it is not part of the FKL
// ladder and does not contribute to the virtual corrections
if((out.front().type == pid::Higgs)
|| event.type() == event_type::unob
|| event.type() == event_type::qqxexb){
q -= out[1].p;
++first_idx;
}
if((out.back().type == pid::Higgs)
|| event.type() == event_type::unof
|| event.type() == event_type::qqxexf){
--last_idx;
}
size_t first_idx_qqx = last_idx;
size_t last_idx_qqx = last_idx;
//if qqxMid event, virtual correction do not occur between
//qqx pair.
if(event.type() == event_type::qqxmid){
const auto backquark = std::find_if(
begin(out) + 1, end(out) - 1 ,
[](Particle const & s){ return (s.type != pid::gluon && is_parton(s.type)); }
);
if(backquark == end(out) || (backquark+1)->type==pid::gluon) return 0;
last_idx = std::distance(begin(out), backquark);
first_idx_qqx = last_idx+1;
}
double exponent = 0;
const double alpha_s = alpha_s_(mur);
for(size_t j = first_idx; j < last_idx; ++j){
exponent += omega0(alpha_s, mur, q)*(
out[j+1].rapidity() - out[j].rapidity()
);
q -= out[j+1].p;
}
if (last_idx != first_idx_qqx) q -= out[last_idx+1].p;
for(size_t j = first_idx_qqx; j < last_idx_qqx; ++j){
exponent += omega0(alpha_s, mur, q)*(
out[j+1].rapidity() - out[j].rapidity()
);
q -= out[j+1].p;
}
assert(
nearby(q, -1*pb, norm)
|| out.back().type == pid::Higgs
|| event.type() == event_type::unof
|| event.type() == event_type::qqxexf
);
return exp(exponent);
}
} // namespace HEJ
namespace {
//! Lipatov vertex for partons emitted into extremal jets
double C2Lipatov(CLHEP::HepLorentzVector qav, CLHEP::HepLorentzVector qbv,
CLHEP::HepLorentzVector p1, CLHEP::HepLorentzVector p2)
{
CLHEP::HepLorentzVector temptrans=-(qav+qbv);
CLHEP::HepLorentzVector p5=qav-qbv;
CLHEP::HepLorentzVector CL=temptrans
+ p1*(qav.m2()/p5.dot(p1) + 2.*p5.dot(p2)/p1.dot(p2))
- p2*(qbv.m2()/p5.dot(p2) + 2.*p5.dot(p1)/p1.dot(p2));
return -CL.dot(CL);
}
//! Lipatov vertex with soft subtraction for partons emitted into extremal jets
double C2Lipatovots(
CLHEP::HepLorentzVector qav,
CLHEP::HepLorentzVector qbv,
CLHEP::HepLorentzVector p1,
CLHEP::HepLorentzVector p2,
double lambda
) {
double kperp=(qav-qbv).perp();
if (kperp>lambda)
return C2Lipatov(qav, qbv, p1, p2)/(qav.m2()*qbv.m2());
else {
double Cls=(C2Lipatov(qav, qbv, p1, p2)/(qav.m2()*qbv.m2()));
return Cls-4./(kperp*kperp);
}
}
//! Lipatov vertex
double C2Lipatov(CLHEP::HepLorentzVector qav, CLHEP::HepLorentzVector qbv,
CLHEP::HepLorentzVector pim, CLHEP::HepLorentzVector pip,
CLHEP::HepLorentzVector pom, CLHEP::HepLorentzVector pop) // B
{
CLHEP::HepLorentzVector temptrans=-(qav+qbv);
CLHEP::HepLorentzVector p5=qav-qbv;
CLHEP::HepLorentzVector CL=temptrans
+ qav.m2()*(1./p5.dot(pip)*pip + 1./p5.dot(pop)*pop)/2.
- qbv.m2()*(1./p5.dot(pim)*pim + 1./p5.dot(pom)*pom)/2.
+ ( pip*(p5.dot(pim)/pip.dot(pim) + p5.dot(pom)/pip.dot(pom))
+ pop*(p5.dot(pim)/pop.dot(pim) + p5.dot(pom)/pop.dot(pom))
- pim*(p5.dot(pip)/pip.dot(pim) + p5.dot(pop)/pop.dot(pim))
- pom*(p5.dot(pip)/pip.dot(pom) + p5.dot(pop)/pop.dot(pom)) )/2.;
return -CL.dot(CL);
}
//! Lipatov vertex with soft subtraction
double C2Lipatovots(
CLHEP::HepLorentzVector qav,
CLHEP::HepLorentzVector qbv,
CLHEP::HepLorentzVector pa,
CLHEP::HepLorentzVector pb,
CLHEP::HepLorentzVector p1,
CLHEP::HepLorentzVector p2,
double lambda
) {
double kperp=(qav-qbv).perp();
if (kperp>lambda)
return C2Lipatov(qav, qbv, pa, pb, p1, p2)/(qav.m2()*qbv.m2());
else {
double Cls=(C2Lipatov(qav, qbv, pa, pb, p1, p2)/(qav.m2()*qbv.m2()));
double temp=Cls-4./(kperp*kperp);
return temp;
}
}
/** Matrix element squared for tree-level current-current scattering
* @param aptype Particle a PDG ID
* @param bptype Particle b PDG ID
* @param pn Particle n Momentum
* @param pb Particle b Momentum
* @param p1 Particle 1 Momentum
* @param pa Particle a Momentum
* @returns ME Squared for Tree-Level Current-Current Scattering
*/
double ME_current(
int aptype, int bptype,
CLHEP::HepLorentzVector const & pn,
CLHEP::HepLorentzVector const & pb,
CLHEP::HepLorentzVector const & p1,
CLHEP::HepLorentzVector const & pa
){
if (aptype==21&&bptype==21) {
return jM2gg(pn,pb,p1,pa);
} else if (aptype==21&&bptype!=21) {
if (bptype > 0)
return jM2qg(pn,pb,p1,pa);
else
return jM2qbarg(pn,pb,p1,pa);
}
else if (bptype==21&&aptype!=21) { // ----- || -----
if (aptype > 0)
return jM2qg(p1,pa,pn,pb);
else
return jM2qbarg(p1,pa,pn,pb);
}
else { // they are both quark
if (bptype>0) {
if (aptype>0)
return jM2qQ(pn,pb,p1,pa);
else
return jM2qQbar(pn,pb,p1,pa);
}
else {
if (aptype>0)
return jM2qQbar(p1,pa,pn,pb);
else
return jM2qbarQbar(pn,pb,p1,pa);
}
}
throw std::logic_error("unknown particle types");
}
/** Matrix element squared for tree-level current-current scattering With W+Jets
* @param aptype Particle a PDG ID
* @param bptype Particle b PDG ID
* @param pn Particle n Momentum
* @param pb Particle b Momentum
* @param p1 Particle 1 Momentum
* @param pa Particle a Momentum
* @param wc Boolean. True->W Emitted from b. Else; emitted from leg a
* @returns ME Squared for Tree-Level Current-Current Scattering
*/
double ME_W_current(
int aptype, int bptype,
CLHEP::HepLorentzVector const & pn,
CLHEP::HepLorentzVector const & pb,
CLHEP::HepLorentzVector const & p1,
CLHEP::HepLorentzVector const & pa,
CLHEP::HepLorentzVector const & plbar,
CLHEP::HepLorentzVector const & pl,
bool const wc
){
// We know it cannot be gg incoming.
assert(!(aptype==21 && bptype==21));
if (aptype==21&&bptype!=21) {
if (bptype > 0)
return jMWqg(pn,plbar,pl,pb,p1,pa);
else
return jMWqbarg(pn,plbar,pl,pb,p1,pa);
}
else if (bptype==21&&aptype!=21) { // ----- || -----
if (aptype > 0)
return jMWqg(p1,plbar,pl,pa,pn,pb);
else
return jMWqbarg(p1,plbar,pl,pa,pn,pb);
}
else { // they are both quark
if (wc==true){ // emission off b, (first argument pbout)
if (bptype>0) {
if (aptype>0)
return jMWqQ(pn,plbar,pl,pb,p1,pa);
else
return jMWqQbar(pn,plbar,pl,pb,p1,pa);
}
else {
if (aptype>0)
return jMWqbarQ(pn,plbar,pl,pb,p1,pa);
else
return jMWqbarQbar(pn,plbar,pl,pb,p1,pa);
}
}
else{ // emission off a, (first argument paout)
if (aptype > 0) {
if (bptype > 0)
return jMWqQ(p1,plbar,pl,pa,pn,pb);
else
return jMWqQbar(p1,plbar,pl,pa,pn,pb);
}
else { // a is anti-quark
if (bptype > 0)
return jMWqbarQ(p1,plbar,pl,pa,pn,pb);
else
return jMWqbarQbar(p1,plbar,pl,pa,pn,pb);
}
}
}
throw std::logic_error("unknown particle types");
}
/** Matrix element squared for backwards uno tree-level current-current
* scattering With W+Jets
*
* @param aptype Particle a PDG ID
* @param bptype Particle b PDG ID
* @param pn Particle n Momentum
* @param pb Particle b Momentum
* @param p1 Particle 1 Momentum
* @param pa Particle a Momentum
* @param pg Unordered gluon momentum
* @param wc Boolean. True->W Emitted from b. Else; emitted from leg a
* @returns ME Squared for unob Tree-Level Current-Current Scattering
*/
double ME_W_unob_current(
int aptype, int bptype,
CLHEP::HepLorentzVector const & pn,
CLHEP::HepLorentzVector const & pb,
CLHEP::HepLorentzVector const & p1,
CLHEP::HepLorentzVector const & pa,
CLHEP::HepLorentzVector const & pg,
CLHEP::HepLorentzVector const & plbar,
CLHEP::HepLorentzVector const & pl,
bool const wc
){
// we know they are not both gluons
if (bptype == 21 && aptype != 21) { // b gluon => W emission off a
if (aptype > 0)
return jM2Wunogqg(pg,p1,plbar,pl,pa,pn,pb);
else
return jM2Wunogqbarg(pg,p1,plbar,pl,pa,pn,pb);
}
else { // they are both quark
if (wc==true) {// emission off b, i.e. b is first current
if (bptype>0){
if (aptype>0)
- return junobMWqQg(pn,plbar,pl,pb,p1,pa,pg);
+ return junobMWqQg(pg,p1,plbar,pl,pa,pn,pb);
else
- return junobMWqQbarg(pn,plbar,pl,pb,p1,pa,pg);
+ return junobMWqQbarg(pg,p1,plbar,pl,pa,pn,pb);
}
else{
if (aptype>0)
- return junobMWqbarQg(pn,plbar,pl,pb,p1,pa,pg);
+ return junobMWqbarQg(pg,p1,plbar,pl,pa,pn,pb);
else
- return junobMWqbarQbarg(pn,plbar,pl,pb,p1,pa,pg);
+ return junobMWqbarQbarg(pg,p1,plbar,pl,pa,pn,pb);
}
}
else {// wc == false, emission off a, i.e. a is first current
if (aptype > 0) {
if (bptype > 0) //qq
return jM2WunogqQ(pg,p1,plbar,pl,pa,pn,pb);
else //qqbar
return jM2WunogqQbar(pg,p1,plbar,pl,pa,pn,pb);
}
else { // a is anti-quark
if (bptype > 0) //qbarq
return jM2WunogqbarQ(pg,p1,plbar,pl,pa,pn,pb);
else //qbarqbar
return jM2WunogqbarQbar(pg,p1,plbar,pl,pa,pn,pb);
}
}
}
}
/** Matrix element squared for uno forward tree-level current-current
* scattering With W+Jets
*
* @param aptype Particle a PDG ID
* @param bptype Particle b PDG ID
* @param pn Particle n Momentum
* @param pb Particle b Momentum
* @param p1 Particle 1 Momentum
* @param pa Particle a Momentum
* @param pg Unordered gluon momentum
* @param wc Boolean. True->W Emitted from b. Else; emitted from leg a
* @returns ME Squared for unof Tree-Level Current-Current Scattering
*/
double ME_W_unof_current(
int aptype, int bptype,
CLHEP::HepLorentzVector const & pn,
CLHEP::HepLorentzVector const & pb,
CLHEP::HepLorentzVector const & p1,
CLHEP::HepLorentzVector const & pa,
CLHEP::HepLorentzVector const & pg,
CLHEP::HepLorentzVector const & plbar,
CLHEP::HepLorentzVector const & pl,
bool const wc
){
// we know they are not both gluons
if (aptype==21 && bptype!=21) {//a gluon => W emission off b
if (bptype > 0)
return jM2Wunogqg(pg, pn,plbar, pl, pb, p1, pa);
else
return jM2Wunogqbarg(pg, pn,plbar, pl, pb, p1, pa);
}
else { // they are both quark
if (wc==true) {// emission off b, i.e. b is first current
if (bptype>0){
if (aptype>0)
return jM2WunogqQ(pg,pn,plbar,pl,pb,p1,pa);
else
return jM2WunogqQbar(pg,pn,plbar,pl,pb,p1,pa);
}
else{
if (aptype>0)
return jM2WunogqbarQ(pg,pn,plbar,pl,pb,p1,pa);
else
return jM2WunogqbarQbar(pg,pn,plbar,pl,pb,p1,pa);
}
}
else {// wc == false, emission off a, i.e. a is first current
if (aptype > 0) {
if (bptype > 0) //qq
return junofMWgqQ(pg,pn,pb,p1,plbar,pl,pa);
else //qqbar
return junofMWgqQbar(pg,pn,pb,p1,plbar,pl,pa);
}
else { // a is anti-quark
if (bptype > 0) //qbarq
return junofMWgqbarQ(pg,pn,pb,p1,plbar,pl,pa);
else //qbarqbar
return junofMWgqbarQbar(pg,pn,pb,p1,plbar,pl,pa);
}
}
}
}
/** \brief Matrix element squared for backward qqx tree-level current-current
* scattering With W+Jets
*
* @param aptype Particle a PDG ID
* @param bptype Particle b PDG ID
* @param pa Initial state a Momentum
* @param pb Initial state b Momentum
* @param pq Final state q Momentum
* @param pqbar Final state qbar Momentum
* @param pn Final state n Momentum
* @param plbar Final state anti-lepton momentum
* @param pl Final state lepton momentum
* @param wc Boolean. True->W Emitted from b. Else; emitted from leg a
* @returns ME Squared for qqxb Tree-Level Current-Current Scattering
*/
double ME_W_qqxb_current(
int aptype, int bptype,
CLHEP::HepLorentzVector const & pa,
CLHEP::HepLorentzVector const & pb,
CLHEP::HepLorentzVector const & pq,
CLHEP::HepLorentzVector const & pqbar,
CLHEP::HepLorentzVector const & pn,
CLHEP::HepLorentzVector const & plbar,
CLHEP::HepLorentzVector const & pl,
bool const wc
){
// CAM factors for the qqx amps, and qqbar ordering (default, qbar extremal)
bool swapQuarkAntiquark=false;
double CFbackward;
if (pqbar.rapidity() > pq.rapidity()){
swapQuarkAntiquark=true;
CFbackward = (0.5*(3.-1./3.)*(pa.minus()/(pq.minus())+(pq.minus())/pa.minus())+1./3.)*3./4.;
}
else{
CFbackward = (0.5*(3.-1./3.)*(pa.minus()/(pqbar.minus())+(pqbar.minus())/pa.minus())+1./3.)*3./4.;
}
// With qqbar we could have 2 incoming gluons and W Emission
if (aptype==21&&bptype==21) {//a gluon, b gluon gg->qqbarWg
// This will be a wqqx emission as there is no other possible W Emission Site.
if (swapQuarkAntiquark){
return jM2Wggtoqqbarg(pa, pqbar, plbar, pl, pq, pn,pb)*CFbackward;}
else {
return jM2Wggtoqbarqg(pa, pq, plbar, pl, pqbar, pn,pb)*CFbackward;}
}
else if (aptype==21&&bptype!=21 ) {//a gluon => W emission off b leg or qqx
if (wc!=1){ // W Emitted from backwards qqx
if (swapQuarkAntiquark){
return jM2WgQtoqqbarQ(pa, pq, plbar, pl, pqbar, pn, pb)*CFbackward;}
else{
return jM2WgQtoqbarqQ(pa, pq, plbar, pl, pqbar, pn, pb)*CFbackward;}
}
else { // W Must be emitted from forwards leg.
if(bptype > 0){
if (swapQuarkAntiquark){
return jM2WgqtoQQqW(pb, pa, pn, pqbar, pq, plbar, pl, false)*CFbackward;}
else{
return jM2WgqtoQQqW(pb, pa, pn, pq, pqbar, plbar, pl, false)*CFbackward;}
} else {
if (swapQuarkAntiquark){
return jM2WgqtoQQqW(pb, pa, pn, pqbar, pq, plbar, pl, true)*CFbackward;}
else{
return jM2WgqtoQQqW(pb, pa, pn, pq, pqbar, plbar, pl, true)*CFbackward;}
}
}
}
else{
throw std::logic_error("Incompatible incoming particle types with qqxb");
}
}
/* \brief Matrix element squared for forward qqx tree-level current-current
* scattering With W+Jets
*
* @param aptype Particle a PDG ID
* @param bptype Particle b PDG ID
* @param pa Initial state a Momentum
* @param pb Initial state b Momentum
* @param pq Final state q Momentum
* @param pqbar Final state qbar Momentum
* @param p1 Final state 1 Momentum
* @param plbar Final state anti-lepton momentum
* @param pl Final state lepton momentum
* @param wc Boolean. True->W Emitted from b. Else; emitted from leg a
* @returns ME Squared for qqxf Tree-Level Current-Current Scattering
*/
double ME_W_qqxf_current(
int aptype, int bptype,
CLHEP::HepLorentzVector const & pa,
CLHEP::HepLorentzVector const & pb,
CLHEP::HepLorentzVector const & pq,
CLHEP::HepLorentzVector const & pqbar,
CLHEP::HepLorentzVector const & p1,
CLHEP::HepLorentzVector const & plbar,
CLHEP::HepLorentzVector const & pl,
bool const wc
){
// CAM factors for the qqx amps, and qqbar ordering (default, qbar extremal)
bool swapQuarkAntiquark=false;
double CFforward;
if (pqbar.rapidity() < pq.rapidity()){
swapQuarkAntiquark=true;
CFforward = (0.5*(3.-1./3.)*(pb.plus()/(pq.plus())+(pq.plus())/pb.plus())+1./3.)*3./4.;
}
else{
CFforward = (0.5*(3.-1./3.)*(pb.plus()/(pqbar.plus())+(pqbar.plus())/pb.plus())+1./3.)*3./4.;
}
// With qqbar we could have 2 incoming gluons and W Emission
if (aptype==21&&bptype==21) {//a gluon, b gluon gg->qqbarWg
// This will be a wqqx emission as there is no other possible W Emission Site.
if (swapQuarkAntiquark){
return jM2Wggtoqqbarg(pb, pqbar, plbar, pl, pq, p1,pa)*CFforward;}
else {
return jM2Wggtoqbarqg(pb, pq, plbar, pl, pqbar, p1,pa)*CFforward;}
}
else if (bptype==21&&aptype!=21) {// b gluon => W emission off a or qqx
if (wc==1){ // W Emitted from forwards qqx
if (swapQuarkAntiquark){
return jM2WgQtoqbarqQ(pb, pq, plbar,pl, pqbar, p1, pa)*CFforward;}
else {
return jM2WgQtoqqbarQ(pb, pq, plbar,pl, pqbar, p1, pa)*CFforward;}
}
// W Must be emitted from backwards leg.
if (aptype > 0){
if (swapQuarkAntiquark){
return jM2WgqtoQQqW(pa,pb, p1, pqbar, pq, plbar, pl, false)*CFforward;}
else{
return jM2WgqtoQQqW(pa,pb, p1, pq, pqbar, plbar, pl, false)*CFforward;}
} else
{
if (swapQuarkAntiquark){
return jM2WgqtoQQqW(pa,pb, p1, pqbar, pq, plbar, pl, true)*CFforward;}
else{
return jM2WgqtoQQqW(pa,pb, p1, pq, pqbar, plbar, pl, true)*CFforward;}
}
}
else{
throw std::logic_error("Incompatible incoming particle types with qqxf");
}
}
/* \brief Matrix element squared for central qqx tree-level current-current
* scattering With W+Jets
*
* @param aptype Particle a PDG ID
* @param bptype Particle b PDG ID
* @param nabove Number of gluons emitted before central qqxpair
* @param nbelow Number of gluons emitted after central qqxpair
* @param pa Initial state a Momentum
* @param pb Initial state b Momentum\
* @param pq Final state qbar Momentum
* @param pqbar Final state q Momentum
* @param partons Vector of all outgoing partons
* @param plbar Final state anti-lepton momentum
* @param pl Final state lepton momentum
* @param wqq Boolean. True siginfies W boson is emitted from Central qqx
* @param wc Boolean. wc=true signifies w boson emitted from leg b; if wqq=false.
* @returns ME Squared for qqxmid Tree-Level Current-Current Scattering
*/
double ME_W_qqxmid_current(
int aptype, int bptype,
int nabove, int nbelow,
CLHEP::HepLorentzVector const & pa,
CLHEP::HepLorentzVector const & pb,
CLHEP::HepLorentzVector const & pq,
CLHEP::HepLorentzVector const & pqbar,
std::vector<HLV> partons,
CLHEP::HepLorentzVector const & plbar,
CLHEP::HepLorentzVector const & pl,
bool const wqq, bool const wc
){
// CAM factors for the qqx amps, and qqbar ordering (default, pq backwards)
bool swapQuarkAntiquark=false;
if (pqbar.rapidity() < pq.rapidity()){
swapQuarkAntiquark=true;
}
double CFforward = (0.5*(3.-1./3.)*( pb.plus()/(partons[partons.size()-1].plus())
+ (partons[partons.size()-1].plus())/pb.plus() )+1./3.)*3./4.;
double CFbackward = (0.5*(3.-1./3.)*( pa.minus()/(partons[0].minus())
+ (partons[0].minus())/pa.minus() )+1./3.)*3./4.;
double wt=1.;
if (aptype==21) wt*=CFbackward;
if (bptype==21) wt*=CFforward;
if (aptype <=0 && bptype <=0){ // Both External AntiQuark
if (wqq==1){//emission from central qqbar
return wt*jM2WqqtoqQQq(pa, pb, pl,plbar, partons,true,true, swapQuarkAntiquark, nabove);
}
else if (wc==1){//emission from b leg
return wt*jM2WqqtoqQQqW(pa, pb, pl,plbar, partons, true,true, swapQuarkAntiquark, nabove, nbelow, true);
}
else { // emission from a leg
return wt*jM2WqqtoqQQqW(pa, pb, pl,plbar, partons, true,true, swapQuarkAntiquark, nabove, nbelow, false);
}
} // end both antiquark
else if (aptype<=0){ // a is antiquark
if (wqq==1){//emission from central qqbar
return wt*jM2WqqtoqQQq(pa, pb, pl,plbar, partons, false, true, swapQuarkAntiquark, nabove);
}
else if (wc==1){//emission from b leg
return wt*jM2WqqtoqQQqW(pa, pb, pl,plbar, partons,false,true, swapQuarkAntiquark, nabove, nbelow, true);
}
else { // emission from a leg
return wt*jM2WqqtoqQQqW(pa, pb, pl,plbar, partons, false, true, swapQuarkAntiquark, nabove, nbelow, false);
}
} // end a is antiquark
else if (bptype<=0){ // b is antiquark
if (wqq==1){//emission from central qqbar
return wt*jM2WqqtoqQQq(pa, pb, pl,plbar, partons, true, false, swapQuarkAntiquark, nabove);
}
else if (wc==1){//emission from b leg
return wt*jM2WqqtoqQQqW(pa, pb, pl,plbar, partons, true, false, swapQuarkAntiquark, nabove, nbelow, true);
}
else { // emission from a leg
return wt*jM2WqqtoqQQqW(pa, pb, pl,plbar, partons, true, false, swapQuarkAntiquark, nabove, nbelow, false);
}
} //end b is antiquark
else{ //Both Quark or gluon
if (wqq==1){//emission from central qqbar
return wt*jM2WqqtoqQQq(pa, pb, pl, plbar, partons, false, false, swapQuarkAntiquark, nabove);}
else if (wc==1){//emission from b leg
return wt*jM2WqqtoqQQqW(pa, pb, pl,plbar, partons, false, false, swapQuarkAntiquark, nabove, nbelow, true);
}
else { // emission from a leg
return wt*jM2WqqtoqQQqW(pa, pb, pl,plbar, partons, false, false, swapQuarkAntiquark, nabove, nbelow, false);
}
}
}
/** \brief Matrix element squared for tree-level current-current scattering with Higgs
* @param aptype Particle a PDG ID
* @param bptype Particle b PDG ID
* @param pn Particle n Momentum
* @param pb Particle b Momentum
* @param p1 Particle 1 Momentum
* @param pa Particle a Momentum
* @param qH t-channel momentum before Higgs
* @param qHp1 t-channel momentum after Higgs
* @returns ME Squared for Tree-Level Current-Current Scattering with Higgs
*/
double ME_Higgs_current(
int aptype, int bptype,
CLHEP::HepLorentzVector const & pn,
CLHEP::HepLorentzVector const & pb,
CLHEP::HepLorentzVector const & p1,
CLHEP::HepLorentzVector const & pa,
CLHEP::HepLorentzVector const & qH, // t-channel momentum before Higgs
CLHEP::HepLorentzVector const & qHp1, // t-channel momentum after Higgs
double mt, bool include_bottom, double mb
){
if (aptype==21&&bptype==21) // gg initial state
return MH2gg(pn,pb,p1,pa,-qHp1,-qH,mt,include_bottom,mb);
else if (aptype==21&&bptype!=21) {
if (bptype > 0)
return MH2qg(pn,pb,p1,pa,-qHp1,-qH,mt,include_bottom,mb)*4./9.;
else
return MH2qbarg(pn,pb,p1,pa,-qHp1,-qH,mt,include_bottom,mb)*4./9.;
}
else if (bptype==21&&aptype!=21) {
if (aptype > 0)
return MH2qg(p1,pa,pn,pb,-qH,-qHp1,mt,include_bottom,mb)*4./9.;
else
return MH2qbarg(p1,pa,pn,pb,-qH,-qHp1,mt,include_bottom,mb)*4./9.;
}
else { // they are both quark
if (bptype>0) {
if (aptype>0)
return MH2qQ(pn,pb,p1,pa,-qHp1,-qH,mt,include_bottom,mb)*4.*4./(9.*9.);
else
return MH2qQbar(pn,pb,p1,pa,-qHp1,-qH,mt,include_bottom,mb)*4.*4./(9.*9.);
}
else {
if (aptype>0)
return MH2qQbar(p1,pa,pn,pb,-qH,-qHp1,mt,include_bottom,mb)*4.*4./(9.*9.);
else
return MH2qbarQbar(pn,pb,p1,pa,-qHp1,-qH,mt,include_bottom,mb)*4.*4./(9.*9.);
}
}
throw std::logic_error("unknown particle types");
}
/** \brief Current matrix element squared with Higgs and unordered forward emission
* @param aptype Particle A PDG ID
* @param bptype Particle B PDG ID
* @param punof Unordered Particle Momentum
* @param pn Particle n Momentum
* @param pb Particle b Momentum
* @param p1 Particle 1 Momentum
* @param pa Particle a Momentum
* @param qH t-channel momentum before Higgs
* @param qHp1 t-channel momentum after Higgs
* @returns ME Squared with Higgs and unordered forward emission
*/
double ME_Higgs_current_unof(
int aptype, int bptype,
CLHEP::HepLorentzVector const & punof,
CLHEP::HepLorentzVector const & pn,
CLHEP::HepLorentzVector const & pb,
CLHEP::HepLorentzVector const & p1,
CLHEP::HepLorentzVector const & pa,
CLHEP::HepLorentzVector const & qH, // t-channel momentum before Higgs
CLHEP::HepLorentzVector const & qHp1, // t-channel momentum after Higgs
double mt, bool include_bottom, double mb
){
if (aptype==21&&bptype!=21) {
if (bptype > 0)
return jM2unogqHg(punof,pn,pb,p1,pa,-qHp1,-qH,mt,include_bottom,mb);
else
return jM2unogqbarHg(punof,pn,pb,p1,pa,-qHp1,-qH,mt,include_bottom,mb);
}
else { // they are both quark
if (bptype>0) {
if (aptype>0)
return jM2unogqHQ(punof,pn,pb,p1,pa,-qHp1,-qH,mt,include_bottom,mb);
else
return jM2unogqHQbar(punof,pn,pb,p1,pa,-qHp1,-qH,mt,include_bottom,mb);
}
else {
if (aptype>0)
return jM2unogqbarHQ(punof,pn,pb,p1,pa,-qHp1,-qH,mt,include_bottom,mb);
else
return jM2unogqbarHQbar(punof,pn,pb,p1,pa,-qHp1,-qH,mt,include_bottom,mb);
}
}
throw std::logic_error("unknown particle types");
}
/** \brief Current matrix element squared with Higgs and unordered backward emission
* @param aptype Particle A PDG ID
* @param bptype Particle B PDG ID
* @param pn Particle n Momentum
* @param pb Particle b Momentum
* @param punob Unordered back Particle Momentum
* @param p1 Particle 1 Momentum
* @param pa Particle a Momentum
* @param qH t-channel momentum before Higgs
* @param qHp1 t-channel momentum after Higgs
* @returns ME Squared with Higgs and unordered backward emission
*/
double ME_Higgs_current_unob(
int aptype, int bptype,
CLHEP::HepLorentzVector const & pn,
CLHEP::HepLorentzVector const & pb,
CLHEP::HepLorentzVector const & punob,
CLHEP::HepLorentzVector const & p1,
CLHEP::HepLorentzVector const & pa,
CLHEP::HepLorentzVector const & qH, // t-channel momentum before Higgs
CLHEP::HepLorentzVector const & qHp1, // t-channel momentum after Higgs
double mt, bool include_bottom, double mb
){
if (bptype==21&&aptype!=21) {
if (aptype > 0)
return jM2unobgHQg(pn,pb,punob,p1,pa,-qHp1,-qH,mt,include_bottom,mb);
else
return jM2unobgHQbarg(pn,pb,punob,p1,pa,-qHp1,-qH,mt,include_bottom,mb);
}
else { // they are both quark
if (aptype>0) {
if (bptype>0)
return jM2unobqHQg(pn,pb,punob,p1,pa,-qHp1,-qH,mt,include_bottom,mb);
else
return jM2unobqbarHQg(pn,pb,punob,p1,pa,-qHp1,-qH,mt,include_bottom,mb);
}
else {
if (bptype>0)
return jM2unobqHQbarg(pn,pb,punob,p1,pa,-qHp1,-qH,mt,include_bottom,mb);
else
return jM2unobqbarHQbarg(pn,pb,punob,p1,pa,-qHp1,-qH,mt,include_bottom,mb);
}
}
throw std::logic_error("unknown particle types");
}
CLHEP::HepLorentzVector to_HepLorentzVector(HEJ::Particle const & particle){
return {particle.p.px(), particle.p.py(), particle.p.pz(), particle.p.E()};
}
void validate(HEJ::MatrixElementConfig const & config) {
#ifndef HEJ_BUILD_WITH_QCDLOOP
if(!config.Higgs_coupling.use_impact_factors) {
throw std::invalid_argument{
"Invalid Higgs coupling settings.\n"
"HEJ without QCDloop support can only use impact factors.\n"
"Set use_impact_factors to true or recompile HEJ.\n"
};
}
#endif
if(config.Higgs_coupling.use_impact_factors
&& config.Higgs_coupling.mt != std::numeric_limits<double>::infinity()) {
throw std::invalid_argument{
"Conflicting settings: "
"impact factors may only be used in the infinite top mass limit"
};
}
}
} // namespace anonymous
namespace HEJ{
MatrixElement::MatrixElement(
std::function<double (double)> alpha_s,
MatrixElementConfig conf
):
alpha_s_{std::move(alpha_s)},
param_{std::move(conf)}
{
validate(param_);
}
double MatrixElement::tree_kin(
Event const & ev
) const {
if(! is_HEJ(ev.type())) return 0.;
auto AWZH_boson = std::find_if(
begin(ev.outgoing()), end(ev.outgoing()),
[](Particle const & p){return is_AWZH_boson(p);}
);
if(AWZH_boson == end(ev.outgoing()))
return tree_kin_jets(ev);
switch(AWZH_boson->type){
case pid::Higgs:
return tree_kin_Higgs(ev);
case pid::Wp:
case pid::Wm:
return tree_kin_W(ev);
// TODO
case pid::photon:
case pid::Z:
default:
throw not_implemented("Emission of boson of unsupported type");
}
}
namespace{
constexpr int extremal_jet_idx = 1;
constexpr int no_extremal_jet_idx = 0;
bool treat_as_extremal(Particle const & parton){
return parton.p.user_index() == extremal_jet_idx;
}
template<class InputIterator>
double FKL_ladder_weight(
InputIterator begin_gluon, InputIterator end_gluon,
CLHEP::HepLorentzVector const & q0,
CLHEP::HepLorentzVector const & pa, CLHEP::HepLorentzVector const & pb,
CLHEP::HepLorentzVector const & p1, CLHEP::HepLorentzVector const & pn,
double lambda
){
double wt = 1;
auto qi = q0;
for(auto gluon_it = begin_gluon; gluon_it != end_gluon; ++gluon_it){
assert(gluon_it->type == pid::gluon);
const auto g = to_HepLorentzVector(*gluon_it);
const auto qip1 = qi - g;
if(treat_as_extremal(*gluon_it)){
wt *= C2Lipatovots(qip1, qi, pa, pb, lambda)*C_A;
} else{
wt *= C2Lipatovots(qip1, qi, pa, pb, p1, pn, lambda)*C_A;
}
qi = qip1;
}
return wt;
}
} // namespace anonymous
std::vector<Particle> MatrixElement::tag_extremal_jet_partons(
Event const & ev
) const{
auto out_partons = filter_partons(ev.outgoing());
if(out_partons.size() == ev.jets().size()){
// no additional emissions in extremal jets, don't need to tag anything
for(auto & parton: out_partons){
parton.p.set_user_index(no_extremal_jet_idx);
}
return out_partons;
}
// TODO: avoid reclustering
fastjet::ClusterSequence cs(to_PseudoJet(out_partons), ev.jet_def());
const auto jets = sorted_by_rapidity(cs.inclusive_jets(ev.min_jet_pt()));
assert(jets.size() >= 2);
auto most_backward = begin(jets);
auto most_forward = end(jets) - 1;
// skip jets caused by unordered emission or qqx
if(ev.type() == event_type::unob || ev.type() == event_type::qqxexb){
assert(jets.size() >= 3);
++most_backward;
}
else if(ev.type() == event_type::unof || ev.type() == event_type::qqxexf){
assert(jets.size() >= 3);
--most_forward;
}
const auto extremal_jet_indices = cs.particle_jet_indices(
{*most_backward, *most_forward}
);
assert(extremal_jet_indices.size() == out_partons.size());
for(size_t i = 0; i < out_partons.size(); ++i){
assert(HEJ::is_parton(out_partons[i]));
const int idx = (extremal_jet_indices[i]>=0)?
extremal_jet_idx:
no_extremal_jet_idx;
out_partons[i].p.set_user_index(idx);
}
return out_partons;
}
double MatrixElement::tree_kin_jets(
Event const & ev
) const {
auto const & incoming = ev.incoming();
const auto partons = tag_extremal_jet_partons(ev);
if(is_uno(ev.type())){
throw not_implemented("unordered emission not implemented for pure jets");
}
const auto pa = to_HepLorentzVector(incoming[0]);
const auto pb = to_HepLorentzVector(incoming[1]);
const auto p1 = to_HepLorentzVector(partons.front());
const auto pn = to_HepLorentzVector(partons.back());
return ME_current(
incoming[0].type, incoming[1].type,
pn, pb, p1, pa
)/(4.*(N_C*N_C - 1.))*FKL_ladder_weight(
begin(partons) + 1, end(partons) - 1,
pa - p1, pa, pb, p1, pn,
param_.regulator_lambda
);
}
namespace{
double tree_kin_W_FKL(
int aptype, int bptype, HLV pa, HLV pb,
std::vector<Particle> const & partons,
HLV plbar, HLV pl,
double lambda
) {
auto p1 = to_HepLorentzVector(partons[0]);
auto pn = to_HepLorentzVector(partons[partons.size() - 1]);
auto begin_ladder = begin(partons) + 1;
auto end_ladder = end(partons) - 1;
bool wc = true;
auto q0 = pa - p1;
if (aptype!=partons[0].type) { //leg a emits w
wc = false;
q0 -=pl + plbar;
}
const double current_factor = ME_W_current(
aptype, bptype, pn, pb,
p1, pa, plbar, pl, wc
);
const double ladder_factor = FKL_ladder_weight(
begin_ladder, end_ladder,
q0, pa, pb, p1, pn,
lambda
);
return current_factor*ladder_factor;
}
double tree_kin_W_unob(
int aptype, int bptype, HLV pa, HLV pb,
std::vector<Particle> const & partons,
HLV plbar, HLV pl,
double lambda
) {
auto pg = to_HepLorentzVector(partons[0]);
auto p1 = to_HepLorentzVector(partons[1]);
auto pn = to_HepLorentzVector(partons[partons.size() - 1]);
auto begin_ladder = begin(partons) + 2;
auto end_ladder = end(partons) - 1;
bool wc = true;
auto q0 = pa - p1 -pg;
if (aptype!=partons[1].type) { //leg a emits w
wc = false;
q0 -=pl + plbar;
}
const double current_factor = ME_W_unob_current(
aptype, bptype, pn, pb,
p1, pa, pg, plbar, pl, wc
);
const double ladder_factor = FKL_ladder_weight(
begin_ladder, end_ladder,
q0, pa, pb, p1, pn,
lambda
);
return current_factor*C_A*C_A/(N_C*N_C-1.)*ladder_factor;
}
double tree_kin_W_unof(
int aptype, int bptype, HLV pa, HLV pb,
std::vector<Particle> const & partons,
HLV plbar, HLV pl,
double lambda
) {
auto p1 = to_HepLorentzVector(partons[0]);
auto pn = to_HepLorentzVector(partons[partons.size() - 2]);
auto pg = to_HepLorentzVector(partons[partons.size() - 1]);
auto begin_ladder = begin(partons) + 1;
auto end_ladder = end(partons) - 2;
bool wc = true;
auto q0 = pa - p1;
if (aptype!=partons[0].type) { //leg a emits w
wc = false;
q0 -=pl + plbar;
}
const double current_factor = ME_W_unof_current(
aptype, bptype, pn, pb,
p1, pa, pg, plbar, pl, wc
);
const double ladder_factor = FKL_ladder_weight(
begin_ladder, end_ladder,
q0, pa, pb, p1, pn,
lambda
);
return current_factor*C_A*C_A/(N_C*N_C-1.)*ladder_factor;
}
double tree_kin_W_qqxb(
int aptype, int bptype, HLV pa, HLV pb,
std::vector<Particle> const & partons,
HLV plbar, HLV pl,
double lambda
) {
HLV pq,pqbar;
if(is_quark(partons[0])){
pq = to_HepLorentzVector(partons[0]);
pqbar = to_HepLorentzVector(partons[1]);
}
else{
pq = to_HepLorentzVector(partons[1]);
pqbar = to_HepLorentzVector(partons[0]);
}
auto p1 = to_HepLorentzVector(partons[0]);
auto pn = to_HepLorentzVector(partons[partons.size() - 1]);
auto begin_ladder = begin(partons) + 2;
auto end_ladder = end(partons) - 1;
bool wc = true;
auto q0 = pa - pq - pqbar;
if (partons[1].type!=partons[0].type) { //leg a emits w
wc = false;
q0 -=pl + plbar;
}
const double current_factor = ME_W_qqxb_current(
aptype, bptype, pa, pb,
pq, pqbar, pn, plbar, pl, wc
);
const double ladder_factor = FKL_ladder_weight(
begin_ladder, end_ladder,
q0, pa, pb, p1, pn,
lambda
);
return current_factor*C_A*C_A/(N_C*N_C-1.)*ladder_factor;
}
double tree_kin_W_qqxf(
int aptype, int bptype, HLV pa, HLV pb,
std::vector<Particle> const & partons,
HLV plbar, HLV pl,
double lambda
) {
HLV pq,pqbar;
if(is_quark(partons[partons.size() - 1])){
pq = to_HepLorentzVector(partons[partons.size() - 1]);
pqbar = to_HepLorentzVector(partons[partons.size() - 2]);
}
else{
pq = to_HepLorentzVector(partons[partons.size() - 2]);
pqbar = to_HepLorentzVector(partons[partons.size() - 1]);
}
auto p1 = to_HepLorentzVector(partons[0]);
auto pn = to_HepLorentzVector(partons[partons.size() - 1]);
auto begin_ladder = begin(partons) + 1;
auto end_ladder = end(partons) - 2;
bool wc = true;
auto q0 = pa - p1;
if (aptype!=partons[0].type) { //leg a emits w
wc = false;
q0 -=pl + plbar;
}
const double current_factor = ME_W_qqxf_current(
aptype, bptype, pa, pb,
pq, pqbar, p1, plbar, pl, wc
);
const double ladder_factor = FKL_ladder_weight(
begin_ladder, end_ladder,
q0, pa, pb, p1, pn,
lambda
);
return current_factor*C_A*C_A/(N_C*N_C-1.)*ladder_factor;
}
double tree_kin_W_qqxmid(
int aptype, int bptype, HLV pa, HLV pb,
std::vector<Particle> const & partons,
HLV plbar, HLV pl,
double lambda
) {
HLV pq,pqbar;
const auto backmidquark = std::find_if(
begin(partons)+1, end(partons)-1,
[](Particle const & s){ return s.type != pid::gluon; }
);
assert(backmidquark!=end(partons)-1);
if (is_quark(backmidquark->type)){
pq = to_HepLorentzVector(*backmidquark);
pqbar = to_HepLorentzVector(*(backmidquark+1));
}
else {
pqbar = to_HepLorentzVector(*backmidquark);
pq = to_HepLorentzVector(*(backmidquark+1));
}
auto p1 = to_HepLorentzVector(partons[0]);
auto pn = to_HepLorentzVector(partons[partons.size() - 1]);
auto q0 = pa - p1;
// t-channel momentum after qqx
auto qqxt = q0;
bool wc, wqq;
if (backmidquark->type == -(backmidquark+1)->type){ // Central qqx does not emit
wqq=false;
if (aptype==partons[0].type) {
wc = true;
}
else{
wc = false;
q0-=pl+plbar;
}
}
else{
wqq = true;
wc = false;
qqxt-=pl+plbar;
}
auto begin_ladder = begin(partons) + 1;
auto end_ladder_1 = (backmidquark);
auto begin_ladder_2 = (backmidquark+2);
auto end_ladder = end(partons) - 1;
for(auto parton_it = begin_ladder; parton_it < begin_ladder_2; ++parton_it){
qqxt -= to_HepLorentzVector(*parton_it);
}
int nabove = std::distance(begin_ladder, backmidquark);
int nbelow = std::distance(begin_ladder_2, end_ladder);
std::vector<HLV> partonsHLV;
partonsHLV.reserve(partons.size());
for (size_t i = 0; i != partons.size(); ++i) {
partonsHLV.push_back(to_HepLorentzVector(partons[i]));
}
const double current_factor = ME_W_qqxmid_current(
aptype, bptype, nabove, nbelow, pa, pb,
pq, pqbar, partonsHLV, plbar, pl, wqq, wc
);
const double ladder_factor = FKL_ladder_weight(
begin_ladder, end_ladder_1,
q0, pa, pb, p1, pn,
lambda
)*FKL_ladder_weight(
begin_ladder_2, end_ladder,
qqxt, pa, pb, p1, pn,
lambda
);
return current_factor*C_A*C_A/(N_C*N_C-1.)*ladder_factor;
}
} // namespace anonymous
double MatrixElement::tree_kin_W(Event const & ev) const {
using namespace event_type;
auto const & incoming(ev.incoming());
auto const & decays(ev.decays());
HLV plbar, pl;
for (auto& x: decays) {
if (x.second.at(0).type < 0){
plbar = to_HepLorentzVector(x.second.at(0));
pl = to_HepLorentzVector(x.second.at(1));
}
else{
pl = to_HepLorentzVector(x.second.at(0));
plbar = to_HepLorentzVector(x.second.at(1));
}
}
const auto pa = to_HepLorentzVector(incoming[0]);
const auto pb = to_HepLorentzVector(incoming[1]);
const auto partons = tag_extremal_jet_partons(ev);
if(ev.type() == unordered_backward){
return tree_kin_W_unob(incoming[0].type, incoming[1].type,
pa, pb, partons, plbar, pl,
param_.regulator_lambda);
}
if(ev.type() == unordered_forward){
return tree_kin_W_unof(incoming[0].type, incoming[1].type,
pa, pb, partons, plbar, pl,
param_.regulator_lambda);
}
if(ev.type() == extremal_qqxb){
return tree_kin_W_qqxb(incoming[0].type, incoming[1].type,
pa, pb, partons, plbar, pl,
param_.regulator_lambda);
}
if(ev.type() == extremal_qqxf){
return tree_kin_W_qqxf(incoming[0].type, incoming[1].type,
pa, pb, partons, plbar, pl,
param_.regulator_lambda);
}
if(ev.type() == central_qqx){
return tree_kin_W_qqxmid(incoming[0].type, incoming[1].type,
pa, pb, partons, plbar, pl,
param_.regulator_lambda);
}
return tree_kin_W_FKL(incoming[0].type, incoming[1].type,
pa, pb, partons, plbar, pl,
param_.regulator_lambda);
}
double MatrixElement::tree_kin_Higgs(
Event const & ev
) const {
if(is_uno(ev.type())){
return tree_kin_Higgs_between(ev);
}
if(ev.outgoing().front().type == pid::Higgs){
return tree_kin_Higgs_first(ev);
}
if(ev.outgoing().back().type == pid::Higgs){
return tree_kin_Higgs_last(ev);
}
return tree_kin_Higgs_between(ev);
}
namespace {
// Colour acceleration multipliers, for gluons see eq. (7) in arXiv:0910.5113
#ifdef HEJ_BUILD_WITH_QCDLOOP
// TODO: code duplication with currents.cc
double K_g(double p1minus, double paminus) {
return 1./2.*(p1minus/paminus + paminus/p1minus)*(C_A - 1./C_A) + 1./C_A;
}
double K_g(
CLHEP::HepLorentzVector const & pout,
CLHEP::HepLorentzVector const & pin
) {
if(pin.z() > 0) return K_g(pout.plus(), pin.plus());
return K_g(pout.minus(), pin.minus());
}
double K(
ParticleID type,
CLHEP::HepLorentzVector const & pout,
CLHEP::HepLorentzVector const & pin
) {
if(type == ParticleID::gluon) return K_g(pout, pin);
return C_F;
}
#endif
// Colour factor in strict MRK limit
double K_MRK(ParticleID type) {
return (type == ParticleID::gluon)?C_A:C_F;
}
}
double MatrixElement::MH2_forwardH(
CLHEP::HepLorentzVector p1out, CLHEP::HepLorentzVector p1in,
ParticleID type2,
CLHEP::HepLorentzVector p2out, CLHEP::HepLorentzVector p2in,
CLHEP::HepLorentzVector pH,
double t1, double t2
) const{
ignore(p2out, p2in);
const double shat = p1in.invariantMass2(p2in);
// gluon case
#ifdef HEJ_BUILD_WITH_QCDLOOP
if(!param_.Higgs_coupling.use_impact_factors){
return K(type2, p2out, p2in)*C_A*1./(16*M_PI*M_PI)*t1/t2*MH2gq_outsideH(
p1out, p1in, p2out, p2in, pH,
param_.Higgs_coupling.mt, param_.Higgs_coupling.include_bottom,
param_.Higgs_coupling.mb
)/(4*(N_C*N_C - 1));
}
#endif
return K_MRK(type2)/C_A*9./2.*shat*shat*(
C2gHgp(p1in,p1out,pH) + C2gHgm(p1in,p1out,pH)
)/(t1*t2);
}
double MatrixElement::tree_kin_Higgs_first(
Event const & ev
) const {
auto const & incoming = ev.incoming();
auto const & outgoing = ev.outgoing();
assert(outgoing.front().type == pid::Higgs);
if(outgoing[1].type != pid::gluon) {
assert(incoming.front().type == outgoing[1].type);
return tree_kin_Higgs_between(ev);
}
const auto pH = to_HepLorentzVector(outgoing.front());
const auto partons = tag_extremal_jet_partons(
ev
);
const auto pa = to_HepLorentzVector(incoming[0]);
const auto pb = to_HepLorentzVector(incoming[1]);
const auto p1 = to_HepLorentzVector(partons.front());
const auto pn = to_HepLorentzVector(partons.back());
const auto q0 = pa - p1 - pH;
const double t1 = q0.m2();
const double t2 = (pn - pb).m2();
return MH2_forwardH(
p1, pa, incoming[1].type, pn, pb, pH,
t1, t2
)*FKL_ladder_weight(
begin(partons) + 1, end(partons) - 1,
q0, pa, pb, p1, pn,
param_.regulator_lambda
);
}
double MatrixElement::tree_kin_Higgs_last(
Event const & ev
) const {
auto const & incoming = ev.incoming();
auto const & outgoing = ev.outgoing();
assert(outgoing.back().type == pid::Higgs);
if(outgoing[outgoing.size()-2].type != pid::gluon) {
assert(incoming.back().type == outgoing[outgoing.size()-2].type);
return tree_kin_Higgs_between(ev);
}
const auto pH = to_HepLorentzVector(outgoing.back());
const auto partons = tag_extremal_jet_partons(
ev
);
const auto pa = to_HepLorentzVector(incoming[0]);
const auto pb = to_HepLorentzVector(incoming[1]);
auto p1 = to_HepLorentzVector(partons.front());
const auto pn = to_HepLorentzVector(partons.back());
auto q0 = pa - p1;
const double t1 = q0.m2();
const double t2 = (pn + pH - pb).m2();
return MH2_forwardH(
pn, pb, incoming[0].type, p1, pa, pH,
t2, t1
)*FKL_ladder_weight(
begin(partons) + 1, end(partons) - 1,
q0, pa, pb, p1, pn,
param_.regulator_lambda
);
}
double MatrixElement::tree_kin_Higgs_between(
Event const & ev
) const {
using namespace event_type;
auto const & incoming = ev.incoming();
auto const & outgoing = ev.outgoing();
const auto the_Higgs = std::find_if(
begin(outgoing), end(outgoing),
[](Particle const & s){ return s.type == pid::Higgs; }
);
assert(the_Higgs != end(outgoing));
const auto pH = to_HepLorentzVector(*the_Higgs);
const auto partons = tag_extremal_jet_partons(ev);
const auto pa = to_HepLorentzVector(incoming[0]);
const auto pb = to_HepLorentzVector(incoming[1]);
auto p1 = to_HepLorentzVector(
partons[(ev.type() == unob)?1:0]
);
auto pn = to_HepLorentzVector(
partons[partons.size() - ((ev.type() == unof)?2:1)]
);
auto first_after_Higgs = begin(partons) + (the_Higgs-begin(outgoing));
assert(
(first_after_Higgs == end(partons) && (
(ev.type() == unob)
|| partons.back().type != pid::gluon
))
|| first_after_Higgs->rapidity() >= the_Higgs->rapidity()
);
assert(
(first_after_Higgs == begin(partons) && (
(ev.type() == unof)
|| partons.front().type != pid::gluon
))
|| (first_after_Higgs-1)->rapidity() <= the_Higgs->rapidity()
);
// always treat the Higgs as if it were in between the extremal FKL partons
if(first_after_Higgs == begin(partons)) ++first_after_Higgs;
else if(first_after_Higgs == end(partons)) --first_after_Higgs;
// t-channel momentum before Higgs
auto qH = pa;
for(auto parton_it = begin(partons); parton_it != first_after_Higgs; ++parton_it){
qH -= to_HepLorentzVector(*parton_it);
}
auto q0 = pa - p1;
auto begin_ladder = begin(partons) + 1;
auto end_ladder = end(partons) - 1;
double current_factor;
if(ev.type() == unob){
current_factor = C_A*C_A/2.*ME_Higgs_current_unob( // 1/2 = "K_uno"
incoming[0].type, incoming[1].type,
pn, pb, to_HepLorentzVector(partons.front()), p1, pa, qH, qH - pH,
param_.Higgs_coupling.mt,
param_.Higgs_coupling.include_bottom, param_.Higgs_coupling.mb
);
const auto p_unob = to_HepLorentzVector(partons.front());
q0 -= p_unob;
p1 += p_unob;
++begin_ladder;
}
else if(ev.type() == unof){
current_factor = C_A*C_A/2.*ME_Higgs_current_unof( // 1/2 = "K_uno"
incoming[0].type, incoming[1].type,
to_HepLorentzVector(partons.back()), pn, pb, p1, pa, qH, qH - pH,
param_.Higgs_coupling.mt,
param_.Higgs_coupling.include_bottom, param_.Higgs_coupling.mb
);
pn += to_HepLorentzVector(partons.back());
--end_ladder;
}
else{
current_factor = ME_Higgs_current(
incoming[0].type, incoming[1].type,
pn, pb, p1, pa, qH, qH - pH,
param_.Higgs_coupling.mt,
param_.Higgs_coupling.include_bottom, param_.Higgs_coupling.mb
);
}
const double ladder_factor = FKL_ladder_weight(
begin_ladder, first_after_Higgs,
q0, pa, pb, p1, pn,
param_.regulator_lambda
)*FKL_ladder_weight(
first_after_Higgs, end_ladder,
qH - pH, pa, pb, p1, pn,
param_.regulator_lambda
);
return current_factor*C_A*C_A/(N_C*N_C-1.)*ladder_factor;
}
namespace {
double get_AWZH_coupling(Event const & ev, double alpha_s) {
const auto AWZH_boson = std::find_if(
begin(ev.outgoing()), end(ev.outgoing()),
[](auto const & p){return is_AWZH_boson(p);}
);
if(AWZH_boson == end(ev.outgoing())) return 1.;
switch(AWZH_boson->type){
case pid::Higgs:
return alpha_s*alpha_s;
case pid::Wp:
case pid::Wm:
return gw*gw*gw*gw/4.;
// TODO
case pid::photon:
case pid::Z:
default:
throw not_implemented("Emission of boson of unsupported type");
}
}
}
double MatrixElement::tree_param(
Event const & ev,
double mur
) const{
assert(is_HEJ(ev.type()));
const auto begin_partons = ev.begin_partons();
const auto end_partons = ev.end_partons();
const auto num_partons = std::distance(begin_partons, end_partons);
const double alpha_s = alpha_s_(mur);
const double gs2 = 4.*M_PI*alpha_s;
double res = std::pow(gs2, num_partons);
if(param_.log_correction){
// use alpha_s(q_perp), evolved to mur
assert(num_partons >= 2);
const auto first_emission = std::next(begin_partons);
const auto last_emission = std::prev(end_partons);
for(auto parton = first_emission; parton != last_emission; ++parton){
res *= 1. + alpha_s/(2.*M_PI)*beta0*log(mur/parton->perp());
}
}
return get_AWZH_coupling(ev, alpha_s)*res;
}
} // namespace HEJ
diff --git a/src/Wjets.cc b/src/Wjets.cc
index 9f75a85..bc76bcb 100644
--- a/src/Wjets.cc
+++ b/src/Wjets.cc
@@ -1,1689 +1,1697 @@
/**
* \authors The HEJ collaboration (see AUTHORS for details)
* \date 2019
* \copyright GPLv2 or later
*/
#include "HEJ/currents.hh"
#include "HEJ/utility.hh"
#include "HEJ/Tensor.hh"
#include "HEJ/Constants.hh"
#include <array>
#include <iostream>
namespace { // Helper Functions
// FKL W Helper Functions
void jW (HLV pout, bool helout, HLV pe, bool hele, HLV pnu, bool helnu,
HLV pin, bool helin, current cur
){
// NOTA BENE: Conventions for W+ --> e+ nu, so that nu is lepton(6), e is
// anti-lepton(5)
// Need to swap e and nu for events with W- --> e- nubar!
if (helin==helout && hele==helnu) {
HLV qa=pout+pe+pnu;
HLV qb=pin-pe-pnu;
double ta(qa.m2()),tb(qb.m2());
current t65,vout,vin,temp2,temp3,temp5;
joo(pnu,helnu,pe,hele,t65);
vout[0]=pout.e();
vout[1]=pout.x();
vout[2]=pout.y();
vout[3]=pout.z();
vin[0]=pin.e();
vin[1]=pin.x();
vin[2]=pin.y();
vin[3]=pin.z();
COM brac615=cdot(t65,vout);
COM brac645=cdot(t65,vin);
// prod1565 and prod6465 are zero for Ws (not Zs)!!
joo(pout,helout,pnu,helout,temp2);
COM prod1665=cdot(temp2,t65);
joi(pe,helin,pin,helin,temp3);
COM prod5465=cdot(temp3,t65);
joo(pout,helout,pe,helout,temp2);
joi(pnu,helnu,pin,helin,temp3);
joi(pout,helout,pin,helin,temp5);
current term1,term2,term3,sum;
cmult(2.*brac615/ta+2.*brac645/tb,temp5,term1);
cmult(prod1665/ta,temp3,term2);
cmult(-prod5465/tb,temp2,term3);
cadd(term1,term2,term3,sum);
cur[0]=sum[0];
cur[1]=sum[1];
cur[2]=sum[2];
cur[3]=sum[3];
}
}
void jWbar (HLV pout, bool helout, HLV pe, bool hele, HLV pnu, bool helnu,
HLV pin, bool helin, current cur
){
// NOTA BENE: Conventions for W+ --> e+ nu, so that nu is lepton(6), e is
// anti-lepton(5)
// Need to swap e and nu for events with W- --> e- nubar!
if (helin==helout && hele==helnu) {
HLV qa=pout+pe+pnu;
HLV qb=pin-pe-pnu;
double ta(qa.m2()),tb(qb.m2());
current t65,vout,vin,temp2,temp3,temp5;
joo(pnu,helnu,pe,hele,t65);
vout[0]=pout.e();
vout[1]=pout.x();
vout[2]=pout.y();
vout[3]=pout.z();
vin[0]=pin.e();
vin[1]=pin.x();
vin[2]=pin.y();
vin[3]=pin.z();
COM brac615=cdot(t65,vout);
COM brac645=cdot(t65,vin);
// prod1565 and prod6465 are zero for Ws (not Zs)!!
joo(pe,helout,pout,helout,temp2); // temp2 is <5|alpha|1>
COM prod5165=cdot(temp2,t65);
jio(pin,helin,pnu,helin,temp3); // temp3 is <4|alpha|6>
COM prod4665=cdot(temp3,t65);
joo(pnu,helout,pout,helout,temp2); // temp2 is now <6|mu|1>
jio(pin,helin,pe,helin,temp3); // temp3 is now <4|mu|5>
jio(pin,helin,pout,helout,temp5); // temp5 is <4|mu|1>
current term1,term2,term3,sum;
cmult(-2.*brac615/ta-2.*brac645/tb,temp5,term1);
cmult(-prod5165/ta,temp3,term2);
cmult(prod4665/tb,temp2,term3);
cadd(term1,term2,term3,sum);
cur[0]=sum[0];
cur[1]=sum[1];
cur[2]=sum[2];
cur[3]=sum[3];
}
}
double WProp (const HLV & plbar, const HLV & pl){
COM propW = COM(0.,-1.)/( (pl+plbar).m2() - HEJ::MW*HEJ::MW + COM(0.,1.)*HEJ::MW*HEJ::GammaW);
double PropFactor=(propW*conj(propW)).real();
return PropFactor;
}
CCurrent jW (HLV pout, bool helout, HLV pe, bool hele, HLV pnu, bool helnu,
HLV pin, bool helin
){
COM cur[4];
cur[0]=0.;
cur[1]=0.;
cur[2]=0.;
cur[3]=0.;
CCurrent sum(0.,0.,0.,0.);
// NOTA BENE: Conventions for W+ --> e+ nu, so that nu is lepton(6), e is
// anti-lepton(5)
// Need to swap e and nu for events with W- --> e- nubar!
if (helin==helout && hele==helnu) {
HLV qa=pout+pe+pnu;
HLV qb=pin-pe-pnu;
double ta(qa.m2()),tb(qb.m2());
CCurrent temp2,temp3,temp5;
CCurrent t65 = joo(pnu,helnu,pe,hele);
CCurrent vout(pout.e(),pout.x(),pout.y(),pout.z());
CCurrent vin(pin.e(),pin.x(),pin.y(),pin.z());
COM brac615=t65.dot(vout);
COM brac645=t65.dot(vin);
// prod1565 and prod6465 are zero for Ws (not Zs)!!
temp2 = joo(pout,helout,pnu,helout);
COM prod1665=temp2.dot(t65);
temp3 = joi(pe,helin,pin,helin);
COM prod5465=temp3.dot(t65);
temp2=joo(pout,helout,pe,helout);
temp3=joi(pnu,helnu,pin,helin);
temp5=joi(pout,helout,pin,helin);
CCurrent term1,term2,term3;
term1=(2.*brac615/ta+2.*brac645/tb)*temp5;
term2=(prod1665/ta)*temp3;
term3=(-prod5465/tb)*temp2;
sum=term1+term2+term3;
}
return sum;
}
CCurrent jWbar (HLV pout, bool helout, HLV pe, bool hele, HLV pnu, bool helnu,
HLV pin, bool helin
){
COM cur[4];
cur[0]=0.;
cur[1]=0.;
cur[2]=0.;
cur[3]=0.;
CCurrent sum(0.,0.,0.,0.);
// NOTA BENE: Conventions for W+ --> e+ nu, so that nu is lepton(6), e is
// anti-lepton(5)
// Need to swap e and nu for events with W- --> e- nubar!
if (helin==helout && hele==helnu) {
HLV qa=pout+pe+pnu;
HLV qb=pin-pe-pnu;
double ta(qa.m2()),tb(qb.m2());
CCurrent temp2,temp3,temp5;
CCurrent t65 = joo(pnu,helnu,pe,hele);
CCurrent vout(pout.e(),pout.x(),pout.y(),pout.z());
CCurrent vin(pin.e(),pin.x(),pin.y(),pin.z());
COM brac615=t65.dot(vout);
COM brac645=t65.dot(vin);
// prod1565 and prod6465 are zero for Ws (not Zs)!!
temp2 = joo(pe,helout,pout,helout); // temp2 is <5|alpha|1>
COM prod5165=temp2.dot(t65);
temp3 = jio(pin,helin,pnu,helin); // temp3 is <4|alpha|6>
COM prod4665=temp3.dot(t65);
temp2=joo(pnu,helout,pout,helout); // temp2 is now <6|mu|1>
temp3=jio(pin,helin,pe,helin); // temp3 is now <4|mu|5>
temp5=jio(pin,helin,pout,helout); // temp5 is <4|mu|1>
CCurrent term1,term2,term3;
term1 =(-2.*brac615/ta-2.*brac645/tb)*temp5;
term2 =(-prod5165/ta)*temp3;
term3 =(prod4665/tb)*temp2;
sum = term1 + term2 + term3;
}
return sum;
}
// Extremal quark current with W emission.
// Using Tensor class rather than CCurrent
Tensor <1> jW(HLV pin, HLV pout, HLV plbar, HLV pl, bool aqline){
// Build the external quark line W Emmision
Tensor<1> ABCurr = TCurrent(pl, false, plbar, false);
Tensor<1> Tp4W = Construct1Tensor((pout+pl+plbar));//p4+pw
Tensor<1> TpbW = Construct1Tensor((pin-pl-plbar));//pb-pw
Tensor<3> J4bBlank;
if (aqline){
J4bBlank = T3Current(pin,false,pout,false);
}
else{
J4bBlank = T3Current(pout,false,pin,false);
}
double t4AB = (pout+pl+plbar).m2();
double tbAB = (pin-pl-plbar).m2();
Tensor<2> J4b1 = (J4bBlank.contract(Tp4W,2))/t4AB;
Tensor<2> J4b2 = (J4bBlank.contract(TpbW,2))/tbAB;
Tensor<2> T4bmMom(0.);
if (aqline){
for(int mu=0; mu<4;mu++){
for(int nu=0;nu<4;nu++){
T4bmMom(mu, nu) = (J4b1(nu,mu) + J4b2(mu,nu))*COM(0,-1);
}
}
}
else{
for(int mu=0; mu<4;mu++){
for(int nu=0;nu<4;nu++){
T4bmMom(nu,mu) = (J4b1(nu,mu) + J4b2(mu,nu))*COM(0,1);
}
}
}
Tensor<1> T4bm = T4bmMom.contract(ABCurr,1);
return T4bm;
}
// Relevant W+Jets Unordered Contribution Helper Functions
// W+Jets Uno
double jM2Wuno(HLV pg, HLV p1,HLV plbar, HLV pl, HLV pa, bool h1,
HLV p2, HLV pb, bool h2, bool pol
){
static bool is_sigma_index_set(false);
if(!is_sigma_index_set){
//std::cout<<"Setting sigma_index...." << std::endl;
if(init_sigma_index())
is_sigma_index_set = true;
else
return 0.;
}
HLV pW = pl+plbar;
HLV q1g=pa-pW-p1-pg;
HLV q1 = pa-p1-pW;
HLV q2 = p2-pb;
const double taW = (pa-pW).m2();
const double taW1 = (pa-pW-p1).m2();
const double tb2 = (pb-p2).m2();
const double tb2g = (pb-p2-pg).m2();
const double s1W = (p1+pW).m2();
const double s1gW = (p1+pW+pg).m2();
const double s1g = (p1+pg).m2();
const double tag = (pa-pg).m2();
const double taWg = (pa-pW-pg).m2();
//use p1 as ref vec in pol tensor
Tensor<1> epsg = eps(pg,p2,pol);
Tensor<1> epsW = TCurrent(pl,false,plbar,false);
Tensor<1> j2b = TCurrent(p2,h2,pb,h2);
Tensor<1> Tq1q2 = Construct1Tensor((q1+q2)/taW1 + (pb/pb.dot(pg)
+ p2/p2.dot(pg)) * tb2/(2*tb2g));
Tensor<1> Tq1g = Construct1Tensor((-pg-q1))/taW1;
Tensor<1> Tq2g = Construct1Tensor((pg-q2));
Tensor<1> TqaW = Construct1Tensor((pa-pW));//pa-pw
Tensor<1> Tqag = Construct1Tensor((pa-pg));
Tensor<1> TqaWg = Construct1Tensor((pa-pg-pW));
Tensor<1> Tp1g = Construct1Tensor((p1+pg));
Tensor<1> Tp1W = Construct1Tensor((p1+pW));//p1+pw
Tensor<1> Tp1gW = Construct1Tensor((p1+pg+pW));//p1+pw+pg
Tensor<2> g=Metric();
Tensor<3> J31a = T3Current(p1, h1, pa, h1);
Tensor<2> J2_qaW =J31a.contract(TqaW/taW, 2);
Tensor<2> J2_p1W =J31a.contract(Tp1W/s1W, 2);
Tensor<3> L1a = outer(Tq1q2, J2_qaW);
Tensor<3> L1b = outer(Tq1q2, J2_p1W);
Tensor<3> L2a = outer(Tq1g,J2_qaW);
Tensor<3> L2b = outer(Tq1g, J2_p1W);
Tensor<3> L3 = outer(g, J2_qaW.contract(Tq2g,1)+J2_p1W.contract(Tq2g,2))/taW1;
Tensor<3> L(0.);
Tensor<5> J51a = T5Current(p1, h1, pa, h1);
Tensor<4> J_qaW = J51a.contract(TqaW,4);
Tensor<4> J_qag = J51a.contract(Tqag,4);
Tensor<4> J_p1gW = J51a.contract(Tp1gW,4);
Tensor<3> U1a = J_qaW.contract(Tp1g,2);
Tensor<3> U1b = J_p1gW.contract(Tp1g,2);
Tensor<3> U1c = J_p1gW.contract(Tp1W,2);
Tensor<3> U1(0.);
Tensor<3> U2a = J_qaW.contract(TqaWg,2);
Tensor<3> U2b = J_qag.contract(TqaWg,2);
Tensor<3> U2c = J_qag.contract(Tp1W,2);
Tensor<3> U2(0.);
for(int nu=0; nu<4;nu++){
for(int mu=0;mu<4;mu++){
for(int rho=0;rho<4;rho++){
L(nu, mu, rho) = L1a(nu,mu,rho) + L1b(nu,rho,mu)
+ L2a(mu,nu,rho) + L2b(mu,rho,nu) + L3(mu,nu,rho);
U1(nu, mu, rho) = U1a(nu, mu, rho) / (s1g*taW)
+ U1b(nu,rho,mu) / (s1g*s1gW) + U1c(rho,nu,mu) / (s1W*s1gW);
U2(nu,mu,rho) = U2a(mu,nu,rho) / (taWg*taW)
+ U2b(mu,rho,nu) / (taWg*tag) + U2c(rho,mu,nu) / (s1W*tag);
}
}
}
COM X = ((((U1-L).contract(epsW,3)).contract(j2b,2)).contract(epsg,1));
COM Y = ((((U2+L).contract(epsW,3)).contract(j2b,2)).contract(epsg,1));
double amp = HEJ::C_A*HEJ::C_F*HEJ::C_F/2.*(norm(X)+norm(Y)) - HEJ::C_F/2.*(X*conj(Y)).real();
double t1 = q1g.m2();
double t2 = q2.m2();
double WPropfact = WProp(plbar, pl);
//Divide by WProp
amp*=WPropfact;
//Divide by t-channels
amp/=(t1*t2);
//Average over initial states
amp/=(4.*HEJ::C_A*HEJ::C_A);
return amp;
}
// Relevant Wqqx Helper Functions.
//g->qxqlxl (Calculates gluon to qqx Current. See JV_\mu in WSubleading Notes)
Tensor <1> gtqqxW(HLV pq,HLV pqbar,HLV pl,HLV plbar){
double s2AB=(pl+plbar+pq).m2();
double s3AB=(pl+plbar+pqbar).m2();
Tensor<1> Tpq = Construct1Tensor(pq);
Tensor<1> Tpqbar = Construct1Tensor(pqbar);
Tensor<1> TAB = Construct1Tensor(pl+plbar);
// Define llx current.
Tensor<1> ABCur = TCurrent(pl, false, plbar, false);
//blank 3 Gamma Current
Tensor<3> JV23 = T3Current(pq,false,pqbar,false);
// Components of g->qqW before W Contraction
Tensor<2> JV1 = JV23.contract((Tpq + TAB),2)/(s2AB);
Tensor<2> JV2 = JV23.contract((Tpqbar + TAB),2)/(s3AB);
// g->qqW Current. Note Minus between terms due to momentum flow.
// Also note: (-I)^2 from W vert. (I) from Quark prop.
Tensor<1> JVCur = (JV1.contract(ABCur,1) - JV2.contract(ABCur,2))*COM(0.,-1.);
return JVCur;
}
// Helper Functions Calculate the Crossed Contribution
Tensor <2> MCrossW(HLV pa, HLV, HLV, HLV, HLV pq, HLV pqbar, HLV pl,
HLV plbar, std::vector<HLV> partons, int nabove
){
// Useful propagator factors
double s2AB=(pl+plbar+pq).m2();
double s3AB=(pl+plbar+pqbar).m2();
HLV q1, q3;
q1=pa;
for(int i=0; i<nabove+1;i++){
q1=q1-partons.at(i);
}
q3 = q1 - pq - pqbar - pl - plbar;
double tcro1=(q3+pq).m2();
double tcro2=(q1-pqbar).m2();
Tensor<1> Tpq = Construct1Tensor(pq);
Tensor<1> Tpqbar = Construct1Tensor(pqbar);
Tensor<1> TAB = Construct1Tensor(pl+plbar);
Tensor<1> Tq1 = Construct1Tensor(q1);
Tensor<1> Tq3 = Construct1Tensor(q3);
// Define llx current.
Tensor<1> ABCur = TCurrent(pl, false, plbar,false);
//Blank 5 gamma Current
Tensor<5> J523 = T5Current(pq,false,pqbar,false);
// 4 gamma currents (with 1 contraction already).
Tensor<4> J_q3q = J523.contract((Tq3+Tpq),2);
Tensor<4> J_2AB = J523.contract((Tpq+TAB),2);
// Components of Crossed Vertex Contribution
Tensor<3> Xcro1 = J_q3q.contract((Tpqbar + TAB),3);
Tensor<3> Xcro2 = J_q3q.contract((Tq1-Tpqbar),3);
Tensor<3> Xcro3 = J_2AB.contract((Tq1-Tpqbar),3);
// Term Denominators Taken Care of at this stage
Tensor<2> Xcro1Cont = Xcro1.contract(ABCur,3)/(tcro1*s3AB);
Tensor<2> Xcro2Cont = Xcro2.contract(ABCur,2)/(tcro1*tcro2);
Tensor<2> Xcro3Cont = Xcro3.contract(ABCur,1)/(s2AB*tcro2);
//Initialise the Crossed Vertex Object
Tensor<2> Xcro(0.);
for(int mu=0; mu<4;mu++){
for(int nu=0;nu<4;nu++){
Xcro(mu,nu) = -(-Xcro1Cont(nu,mu)+Xcro2Cont(nu,mu)+Xcro3Cont(nu,mu));
}
}
return Xcro;
}
// Helper Functions Calculate the Uncrossed Contribution
Tensor <2> MUncrossW(HLV pa, HLV, HLV, HLV, HLV pq, HLV pqbar,
HLV pl, HLV plbar, std::vector<HLV> partons, int nabove
){
double s2AB=(pl+plbar+pq).m2();
double s3AB=(pl+plbar+pqbar).m2();
HLV q1, q3;
q1=pa;
for(int i=0; i<nabove+1;i++){
q1=q1-partons.at(i);
}
q3 = q1 - pl - plbar - pq - pqbar;
double tunc1 = (q1-pq).m2();
double tunc2 = (q3+pqbar).m2();
Tensor<1> Tpq = Construct1Tensor(pq);
Tensor<1> Tpqbar = Construct1Tensor(pqbar);
Tensor<1> TAB = Construct1Tensor(pl+plbar);
Tensor<1> Tq1 = Construct1Tensor(q1);
Tensor<1> Tq3 = Construct1Tensor(q3);
// Define llx current.
Tensor<1> ABCur = TCurrent(pl, false, plbar, false);
//Blank 5 gamma Current
Tensor<5> J523 = T5Current(pq,false,pqbar,false);
// 4 gamma currents (with 1 contraction already).
Tensor<4> J_2AB = J523.contract((Tpq+TAB),2);
Tensor<4> J_q1q = J523.contract((Tq1-Tpq),2);
// 2 Contractions taken care of.
Tensor<3> Xunc1 = J_2AB.contract((Tq3+Tpqbar),3);
Tensor<3> Xunc2 = J_q1q.contract((Tq3+Tpqbar),3);
Tensor<3> Xunc3 = J_q1q.contract((Tpqbar+TAB),3);
// Term Denominators Taken Care of at this stage
Tensor<2> Xunc1Cont = Xunc1.contract(ABCur,1)/(s2AB*tunc2);
Tensor<2> Xunc2Cont = Xunc2.contract(ABCur,2)/(tunc1*tunc2);
Tensor<2> Xunc3Cont = Xunc3.contract(ABCur,3)/(tunc1*s3AB);
//Initialise the Uncrossed Vertex Object
Tensor<2> Xunc(0.);
for(int mu=0; mu<4;mu++){
for(int nu=0;nu<4;nu++){
Xunc(mu,nu) = -(- Xunc1Cont(mu,nu)+Xunc2Cont(mu,nu) +Xunc3Cont(mu,nu));
}
}
return Xunc;
}
// Helper Functions Calculate the g->qqxW (Eikonal) Contributions
Tensor <2> MSymW(HLV pa, HLV p1, HLV pb, HLV p4, HLV pq, HLV pqbar,
HLV pl,HLV plbar, std::vector<HLV> partons, int nabove
){
double sa2=(pa+pq).m2();
double s12=(p1+pq).m2();
double sa3=(pa+pqbar).m2();
double s13=(p1+pqbar).m2();
double saA=(pa+pl).m2();
double s1A=(p1+pl).m2();
double saB=(pa+plbar).m2();
double s1B=(p1+plbar).m2();
double sb2=(pb+pq).m2();
double s42=(p4+pq).m2();
double sb3=(pb+pqbar).m2();
double s43=(p4+pqbar).m2();
double sbA=(pb+pl).m2();
double s4A=(p4+pl).m2();
double sbB=(pb+plbar).m2();
double s4B=(p4+plbar).m2();
double s23AB=(pl+plbar+pq+pqbar).m2();
HLV q1,q3;
q1=pa;
for(int i=0;i<nabove+1;i++){
q1-=partons.at(i);
}
q3=q1-pq-pqbar-plbar-pl;
double t1 = (q1).m2();
double t3 = (q3).m2();
//Define Tensors to be used
Tensor<1> Tp1 = Construct1Tensor(p1);
Tensor<1> Tp4 = Construct1Tensor(p4);
Tensor<1> Tpa = Construct1Tensor(pa);
Tensor<1> Tpb = Construct1Tensor(pb);
Tensor<1> Tpq = Construct1Tensor(pq);
Tensor<1> Tpqbar = Construct1Tensor(pqbar);
Tensor<1> TAB = Construct1Tensor(pl+plbar);
Tensor<1> Tq1 = Construct1Tensor(q1);
Tensor<1> Tq3 = Construct1Tensor(q3);
Tensor<2> g=Metric();
// g->qqW Current (Factors of sqrt2 dealt with in this function.)
Tensor<1> JV = gtqqxW(pq,pqbar,pl,plbar);
// 1a gluon emisson Contribution
Tensor<3> X1a = outer(g, Tp1*(t1/(s12+s13+s1A+s1B))
+ Tpa*(t1/(sa2+sa3+saA+saB)) );
Tensor<2> X1aCont = X1a.contract(JV,3);
//4b gluon emission Contribution
Tensor<3> X4b = outer(g, Tp4*(t3/(s42+s43+s4A+s4B))
+ Tpb*(t3/(sb2+sb3+sbA+sbB)) );
Tensor<2> X4bCont = X4b.contract(JV,3);
//Set up each term of 3G diagram.
Tensor<3> X3g1 = outer(Tq1+Tpq+Tpqbar+TAB, g);
Tensor<3> X3g2 = outer(Tq3-Tpq-Tpqbar-TAB, g);
Tensor<3> X3g3 = outer(Tq1+Tq3, g);
// Note the contraction of indices changes term by term
Tensor<2> X3g1Cont = X3g1.contract(JV,3);
Tensor<2> X3g2Cont = X3g2.contract(JV,2);
Tensor<2> X3g3Cont = X3g3.contract(JV,1);
// XSym is an amalgamation of x1a, X4b and X3g.
// Makes sense from a colour factor point of view.
Tensor<2>Xsym(0.);
for(int mu=0; mu<4;mu++){
for(int nu=0;nu<4;nu++){
Xsym(mu,nu) = (X3g1Cont(nu,mu) + X3g2Cont(mu,nu) - X3g3Cont(nu,mu))
+ (X1aCont(mu,nu) - X4bCont(mu,nu));
}
}
return Xsym/s23AB;
}
Tensor <2> MCross(HLV pa, HLV pq, HLV pqbar, std::vector<HLV> partons,
bool hq, int nabove
){
HLV q1;
q1=pa;
for(int i=0;i<nabove+1;i++){
q1-=partons.at(i);
}
double t2=(q1-pqbar).m2();
Tensor<1> Tq1 = Construct1Tensor(q1-pqbar);
//Blank 3 gamma Current
Tensor<3> J323 = T3Current(pq,hq,pqbar,hq);
// 2 gamma current (with 1 contraction already).
Tensor<2> XCroCont = J323.contract((Tq1),2)/(t2);
//Initialise the Crossed Vertex
Tensor<2> Xcro(0.);
for(int mu=0; mu<4;mu++){
for(int nu=0;nu<4;nu++){
Xcro(mu,nu) = XCroCont(nu,mu);
}
}
return Xcro;
}
// Helper Functions Calculate the Uncrossed Contribution
Tensor <2> MUncross(HLV pa, HLV pq,HLV pqbar, std::vector<HLV> partons,
bool hq, int nabove
){
HLV q1;
q1=pa;
for(int i=0;i<nabove+1;i++){
q1-=partons.at(i);
}
double t2 = (q1-pq).m2();
Tensor<1> Tq1 = Construct1Tensor(q1-pq);
//Blank 3 gamma Current
Tensor<3> J323 = T3Current(pq,hq,pqbar,hq);
// 2 gamma currents (with 1 contraction already).
Tensor<2> XUncCont = J323.contract((Tq1),2)/t2;
//Initialise the Uncrossed Vertex
Tensor<2> Xunc(0.);
for(int mu=0; mu<4;mu++){
for(int nu=0;nu<4;nu++){
Xunc(mu,nu) = -XUncCont(mu,nu);
}
}
return Xunc;
}
// Helper Functions Calculate the Eikonal Contributions
Tensor <2> MSym(HLV pa, HLV p1, HLV pb, HLV p4, HLV pq, HLV pqbar,
std::vector<HLV> partons, bool hq, int nabove
){
HLV q1, q3;
q1=pa;
for(int i=0;i<nabove+1;i++){
q1-=partons.at(i);
}
q3 = q1-pq-pqbar;
double t1 = (q1).m2();
double t3 = (q3).m2();
double s23 = (pq+pqbar).m2();
double sa2 = (pa+pq).m2();
double sa3 = (pa+pqbar).m2();
double s12 = (p1+pq).m2();
double s13 = (p1+pqbar).m2();
double sb2 = (pb+pq).m2();
double sb3 = (pb+pqbar).m2();
double s42 = (p4+pq).m2();
double s43 = (p4+pqbar).m2();
//Define Tensors to be used
Tensor<1> Tp1 = Construct1Tensor(p1);
Tensor<1> Tp4 = Construct1Tensor(p4);
Tensor<1> Tpa = Construct1Tensor(pa);
Tensor<1> Tpb = Construct1Tensor(pb);
Tensor<1> Tpq = Construct1Tensor(pq);
Tensor<1> Tpqbar = Construct1Tensor(pqbar);
Tensor<1> Tq1 = Construct1Tensor(q1);
Tensor<1> Tq3 = Construct1Tensor(q3);
Tensor<2> g=Metric();
Tensor<1> qqxCur = TCurrent(pq, hq, pqbar, hq);
// // 1a gluon emisson Contribution
Tensor<3> X1a = outer(g, Tp1*(t1/(s12+s13))+Tpa*(t1/(sa2+sa3)));
Tensor<2> X1aCont = X1a.contract(qqxCur,3);
// //4b gluon emission Contribution
Tensor<3> X4b = outer(g, Tp4*(t3/(s42+s43)) + Tpb*(t3/(sb2+sb3)));
Tensor<2> X4bCont = X4b.contract(qqxCur,3);
// New Formulation Corresponding to New Analytics
Tensor<3> X3g1 = outer(Tq1+Tpq+Tpqbar, g);
Tensor<3> X3g2 = outer(Tq3-Tpq-Tpqbar, g);
Tensor<3> X3g3 = outer(Tq1+Tq3, g);
// Note the contraction of indices changes term by term
Tensor<2> X3g1Cont = X3g1.contract(qqxCur,3);
Tensor<2> X3g2Cont = X3g2.contract(qqxCur,2);
Tensor<2> X3g3Cont = X3g3.contract(qqxCur,1);
Tensor<2>Xsym(0.);
for(int mu=0; mu<4;mu++){
for(int nu=0;nu<4;nu++){
Xsym(mu, nu) = COM(0,1) * ( (X3g1Cont(nu,mu) + X3g2Cont(mu,nu)
- X3g3Cont(nu,mu)) + (X1aCont(mu,nu) - X4bCont(mu,nu)) );
}
}
return Xsym/s23;
}
} // Anonymous Namespace helper functions
// W+Jets FKL Contributions
// Calculates the square of the current contractions for qQ->qenuQ scattering
// p1: quark (with W emittance)
// p2: Quark
double jMWqQ (HLV p1out, HLV pe, HLV pnu,HLV p1in, HLV p2out, HLV p2in){
current mj1m,mj2p,mj2m;
HLV q1=p1in-p1out-pe-pnu;
HLV q2=-(p2in-p2out);
jW(p1out,false,pe,false,pnu,false,p1in,false,mj1m);
joi(p2out,true,p2in,true,mj2p);
joi(p2out,false,p2in,false,mj2m);
COM Mmp=cdot(mj1m,mj2p);
// mj1m.mj2m
COM Mmm=cdot(mj1m,mj2m);
// sum of spinor strings ||^2
double a2Mmp=abs2(Mmp);
double a2Mmm=abs2(Mmm);
double WPropfact = WProp(pe, pnu);
// Division by colour and Helicity average (Nc2-1)(4)
// Multiply by Cf^2
return HEJ::C_F*HEJ::C_F*WPropfact*(a2Mmp+a2Mmm)/(q1.m2()*q2.m2()*(HEJ::N_C*HEJ::N_C - 1)*4);
}
// Calculates the square of the current contractions for qQ->qenuQ scattering
// p1: quark (with W emittance)
// p2: Quark
double jMWqQbar (HLV p1out, HLV pe, HLV pnu,HLV p1in, HLV p2out, HLV p2in){
current mj1m,mj2p,mj2m;
HLV q1=p1in-p1out-pe-pnu;
HLV q2=-(p2in-p2out);
jW(p1out,false,pe,false,pnu,false,p1in,false,mj1m);
jio(p2in,true,p2out,true,mj2p);
jio(p2in,false,p2out,false,mj2m);
COM Mmp=cdot(mj1m,mj2p);
// mj1m.mj2m
COM Mmm=cdot(mj1m,mj2m);
// sum of spinor strings ||^2
double a2Mmp=abs2(Mmp);
double a2Mmm=abs2(Mmm);
double WPropfact = WProp(pe, pnu);
// Division by colour and Helicity average (Nc2-1)(4)
// Multiply by Cf^2
return HEJ::C_F*HEJ::C_F*WPropfact*(a2Mmp+a2Mmm)/(q1.m2()*q2.m2()*(HEJ::N_C*HEJ::N_C - 1)*4);
}
// Calculates the square of the current contractions for qQ->qenuQ scattering
// p1: quark (with W emittance)
// p2: Quark
double jMWqbarQ (HLV p1out, HLV pe, HLV pnu,HLV p1in, HLV p2out, HLV p2in){
current mj1m,mj2p,mj2m;
HLV q1=p1in-p1out-pe-pnu;
HLV q2=-(p2in-p2out);
jWbar(p1out,false,pe,false,pnu,false,p1in,false,mj1m);
joi(p2out,true,p2in,true,mj2p);
joi(p2out,false,p2in,false,mj2m);
COM Mmp=cdot(mj1m,mj2p);
// mj1m.mj2m
COM Mmm=cdot(mj1m,mj2m);
// sum of spinor strings ||^2
double a2Mmp=abs2(Mmp);
double a2Mmm=abs2(Mmm);
double WPropfact = WProp(pe, pnu);
// Division by colour and Helicity average (Nc2-1)(4)
// Multiply by Cf^2
return HEJ::C_F*HEJ::C_F*WPropfact*(a2Mmp+a2Mmm)/(q1.m2()*q2.m2()*(HEJ::N_C*HEJ::N_C - 1)*4);
}
// Calculates the square of the current contractions for qQ->qenuQ scattering
// p1: quark (with W emittance)
// p2: Quark
double jMWqbarQbar (HLV p1out, HLV pe, HLV pnu,HLV p1in, HLV p2out, HLV p2in){
current mj1m,mj2p,mj2m;
HLV q1=p1in-p1out-pe-pnu;
HLV q2=-(p2in-p2out);
jWbar(p1out,false,pe,false,pnu,false,p1in,false,mj1m);
jio(p2in,true,p2out,true,mj2p);
jio(p2in,false,p2out,false,mj2m);
COM Mmp=cdot(mj1m,mj2p);
// mj1m.mj2m
COM Mmm=cdot(mj1m,mj2m);
// sum of spinor strings ||^2
double a2Mmp=abs2(Mmp);
double a2Mmm=abs2(Mmm);
double WPropfact = WProp(pe, pnu);
// Division by colour and Helicity average (Nc2-1)(4)
// Multiply by Cf^2
return HEJ::C_F*HEJ::C_F*WPropfact*(a2Mmp+a2Mmm)/(q1.m2()*q2.m2()*(HEJ::N_C*HEJ::N_C - 1)*4);
}
// Calculates the square of the current contractions for qg->qenug scattering
// p1: quark
// p2: gluon
double jMWqg (HLV p1out, HLV pe, HLV pnu,HLV p1in, HLV p2out, HLV p2in){
HLV q1=p1in-p1out-pe-pnu;
HLV q2=-(p2in-p2out);
current mj1m,mj2p,mj2m;
jW(p1out,false,pe,false,pnu,false,p1in,false,mj1m);
joi(p2out,true,p2in,true,mj2p);
joi(p2out,false,p2in,false,mj2m);
// mj1m.mj2p
COM Mmp=cdot(mj1m,mj2p);
// mj1m.mj2m
COM Mmm=cdot(mj1m,mj2m);
const double K = K_g(p2out, p2in);
// sum of spinor strings ||^2
double a2Mmp=abs2(Mmp);
double a2Mmm=abs2(Mmm);
double sst = K/HEJ::C_A*(a2Mmp+a2Mmm);
double WPropfact = WProp(pe, pnu);
// Division by colour and Helicity average (Nc2-1)(4)
// Multiply by Cf*Ca=4
return HEJ::C_F*HEJ::C_A*WPropfact*sst/(q1.m2()*q2.m2()*(HEJ::N_C*HEJ::N_C - 1)*4);
}
// Calculates the square of the current contractions for qg->qenug scattering
// p1: quark
// p2: gluon
double jMWqbarg (HLV p1out, HLV pe, HLV pnu,HLV p1in, HLV p2out, HLV p2in){
HLV q1=p1in-p1out-pe-pnu;
HLV q2=-(p2in-p2out);
current mj1m,mj2p,mj2m;
jWbar(p1out,false,pe,false,pnu,false,p1in,false,mj1m);
joi(p2out,true,p2in,true,mj2p);
joi(p2out,false,p2in,false,mj2m);
// mj1m.mj2p
COM Mmp=cdot(mj1m,mj2p);
// mj1m.mj2m
COM Mmm=cdot(mj1m,mj2m);
const double K = K_g(p2out, p2in);
// sum of spinor strings ||^2
double a2Mmp=abs2(Mmp);
double a2Mmm=abs2(Mmm);
double sst = K/HEJ::C_A*(a2Mmp+a2Mmm);
double WPropfact = WProp(pe, pnu);
// Division by colour and Helicity average (Nc2-1)(4)
// Multiply by Cf*Ca=4
return HEJ::C_F*HEJ::C_A*WPropfact*sst/(q1.m2()*q2.m2()*(HEJ::N_C*HEJ::N_C - 1)*4);
}
/**
* @brief W+Jets Unordered Contributions, function to handle all incoming types.
+ * @param p1out Outgoing Particle 1. (W emission)
+ * @param pe Outgoing election momenta
+ * @param pnu Outgoing neutrino momenta
+ * @param p1in Incoming Particle 1. (W emission)
+ * @param p2out Outgoing Particle 2 (Quark, unordered emission this side.)
+ * @param p2in Incoming Particle 2 (Quark, unordered emission this side.)
+ * @param pg Unordered Gluon momenta
+ * @param aqlineb Bool. Is Backwards quark line an anti-quark line?
+ * @param aqlinef Bool. Is Forwards quark line an anti-quark line?
*
* Calculates j_W ^\mu j_{uno}_\mu. Ie, unordered with W emission opposite side.
- * All possible incoming particles possible.
+ * Handles all possible incoming states.
*/
-
double jWjuno (HLV p1out, HLV pe, HLV pnu,HLV p1in, HLV p2out,
HLV p2in, HLV pg, bool aqlineb, bool aqlinef){
CCurrent mj1m,mj2p,mj2m, jgbm,jgbp,j2gm,j2gp;
HLV q1=p1in-p1out-pe-pnu;
HLV q2=-(p2in-p2out-pg);
HLV q3=-(p2in-p2out);
if(aqlineb) mj1m=jWbar(p1out,false,pe,false,pnu,false,p1in,false);
else mj1m=jW(p1out,false,pe,false,pnu,false,p1in,false);
if(aqlinef){
mj2p=jio(p2in,true,p2out,true);
mj2m=jio(p2in,false,p2out,false);
j2gp=joo(pg,true,p2out,true);
j2gm=joo(pg,false,p2out,false);
jgbp=jio(p2in,true,pg,true);
jgbm=jio(p2in,false,pg,false);
} else{
mj2p=joi(p2out,true,p2in,true);
mj2m=joi(p2out,false,p2in,false);
j2gp=joo(p2out,true,pg,true);
j2gm=joo(p2out,false,pg,false);
jgbp=joi(pg,true,p2in,true);
jgbm=joi(pg,false,p2in,false);
}
// Dot products of these which occur again and again
COM MWmp=mj1m.dot(mj2p); // And now for the Higgs ones
COM MWmm=mj1m.dot(mj2m);
CCurrent qsum(q2+q3);
CCurrent Lmp,Lmm,Lpp,Lpm,U1mp,U1mm,U1pp,U1pm,U2mp,U2mm,U2pp,U2pm,p1o(p1out),p1i(p1in);
CCurrent p2o(p2out);
CCurrent p2i(p2in);
Lmm=( (-1.)*qsum*(MWmm) + (-2.*mj1m.dot(pg))*mj2m + 2.*mj2m.dot(pg)*mj1m
+ ( p1o/pg.dot(p1out) + p1i/pg.dot(p1in) )*( q2.m2()*MWmm/2. ) )/q3.m2();
Lmp=( (-1.)*qsum*(MWmp) + (-2.*mj1m.dot(pg))*mj2p + 2.*mj2p.dot(pg)*mj1m
+ ( p1o/pg.dot(p1out) + p1i/pg.dot(p1in) )*( q2.m2()*MWmp/2. ) )/q3.m2();
U1mm=(jgbm.dot(mj1m)*j2gm+2.*p2o*MWmm)/(p2out+pg).m2();
U1mp=(jgbp.dot(mj1m)*j2gp+2.*p2o*MWmp)/(p2out+pg).m2();
U2mm=((-1.)*j2gm.dot(mj1m)*jgbm+2.*p2i*MWmm)/(p2in-pg).m2();
U2mp=((-1.)*j2gp.dot(mj1m)*jgbp+2.*p2i*MWmp)/(p2in-pg).m2();
double amm,amp;
amm=HEJ::C_F*(2.*vre(Lmm-U1mm,Lmm+U2mm))+2.*HEJ::C_F*HEJ::C_F/3.*vabs2(U1mm+U2mm);
amp=HEJ::C_F*(2.*vre(Lmp-U1mp,Lmp+U2mp))+2.*HEJ::C_F*HEJ::C_F/3.*vabs2(U1mp+U2mp);
double ampsq=-(amm+amp);
//Divide by WProp
ampsq*=WProp(pe, pnu);
return ampsq/((16)*(q2.m2()*q1.m2()));
}
/** \brief Backwards unordered, W opposite side. qq incoming
* \see jWjuno */
-double junobMWqQg (HLV p1out, HLV pe, HLV pnu,HLV p1in,
- HLV p2out, HLV p2in, HLV pg){
+double junobMWqQg(HLV pg, HLV p1out, HLV p1in, HLV p2out,
+ HLV pe, HLV pnu, HLV p2in){
return jWjuno(p1out, pe, pnu, p1in, p2out, p2in, pg, false, false);
}
/** \brief Backwards unordered, W opposite side. qqbar incoming
* \see jWjuno */
-double junobMWqQbarg (HLV p1out, HLV pe, HLV pnu,HLV p1in,
- HLV p2out, HLV p2in, HLV pg){
+double junobMWqQbarg(HLV pg, HLV p1out, HLV p1in, HLV p2out,
+ HLV pe, HLV pnu, HLV p2in){
return jWjuno(p1out, pe, pnu, p1in, p2out, p2in, pg, false, true);
}
/** \brief Backwards unordered, W opposite side. qbarq incoming
* \see jWjuno */
-double junobMWqbarQg (HLV p1out, HLV pe, HLV pnu,HLV p1in,
- HLV p2out, HLV p2in, HLV pg){
+double junobMWqbarQg(HLV pg, HLV p1out, HLV p1in, HLV p2out,
+ HLV pe, HLV pnu, HLV p2in){
return jWjuno(p1out, pe, pnu, p1in, p2out, p2in, pg, true, false);
}
/** \brief Backwards unordered, W opposite side. qbarqbar incoming
* \see jWjuno */
-double junobMWqbarQbarg (HLV p1out, HLV pe, HLV pnu,HLV p1in,
- HLV p2out, HLV p2in, HLV pg){
+double junobMWqbarQbarg(HLV pg, HLV p1out, HLV p1in, HLV p2out,
+ HLV pe, HLV pnu, HLV p2in){
return jWjuno(p1out, pe, pnu, p1in, p2out, p2in, pg, true, true);
}
/** \brief Forwards unordered, W opposite side. qq incoming
* \see jWjuno */
-double junofMWgqQ (HLV pg,HLV p1out,HLV p1in, HLV p2out,
+double junofMWgqQ(HLV pg, HLV p1out, HLV p1in, HLV p2out,
HLV pe, HLV pnu, HLV p2in){
return jWjuno(p2out, pe, pnu, p2in, p1out, p1in, pg, false, false);
}
/** \brief Forwards unordered, W opposite side. qbarq incoming
* \see jWjuno */
-double junofMWgqQbar (HLV pg,HLV p1out,HLV p1in, HLV p2out,
+double junofMWgqQbar(HLV pg, HLV p1out, HLV p1in, HLV p2out,
HLV pe, HLV pnu, HLV p2in){
return jWjuno(p2out, pe, pnu, p2in, p1out, p1in, pg, true, false);
}
/** \brief Forwards unordered, W opposite side. qqbar incoming
* \see jWjuno */
-double junofMWgqbarQ (HLV pg,HLV p1out,HLV p1in, HLV p2out,
+double junofMWgqbarQ(HLV pg, HLV p1out, HLV p1in, HLV p2out,
HLV pe, HLV pnu, HLV p2in){
return jWjuno(p2out, pe, pnu, p2in, p1out, p1in, pg, false, true);
}
/** \brief Forwards unordered, W opposite side. qbarqbar incoming
* \see jWjuno */
-double junofMWgqbarQbar (HLV pg,HLV p1out,HLV p1in, HLV p2out,
+double junofMWgqbarQbar(HLV pg, HLV p1out, HLV p1in, HLV p2out,
HLV pe, HLV pnu, HLV p2in){
return jWjuno(p2out, pe, pnu, p2in, p1out, p1in, pg, true, true);
}
///TODO make this comment more visible
/// Naming scheme jM2-Wuno-g-({q/qbar}{Q/Qbar/g})
///TODO Spit naming for more complicated functions?
/// e.g. jM2WqqtoqQQq -> jM2_Wqq_to_qQQq
double jM2WunogqQ(HLV pg, HLV p1out,HLV plbar,HLV pl, HLV p1in,
HLV p2out, HLV p2in
){
//COM temp;
double ME2mpp=0.;
double ME2mpm=0.;
double ME2mmp=0.;
double ME2mmm=0.;
double ME2;
ME2mpp = jM2Wuno(pg, p1out,plbar,pl,p1in,false,p2out,p2in,true,true);
ME2mpm = jM2Wuno(pg, p1out,plbar,pl,p1in,false,p2out,p2in,true,false);
ME2mmp = jM2Wuno(pg, p1out,plbar,pl,p1in,false,p2out,p2in,false,true);
ME2mmm = jM2Wuno(pg, p1out,plbar,pl,p1in,false,p2out,p2in,false,false);
//Helicity sum
ME2 = ME2mpp + ME2mpm + ME2mmp + ME2mmm;
return ME2;
}
//same as function above but actually obtaining the antiquark line by crossing
//symmetry, where p1out and p1in are expected to be negative.
//should give same result as jM2WunogqbarQ below (verified)
double jM2WunogqQ_crossqQ(HLV pg, HLV p1out,HLV plbar,HLV pl, HLV p1in,
HLV p2out, HLV p2in
){
//COM temp;
double ME2mpp=0.;
double ME2mpm=0.;
double ME2mmp=0.;
double ME2mmm=0.;
double ME2;
ME2mpp = jM2Wuno(pg, p1out,plbar,pl,p1in,false,p2out,p2in,true,true);
ME2mpm = jM2Wuno(pg, p1out,plbar,pl,p1in,false,p2out,p2in,true,false);
ME2mmp = jM2Wuno(pg, p1out,plbar,pl,p1in,false,p2out,p2in,false,true);
ME2mmm = jM2Wuno(pg, p1out,plbar,pl,p1in,false,p2out,p2in,false,false);
//Helicity sum
ME2 = ME2mpp + ME2mpm + ME2mmp + ME2mmm;
return ME2;
}
double jM2WunogqQbar(HLV pg, HLV p1out,HLV plbar,HLV pl, HLV p1in,
HLV p2out, HLV p2in
){
//COM temp;
double ME2mpp=0.;
double ME2mpm=0.;
double ME2mmp=0.;
double ME2mmm=0.;
double ME2;
ME2mpp = jM2Wuno(pg, p1out,plbar,pl,p1in,false,p2out,p2in,true,true);
ME2mpm = jM2Wuno(pg, p1out,plbar,pl,p1in,false,p2out,p2in,true,false);
ME2mmp = jM2Wuno(pg, p1out,plbar,pl,p1in,false,p2out,p2in,false,true);
ME2mmm = jM2Wuno(pg, p1out,plbar,pl,p1in,false,p2out,p2in,false,false);
//Helicity sum
ME2 = ME2mpp + ME2mpm + ME2mmp + ME2mmm;
return ME2;
}
double jM2Wunogqg(HLV pg, HLV p1out,HLV plbar,HLV pl, HLV p1in,
HLV p2out, HLV p2in
){
//COM temp;
double ME2mpp=0.;
double ME2mpm=0.;
double ME2mmp=0.;
double ME2mmm=0.;
double ME2;
ME2mpp = jM2Wuno(pg, p1out,plbar,pl,p1in,false,p2out,p2in,true,true);
ME2mpm = jM2Wuno(pg, p1out,plbar,pl,p1in,false,p2out,p2in,true,false);
ME2mmp = jM2Wuno(pg, p1out,plbar,pl,p1in,false,p2out,p2in,false,true);
ME2mmm = jM2Wuno(pg, p1out,plbar,pl,p1in,false,p2out,p2in,false,false);
//Helicity sum
ME2 = ME2mpp + ME2mpm + ME2mmp + ME2mmm;
double ratio; // p2-/pb- in the notes
if (p2in.pz()>0.) // if the gluon is the positive
ratio=p2out.plus()/p2in.plus();
else // the gluon is the negative
ratio=p2out.minus()/p2in.minus();
double cam = ( (HEJ::C_A - 1/HEJ::C_A)*(ratio + 1./ratio)/2. + 1/HEJ::C_A)/HEJ::C_F;
ME2*=cam;
return ME2;
}
double jM2WunogqbarQ(HLV pg, HLV p1out,HLV plbar,HLV pl, HLV p1in,
HLV p2out, HLV p2in
){
//COM temp;
double ME2mpp=0.;
double ME2mpm=0.;
double ME2mmp=0.;
double ME2mmm=0.;
double ME2;
ME2mpp = jM2Wuno(pg, p1out,plbar,pl,p1in,true,p2out,p2in,true,true);
ME2mpm = jM2Wuno(pg, p1out,plbar,pl,p1in,true,p2out,p2in,true,false);
ME2mmp = jM2Wuno(pg, p1out,plbar,pl,p1in,true,p2out,p2in,false,true);
ME2mmm = jM2Wuno(pg, p1out,plbar,pl,p1in,true,p2out,p2in,false,false);
//Helicity sum
ME2 = ME2mpp + ME2mpm + ME2mmp + ME2mmm;
return ME2;
}
double jM2WunogqbarQbar(HLV pg, HLV p1out,HLV plbar,HLV pl, HLV p1in,
HLV p2out, HLV p2in
){
//COM temp;
double ME2mpp=0.;
double ME2mpm=0.;
double ME2mmp=0.;
double ME2mmm=0.;
double ME2;
ME2mpp = jM2Wuno(pg, p1out,plbar,pl,p1in,true,p2out,p2in,true,true);
ME2mpm = jM2Wuno(pg, p1out,plbar,pl,p1in,true,p2out,p2in,true,false);
ME2mmp = jM2Wuno(pg, p1out,plbar,pl,p1in,true,p2out,p2in,false,true);
ME2mmm = jM2Wuno(pg, p1out,plbar,pl,p1in,true,p2out,p2in,false,false);
//Helicity sum
ME2 = ME2mpp + ME2mpm + ME2mmp + ME2mmm;
return ME2;
}
double jM2Wunogqbarg(HLV pg, HLV p1out,HLV plbar,HLV pl, HLV p1in,
HLV p2out, HLV p2in
){
//COM temp;
double ME2mpp=0.;
double ME2mpm=0.;
double ME2mmp=0.;
double ME2mmm=0.;
double ME2;
ME2mpp = jM2Wuno(pg, p1out,plbar,pl,p1in,true,p2out,p2in,true,true);
ME2mpm = jM2Wuno(pg, p1out,plbar,pl,p1in,true,p2out,p2in,true,false);
ME2mmp = jM2Wuno(pg, p1out,plbar,pl,p1in,true,p2out,p2in,false,true);
ME2mmm = jM2Wuno(pg, p1out,plbar,pl,p1in,true,p2out,p2in,false,false);
//Helicity sum
ME2 = ME2mpp + ME2mpm + ME2mmp + ME2mmm;
double ratio; // p2-/pb- in the notes
if (p2in.pz()>0.) // if the gluon is the positive
ratio=p2out.plus()/p2in.plus();
else // the gluon is the negative
ratio=p2out.minus()/p2in.minus();
double cam = ( (HEJ::C_A - 1/HEJ::C_A)*(ratio + 1./ratio)/2. + 1/HEJ::C_A)/HEJ::C_F;
ME2*=cam;
return ME2;
}
// W+Jets qqxExtremal
// W+Jets qqxExtremal Currents - wqq emission
double jM2WgQtoqbarqQ(HLV pgin, HLV pqout,HLV plbar,HLV pl,
HLV pqbarout, HLV p2out, HLV p2in
){
//COM temp;
double ME2mpp=0.;
double ME2mpm=0.;
double ME2mmp=0.;
double ME2mmm=0.;
double ME2;
ME2mpp = jM2Wuno(-pgin, pqout,plbar,pl,-pqbarout,false,p2out,p2in,true,true);
ME2mpm = jM2Wuno(-pgin, pqout,plbar,pl,-pqbarout,false,p2out,p2in,true,false);
ME2mmp = jM2Wuno(-pgin, pqout,plbar,pl,-pqbarout,false,p2out,p2in,false,true);
ME2mmm = jM2Wuno(-pgin, pqout,plbar,pl,-pqbarout,false,p2out,p2in,false,false);
//Helicity sum
ME2 = ME2mpp + ME2mpm + ME2mmp + ME2mmm;
//Correct colour averaging
ME2*=(3.0/8.0);
return ME2;
}
double jM2WgQtoqqbarQ(HLV pgin, HLV pqbarout,HLV plbar,HLV pl,
HLV pqout, HLV p2out, HLV p2in
){
//COM temp;
double ME2mpp=0.;
double ME2mpm=0.;
double ME2mmp=0.;
double ME2mmm=0.;
double ME2;
ME2mpp = jM2Wuno(-pgin, pqbarout,plbar,pl,-pqout,true,p2out,p2in,true,true);
ME2mpm = jM2Wuno(-pgin, pqbarout,plbar,pl,-pqout,true,p2out,p2in,true,false);
ME2mmp = jM2Wuno(-pgin, pqbarout,plbar,pl,-pqout,true,p2out,p2in,false,true);
ME2mmm = jM2Wuno(-pgin, pqbarout,plbar,pl,-pqout,true,p2out,p2in,false,false);
//Helicity sum
ME2 = ME2mpp + ME2mpm + ME2mmp + ME2mmm;
//Correct colour averaging
ME2*=(3.0/8.0);
return ME2;
}
double jM2Wggtoqbarqg(HLV pgin, HLV pqout,HLV plbar,HLV pl,
HLV pqbarout, HLV p2out, HLV p2in
){
double ME2mpp=0.;
double ME2mpm=0.;
double ME2mmp=0.;
double ME2mmm=0.;
double ME2;
ME2mpp = jM2Wuno(-pgin, pqout,plbar,pl,-pqbarout,false,p2out,p2in,true,true);
ME2mpm = jM2Wuno(-pgin, pqout,plbar,pl,-pqbarout,false,p2out,p2in,true,false);
ME2mmp = jM2Wuno(-pgin, pqout,plbar,pl,-pqbarout,false,p2out,p2in,false,true);
ME2mmm = jM2Wuno(-pgin, pqout,plbar,pl,-pqbarout,false,p2out,p2in,false,false);
//Helicity sum
ME2 = ME2mpp + ME2mpm + ME2mmp + ME2mmm;
double ratio; // p2-/pb- in the notes
if (p2in.pz()>0.) // if the gluon is the positive
ratio=p2out.plus()/p2in.plus();
else // the gluon is the negative
ratio=p2out.minus()/p2in.minus();
double cam = ( (HEJ::C_A - 1/HEJ::C_A)*(ratio + 1./ratio)/2. + 1/HEJ::C_A)/HEJ::C_F;
ME2*=cam;
//Correct colour averaging
ME2*=(3.0/8.0);
return ME2;
}
double jM2Wggtoqqbarg(HLV pgin, HLV pqbarout, HLV plbar, HLV pl,
HLV pqout, HLV p2out, HLV p2in
){
//COM temp;
double ME2mpp=0.;
double ME2mpm=0.;
double ME2mmp=0.;
double ME2mmm=0.;
double ME2;
ME2mpp = jM2Wuno(-pgin, pqbarout,plbar,pl,-pqout,true,p2out,p2in,true,true);
ME2mpm = jM2Wuno(-pgin, pqbarout,plbar,pl,-pqout,true,p2out,p2in,true,false);
ME2mmp = jM2Wuno(-pgin, pqbarout,plbar,pl,-pqout,true,p2out,p2in,false,true);
ME2mmm = jM2Wuno(-pgin, pqbarout,plbar,pl,-pqout,true,p2out,p2in,false,false);
//Helicity sum
ME2 = ME2mpp + ME2mpm + ME2mmp + ME2mmm;
double ratio; // p2-/pb- in the notes
if (p2in.pz()>0.) // if the gluon is the positive
ratio=p2out.plus()/p2in.plus();
else // the gluon is the negative
ratio=p2out.minus()/p2in.minus();
double cam = ( (HEJ::C_A - 1/HEJ::C_A)*(ratio + 1./ratio)/2. + 1/HEJ::C_A)/HEJ::C_F;
ME2*=cam;
//Correct colour averaging
ME2*=(3.0/8.0);
return ME2;
}
namespace {
//Function to calculate Term 1 in Equation 3.23 in James Cockburn's Thesis.
Tensor<1> qggm1(HLV pb, HLV p2, HLV p3, bool hel2, bool helg, HLV refmom){
double t1 = (p3-pb)*(p3-pb);
Tensor<1> Tp3 = Construct1Tensor((p3));//p3
Tensor<1> Tpb = Construct1Tensor((pb));//pb
// Gauge choice in polarisation tensor. (see JC's Thesis)
Tensor<1> epsg = eps(pb, refmom, helg);
Tensor<3> qqCurBlank = T3Current(p2,hel2,p3,hel2);
Tensor<2> qqCur = qqCurBlank.contract(Tp3-Tpb,2);
Tensor<1> gqqCur = qqCur.contract(epsg,2)/t1;
return gqqCur*(-1);
}
//Function to calculate Term 2 in Equation 3.23 in James Cockburn's Thesis.
Tensor<1> qggm2(HLV pb, HLV p2, HLV p3, bool hel2, bool helg, HLV refmom){
double t1 = (p2-pb)*(p2-pb);
Tensor<1> Tp2 = Construct1Tensor((p2));//p2
Tensor<1> Tpb = Construct1Tensor((pb));//pb
// Gauge choice in polarisation tensor. (see JC's Thesis)
Tensor<1> epsg = eps(pb,refmom, helg);
Tensor<3> qqCurBlank = T3Current(p2,hel2,p3,hel2);
Tensor<2> qqCur = qqCurBlank.contract(Tp2-Tpb,2);
Tensor<1> gqqCur = qqCur.contract(epsg,1)/t1;
return gqqCur;
}
//Function to calculate Term 3 in Equation 3.23 in James Cockburn's Thesis.
Tensor<1> qggm3(HLV pb, HLV p2, HLV p3, bool hel2, bool helg, HLV refmom){
double s23 = (p2+p3)*(p2+p3);
Tensor<1> Tp2 = Construct1Tensor((p2));//p2
Tensor<1> Tp3 = Construct1Tensor((p3));//p3
Tensor<1> Tpb = Construct1Tensor((pb));//pb
// Gauge choice in polarisation tensor. (see JC's Thesis)
Tensor<1> epsg = eps(pb, refmom, helg);
Tensor<2> g=Metric();
Tensor<3> qqCurBlank1 = outer(Tp2+Tp3, g)/s23;
Tensor<3> qqCurBlank2 = outer(Tpb, g)/s23;
Tensor<1> Cur23 = TCurrent(p2,hel2, p3,hel2);
Tensor<2> qqCur1 = qqCurBlank1.contract(Cur23,3);
Tensor<2> qqCur2 = qqCurBlank2.contract(Cur23,3);
Tensor<2> qqCur3 = qqCurBlank2.contract(Cur23,1);
Tensor<1> gqqCur = (qqCur1.contract(epsg,1)
- qqCur2.contract(epsg,2)
+ qqCur3.contract(epsg,1))*2*COM(0,1);
return gqqCur;
}
}
// no wqq emission
double jM2WgqtoQQqW(HLV pa, HLV pb, HLV p1, HLV p2, HLV p3,HLV plbar, HLV pl,
bool aqlinepa
){
static bool is_sigma_index_set(false);
if(!is_sigma_index_set){
if(init_sigma_index())
is_sigma_index_set = true;
else
return 0.;}
// 2 independent helicity choices (complex conjugation related).
Tensor<1> TMmmm1 = qggm1(pb,p2,p3,false,false, pa);
Tensor<1> TMmmm2 = qggm2(pb,p2,p3,false,false, pa);
Tensor<1> TMmmm3 = qggm3(pb,p2,p3,false,false, pa);
Tensor<1> TMpmm1 = qggm1(pb,p2,p3,false,true, pa);
Tensor<1> TMpmm2 = qggm2(pb,p2,p3,false,true, pa);
Tensor<1> TMpmm3 = qggm3(pb,p2,p3,false,true, pa);
// Build the external quark line W Emmision
Tensor<1> cur1a = jW(pa,p1,plbar,pl, aqlinepa);
//Contract with the qqxCurrent.
COM Mmmm1 = TMmmm1.contract(cur1a,1);
COM Mmmm2 = TMmmm2.contract(cur1a,1);
COM Mmmm3 = TMmmm3.contract(cur1a,1);
COM Mpmm1 = TMpmm1.contract(cur1a,1);
COM Mpmm2 = TMpmm2.contract(cur1a,1);
COM Mpmm3 = TMpmm3.contract(cur1a,1);
//Colour factors:
COM cm1m1,cm2m2,cm3m3,cm1m2,cm1m3,cm2m3;
cm1m1=8./3.;
cm2m2=8./3.;
cm3m3=6.;
cm1m2 =-1./3.;
cm1m3 = -3.*COM(0.,1.);
cm2m3 = 3.*COM(0.,1.);
//Sqaure and sum for each helicity config:
double Mmmm = real( cm1m1*pow(abs(Mmmm1),2) + cm2m2*pow(abs(Mmmm2),2)
+ cm3m3*pow(abs(Mmmm3),2) + 2.*real(cm1m2*Mmmm1*conj(Mmmm2))
+ 2.*real(cm1m3*Mmmm1*conj(Mmmm3))
+ 2.*real(cm2m3*Mmmm2*conj(Mmmm3)) );
double Mpmm = real( cm1m1*pow(abs(Mpmm1),2) + cm2m2*pow(abs(Mpmm2),2)
+ cm3m3*pow(abs(Mpmm3),2) + 2.*real(cm1m2*Mpmm1*conj(Mpmm2))
+ 2.*real(cm1m3*Mpmm1*conj(Mpmm3))
+ 2.*real(cm2m3*Mpmm2*conj(Mpmm3)) );
// Divide by WProp
double WPropfact = WProp(plbar, pl);
return (2*WPropfact*(Mmmm+Mpmm)/24./4.)/(pa-p1-pl-plbar).m2()/(p2+p3-pb).m2();
}
// W+Jets qqxCentral
double jM2WqqtoqQQq(HLV pa, HLV pb,HLV pl, HLV plbar, std::vector<HLV> partons,
bool aqlinepa, bool aqlinepb, bool qqxmarker, int nabove
){
static bool is_sigma_index_set(false);
if(!is_sigma_index_set){
if(init_sigma_index())
is_sigma_index_set = true;
else
return 0.;}
HLV pq, pqbar, p1, p4;
if (qqxmarker){
pqbar = partons[nabove+1];
pq = partons[nabove+2];}
else{
pq = partons[nabove+1];
pqbar = partons[nabove+2];}
p1 = partons.front();
p4 = partons.back();
Tensor<1> T1am, T4bm, T1ap, T4bp;
if(!(aqlinepa)){
T1ap = TCurrent(p1, true, pa, true);
T1am = TCurrent(p1, false, pa, false);}
else if(aqlinepa){
T1ap = TCurrent(pa, true, p1, true);
T1am = TCurrent(pa, false, p1, false);}
if(!(aqlinepb)){
T4bp = TCurrent(p4, true, pb, true);
T4bm = TCurrent(p4, false, pb, false);}
else if(aqlinepb){
T4bp = TCurrent(pb, true, p4, true);
T4bm = TCurrent(pb, false, p4, false);}
// Calculate the 3 separate contributions to the effective vertex
Tensor<2> Xunc = MUncrossW(pa, p1, pb, p4, pq, pqbar, pl, plbar, partons, nabove);
Tensor<2> Xcro = MCrossW( pa, p1, pb, p4, pq, pqbar, pl, plbar, partons, nabove);
Tensor<2> Xsym = MSymW( pa, p1, pb, p4, pq, pqbar, pl, plbar, partons, nabove);
// 4 Different Helicity Choices (Differs from Pure Jet Case, where there is
// also the choice in qqbar helicity.
// (- - hel choice)
COM M_mmUnc = (((Xunc).contract(T1am,1)).contract(T4bm,1));
COM M_mmCro = (((Xcro).contract(T1am,1)).contract(T4bm,1));
COM M_mmSym = (((Xsym).contract(T1am,1)).contract(T4bm,1));
// (- + hel choice)
COM M_mpUnc = (((Xunc).contract(T1am,1)).contract(T4bp,1));
COM M_mpCro = (((Xcro).contract(T1am,1)).contract(T4bp,1));
COM M_mpSym = (((Xsym).contract(T1am,1)).contract(T4bp,1));
// (+ - hel choice)
COM M_pmUnc = (((Xunc).contract(T1ap,1)).contract(T4bm,1));
COM M_pmCro = (((Xcro).contract(T1ap,1)).contract(T4bm,1));
COM M_pmSym = (((Xsym).contract(T1ap,1)).contract(T4bm,1));
// (+ + hel choice)
COM M_ppUnc = (((Xunc).contract(T1ap,1)).contract(T4bp,1));
COM M_ppCro = (((Xcro).contract(T1ap,1)).contract(T4bp,1));
COM M_ppSym = (((Xsym).contract(T1ap,1)).contract(T4bp,1));
//Colour factors:
COM cmsms,cmumu,cmcmc,cmsmu,cmsmc,cmumc;
cmsms=3.;
cmumu=4./3.;
cmcmc=4./3.;
cmsmu =3./2.*COM(0.,1.);
cmsmc = -3./2.*COM(0.,1.);
cmumc = -1./6.;
// Work Out Interference in each case of helicity:
double amp_mm = real(cmsms*pow(abs(M_mmSym),2)
+cmumu*pow(abs(M_mmUnc),2)
+cmcmc*pow(abs(M_mmCro),2)
+2.*real(cmsmu*M_mmSym*conj(M_mmUnc))
+2.*real(cmsmc*M_mmSym*conj(M_mmCro))
+2.*real(cmumc*M_mmUnc*conj(M_mmCro)));
double amp_mp = real(cmsms*pow(abs(M_mpSym),2)
+cmumu*pow(abs(M_mpUnc),2)
+cmcmc*pow(abs(M_mpCro),2)
+2.*real(cmsmu*M_mpSym*conj(M_mpUnc))
+2.*real(cmsmc*M_mpSym*conj(M_mpCro))
+2.*real(cmumc*M_mpUnc*conj(M_mpCro)));
double amp_pm = real(cmsms*pow(abs(M_pmSym),2)
+cmumu*pow(abs(M_pmUnc),2)
+cmcmc*pow(abs(M_pmCro),2)
+2.*real(cmsmu*M_pmSym*conj(M_pmUnc))
+2.*real(cmsmc*M_pmSym*conj(M_pmCro))
+2.*real(cmumc*M_pmUnc*conj(M_pmCro)));
double amp_pp = real(cmsms*pow(abs(M_ppSym),2)
+cmumu*pow(abs(M_ppUnc),2)
+cmcmc*pow(abs(M_ppCro),2)
+2.*real(cmsmu*M_ppSym*conj(M_ppUnc))
+2.*real(cmsmc*M_ppSym*conj(M_ppCro))
+2.*real(cmumc*M_ppUnc*conj(M_ppCro)));
double amp=((amp_mm+amp_mp+amp_pm+amp_pp)/(9.*4.));
HLV q1,q3;
q1=pa;
for(int i=0;i<nabove+1;i++){
q1-=partons.at(i);
}
q3 = q1 - pq - pqbar - pl - plbar;
double t1 = (q1).m2();
double t3 = (q3).m2();
//Divide by t-channels
amp/=(t1*t1*t3*t3);
//Divide by WProp
double WPropfact = WProp(plbar, pl);
amp*=WPropfact;
return amp;
}
// no wqq emission
double jM2WqqtoqQQqW(HLV pa, HLV pb,HLV pl,HLV plbar, std::vector<HLV> partons,
bool aqlinepa, bool aqlinepb, bool qqxmarker, int nabove,
int nbelow, bool forwards
){
static bool is_sigma_index_set(false);
if(!is_sigma_index_set){
if(init_sigma_index())
is_sigma_index_set = true;
else
return 0.;
}
if (!forwards){ //If Emission from Leg a instead, flip process.
HLV dummymom = pa;
bool dummybool= aqlinepa;
int dummyint = nabove;
pa = pb;
pb = dummymom;
std::reverse(partons.begin(),partons.end());
qqxmarker = !(qqxmarker);
aqlinepa = aqlinepb;
aqlinepb = dummybool;
nabove = nbelow;
nbelow = dummyint;
}
HLV pq, pqbar, p1,p4;
if (qqxmarker){
pqbar = partons[nabove+1];
pq = partons[nabove+2];}
else{
pq = partons[nabove+1];
pqbar = partons[nabove+2];}
p1 = partons.front();
p4 = partons.back();
Tensor<1> T1am(0.), T1ap(0.);
if(!(aqlinepa)){
T1ap = TCurrent(p1, true, pa, true);
T1am = TCurrent(p1, false, pa, false);}
else if(aqlinepa){
T1ap = TCurrent(pa, true, p1, true);
T1am = TCurrent(pa, false, p1, false);}
Tensor <1> T4bm = jW(pb, p4, plbar, pl, aqlinepb);
// Calculate the 3 separate contributions to the effective vertex
Tensor<2> Xunc_m = MUncross(pa, pq, pqbar,partons, false, nabove);
Tensor<2> Xcro_m = MCross( pa, pq, pqbar,partons, false, nabove);
Tensor<2> Xsym_m = MSym( pa, p1, pb, p4, pq, pqbar, partons, false, nabove);
Tensor<2> Xunc_p = MUncross(pa, pq, pqbar,partons, true, nabove);
Tensor<2> Xcro_p = MCross( pa, pq, pqbar,partons, true, nabove);
Tensor<2> Xsym_p = MSym( pa, p1, pb, p4, pq, pqbar, partons, true, nabove);
// (- - hel choice)
COM M_mmUnc = (((Xunc_m).contract(T1am,1)).contract(T4bm,1));
COM M_mmCro = (((Xcro_m).contract(T1am,1)).contract(T4bm,1));
COM M_mmSym = (((Xsym_m).contract(T1am,1)).contract(T4bm,1));
// (- + hel choice)
COM M_mpUnc = (((Xunc_p).contract(T1am,1)).contract(T4bm,1));
COM M_mpCro = (((Xcro_p).contract(T1am,1)).contract(T4bm,1));
COM M_mpSym = (((Xsym_p).contract(T1am,1)).contract(T4bm,1));
// (+ - hel choice)
COM M_pmUnc = (((Xunc_m).contract(T1ap,1)).contract(T4bm,1));
COM M_pmCro = (((Xcro_m).contract(T1ap,1)).contract(T4bm,1));
COM M_pmSym = (((Xsym_m).contract(T1ap,1)).contract(T4bm,1));
// (+ + hel choice)
COM M_ppUnc = (((Xunc_p).contract(T1ap,1)).contract(T4bm,1));
COM M_ppCro = (((Xcro_p).contract(T1ap,1)).contract(T4bm,1));
COM M_ppSym = (((Xsym_p).contract(T1ap,1)).contract(T4bm,1));
//Colour factors:
COM cmsms,cmumu,cmcmc,cmsmu,cmsmc,cmumc;
cmsms=3.;
cmumu=4./3.;
cmcmc=4./3.;
cmsmu =3./2.*COM(0.,1.);
cmsmc = -3./2.*COM(0.,1.);
cmumc = -1./6.;
// Work Out Interference in each case of helicity:
double amp_mm = real(cmsms*pow(abs(M_mmSym),2)
+cmumu*pow(abs(M_mmUnc),2)
+cmcmc*pow(abs(M_mmCro),2)
+2.*real(cmsmu*M_mmSym*conj(M_mmUnc))
+2.*real(cmsmc*M_mmSym*conj(M_mmCro))
+2.*real(cmumc*M_mmUnc*conj(M_mmCro)));
double amp_mp = real(cmsms*pow(abs(M_mpSym),2)
+cmumu*pow(abs(M_mpUnc),2)
+cmcmc*pow(abs(M_mpCro),2)
+2.*real(cmsmu*M_mpSym*conj(M_mpUnc))
+2.*real(cmsmc*M_mpSym*conj(M_mpCro))
+2.*real(cmumc*M_mpUnc*conj(M_mpCro)));
double amp_pm = real(cmsms*pow(abs(M_pmSym),2)
+cmumu*pow(abs(M_pmUnc),2)
+cmcmc*pow(abs(M_pmCro),2)
+2.*real(cmsmu*M_pmSym*conj(M_pmUnc))
+2.*real(cmsmc*M_pmSym*conj(M_pmCro))
+2.*real(cmumc*M_pmUnc*conj(M_pmCro)));
double amp_pp = real(cmsms*pow(abs(M_ppSym),2)
+cmumu*pow(abs(M_ppUnc),2)
+cmcmc*pow(abs(M_ppCro),2)
+2.*real(cmsmu*M_ppSym*conj(M_ppUnc))
+2.*real(cmsmc*M_ppSym*conj(M_ppCro))
+2.*real(cmumc*M_ppUnc*conj(M_ppCro)));
double amp=((amp_mm+amp_mp+amp_pm+amp_pp)/(9.*4.));
HLV q1,q3;
q1=pa;
for(int i=0;i<nabove+1;i++){
q1-=partons.at(i);
}
q3 = q1 - pq - pqbar;
double t1 = (q1).m2();
double t3 = (q3).m2();
//Divide by t-channels
amp/=(t1*t1*t3*t3);
//Divide by WProp
double WPropfact = WProp(plbar, pl);
amp*=WPropfact;
return amp;
}