diff --git a/src/Wjets.cc b/src/Wjets.cc
index 32a89e7..1a0ad1a 100644
--- a/src/Wjets.cc
+++ b/src/Wjets.cc
@@ -1,830 +1,791 @@
/**
* \authors The HEJ collaboration (see AUTHORS for details)
* \date 2019
* \copyright GPLv2 or later
*/
#include "HEJ/Wjets.hh"
#include <array>
#include <iostream>
#include "HEJ/Constants.hh"
#include "HEJ/EWConstants.hh"
#include "HEJ/jets.hh"
#include "HEJ/Tensor.hh"
#include "HEJ/LorentzVector.hh"
#include "HEJ/exceptions.hh"
// generated headers
#include "HEJ/currents/jWuno_j.hh"
#include "HEJ/currents/jWqqbar_j.hh"
#include "HEJ/currents/jW_qqbar_j.hh"
#include "HEJ/currents/j_Wqqbar_j.hh"
+#include "HEJ/currents/jW_jqqbar.hh"
using HEJ::Tensor;
using HEJ::init_sigma_index;
using HEJ::metric;
using HEJ::rank3_current;
using HEJ::rank5_current;
using HEJ::eps;
using HEJ::to_tensor;
using HEJ::Helicity;
using HEJ::angle;
using HEJ::square;
using HEJ::flip;
using HEJ::ParticleProperties;
namespace helicity = HEJ::helicity;
namespace { // Helper Functions
// FKL W Helper Functions
double WProp (const HLV & plbar, const HLV & pl, ParticleProperties const & wprop){
COM propW = COM(0.,-1.)/( (pl+plbar).m2() - wprop.mass*wprop.mass
+ COM(0.,1.)*wprop.mass*wprop.width);
double PropFactor=(propW*conj(propW)).real();
return PropFactor;
}
namespace {
// FKL current including W emission off negative helicities
// See eq. (87) {eq:jW-} in developer manual
// Note that the terms are rearranged
Tensor<1> jW_minus(
HLV const & pa, HLV const & p1,
HLV const & plbar, HLV const & pl
){
using HEJ::helicity::minus;
const double tWin = (pa-pl-plbar).m2();
const double tWout = (p1+pl+plbar).m2();
// C++ arithmetic operators are evaluated left-to-right,
// so the following first computes complex scalar coefficients,
// which then multiply a current, reducing the number
// of multiplications
return 2.*(
+ angle(p1, pl)*square(p1, plbar)/tWout
+ square(pa, plbar)*angle(pa, pl)/tWin
)*HEJ::current(p1, pa, helicity::minus)
+ 2.*angle(p1, pl)*square(pl, plbar)/tWout
*HEJ::current(pl, pa, helicity::minus)
+ 2.*square(pa, plbar)*angle(pl, plbar)/tWin
*HEJ::current(p1, plbar, helicity::minus);
}
}
// FKL current including W emission
// see eqs. (87), (88) {eq:jW-}, {eq:jW+} in developer manual
Tensor<1> jW(
HLV const & pa, HLV const & p1,
HLV const & plbar, HLV const & pl,
Helicity h
){
if(h == helicity::minus) {
return jW_minus(pa, p1, plbar, pl);
}
return jW_minus(pa, p1, pl, plbar).complex_conj();
}
/**
* @brief Contraction of W + unordered jet current with FKL current
*
* See eq:wunocurrent in the developer manual for the definition
* of the W + unordered jet current
*/
template<Helicity h1, Helicity h2, Helicity pol>
double jM2Wuno(
HLV const & pg, HLV const & p1, HLV const & plbar, HLV const & pl,
HLV const & pa, HLV const & p2, HLV const & pb,
ParticleProperties const & wprop
){
using HEJ::C_A;
using HEJ::C_F;
const COM U1 = HEJ::U1<h1, h2, pol>(p1, p2, pa, pb, pg, pl, plbar);
const COM U2 = HEJ::U2<h1, h2, pol>(p1, p2, pa, pb, pg, pl, plbar);
const COM L = HEJ::L<h1, h2, pol>(p1, p2, pa, pb, pg, pl, plbar);
const COM X = U1 - L;
const COM Y = U2 + L;
double amp = C_A*C_F*C_F/2.*(norm(X)+norm(Y)) - HEJ::C_F/2.*(X*conj(Y)).real();
amp *= WProp(plbar, pl, wprop);
const HLV q1g = pa-pl-plbar-p1-pg;
const HLV q2 = p2-pb;
const double t1 = q1g.m2();
const double t2 = q2.m2();
amp /= (t1*t2);
return amp;
}
/**
* @brief Contraction of W + extremal qqbar current with FKL current
*
* See eq:crossed in the developer manual for the definition
* of the W + extremal qqbar current.
*
*/
template<Helicity h1, Helicity h2, Helicity hg>
double jM2_W_extremal_qqbar(
HLV const & pg, HLV const & pq, HLV const & plbar, HLV const & pl,
HLV const & pqbar, HLV const & p3, HLV const & pb,
ParticleProperties const & wprop
){
using HEJ::C_A;
using HEJ::C_F;
const COM U1Xcontr = HEJ::U1X<h1, h2, hg>(pg, pq, plbar, pl, pqbar, p3, pb);
const COM U2Xcontr = HEJ::U2X<h1, h2, hg>(pg, pq, plbar, pl, pqbar, p3, pb);
const COM LXcontr = HEJ::LX<h1, h2, hg>(pg, pq, plbar, pl, pqbar, p3, pb);
const COM X = U1Xcontr - LXcontr;
const COM Y = U2Xcontr + LXcontr;
double amp = C_A*C_F*C_F/2.*(norm(X)+norm(Y)) - HEJ::C_F/2.*(X*conj(Y)).real();
amp *= WProp(plbar, pl, wprop);
// what do I have to put here?
const HLV q1 = pg-pl-plbar-pq-pqbar;
const HLV q2 = p3-pb;
const double t1 = q1.m2();
const double t2 = q2.m2();
amp /= (t1*t2);
return amp;
}
//! W+Jets FKL Contributions
/**
* @brief W+Jets FKL Contributions, function to handle all incoming types.
* @param p1out Outgoing Particle 1. (W emission)
* @param plbar Outgoing election momenta
* @param pl Outgoing neutrino momenta
* @param p1in Incoming Particle 1. (W emission)
* @param p2out Outgoing Particle 2
* @param p2in Incoming Particle 2
* @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_\mu.
* Handles all possible incoming states.
*/
double jW_j( HLV p1out, HLV plbar, HLV pl, HLV p1in, HLV p2out, HLV p2in,
bool aqlineb, bool /* aqlinef */,
ParticleProperties const & wprop
){
using helicity::minus;
using helicity::plus;
const HLV q1=p1in-p1out-plbar-pl;
const HLV q2=-(p2in-p2out);
const double WPropfact = WProp(plbar, pl, wprop);
const auto j_W = COM{0,-1}*jW(p1in, p1out, plbar, pl, aqlineb?plus:minus);
double Msqr = 0.;
for(const auto h: {plus, minus}) {
const auto j = HEJ::current(p2out, p2in, h);
Msqr += abs2(j_W.contract(j, 1));
}
// Division by colour and Helicity average (Nc2-1)(4)
// Multiply by Cf^2
return HEJ::C_F*HEJ::C_F*WPropfact*Msqr/(q1.m2()*q2.m2()*(HEJ::N_C*HEJ::N_C - 1)*4);
}
} // Anonymous Namespace
double ME_W_qQ (HLV p1out, HLV plbar, HLV pl,HLV p1in, HLV p2out, HLV p2in,
ParticleProperties const & wprop
){
return jW_j(p1out, plbar, pl, p1in, p2out, p2in, false, false, wprop);
}
double ME_W_qQbar (HLV p1out, HLV plbar, HLV pl,HLV p1in, HLV p2out, HLV p2in,
ParticleProperties const & wprop
){
return jW_j(p1out, plbar, pl, p1in, p2out, p2in, false, true, wprop);
}
double ME_W_qbarQ (HLV p1out, HLV plbar, HLV pl,HLV p1in, HLV p2out, HLV p2in,
ParticleProperties const & wprop
){
return jW_j(p1out, plbar, pl, p1in, p2out, p2in, true, false, wprop);
}
double ME_W_qbarQbar (HLV p1out, HLV plbar, HLV pl,HLV p1in, HLV p2out, HLV p2in,
ParticleProperties const & wprop
){
return jW_j(p1out, plbar, pl, p1in, p2out, p2in, true, true, wprop);
}
double ME_W_qg (HLV p1out, HLV plbar, HLV pl,HLV p1in, HLV p2out, HLV p2in,
ParticleProperties const & wprop
){
return jW_j(p1out, plbar, pl, p1in, p2out, p2in, false, false, wprop)
*K_g(p2out, p2in)/HEJ::C_F;
}
double ME_W_qbarg (HLV p1out, HLV plbar, HLV pl,HLV p1in, HLV p2out, HLV p2in,
ParticleProperties const & wprop
){
return jW_j(p1out, plbar, pl, p1in, p2out, p2in, true, false, wprop)
*K_g(p2out, p2in)/HEJ::C_F;
}
namespace{
/**
* @brief W+Jets Unordered Contributions, function to handle all incoming types.
* @param p1out Outgoing Particle 1. (W emission)
* @param plbar Outgoing election momenta
* @param pl 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.
* Handles all possible incoming states.
*/
double jW_juno(HLV p1out, HLV plbar, HLV pl,HLV p1in, HLV p2out,
HLV p2in, HLV pg, bool aqlineb, bool aqlinef,
ParticleProperties const & wprop
){
using helicity::minus;
using helicity::plus;
const HLV q1=p1in-p1out-plbar-pl;
const HLV q2=-(p2in-p2out-pg);
const HLV q3=-(p2in-p2out);
const Helicity fhel = aqlinef?plus:minus;
const auto j_W = jW(p1in, p1out, plbar, pl, aqlineb?plus:minus);
const auto mj2p = HEJ::current(p2out, p2in, flip(fhel));
const auto mj2m = HEJ::current(p2out, p2in, fhel);
const auto jgbp = HEJ::current(pg, p2in, flip(fhel));
const auto jgbm = HEJ::current(pg, p2in, fhel);
const auto j2gp = HEJ::current(p2out, pg, flip(fhel));
const auto j2gm = HEJ::current(p2out, pg, fhel);
// Dot products of these which occur again and again
COM MWmp=j_W.dot(mj2p); // And now for the Higgs ones
COM MWmm=j_W.dot(mj2m);
const auto qsum = to_tensor(q2+q3);
const auto p1o = to_tensor(p1out);
const auto p1i = to_tensor(p1in);
const auto p2o = to_tensor(p2out);
const auto p2i = to_tensor(p2in);
const auto Lmm=( (-1.)*qsum*(MWmm) + (-2.*COM{j_W.dot(pg)})*mj2m + 2.*COM{mj2m.dot(pg)}*j_W
+ ( p1o/pg.dot(p1out) + p1i/pg.dot(p1in) )*( q2.m2()*MWmm/2. ) )/q3.m2();
const auto Lmp=( (-1.)*qsum*(MWmp) + (-2.*COM{j_W.dot(pg)})*mj2p + 2.*COM{mj2p.dot(pg)}*j_W
+ ( p1o/pg.dot(p1out) + p1i/pg.dot(p1in) )*( q2.m2()*MWmp/2. ) )/q3.m2();
const auto U1mm=(COM{jgbm.dot(j_W)}*j2gm+2.*p2o*MWmm)/(p2out+pg).m2();
const auto U1mp=(COM{jgbp.dot(j_W)}*j2gp+2.*p2o*MWmp)/(p2out+pg).m2();
const auto U2mm=((-1.)*COM{j2gm.dot(j_W)}*jgbm+2.*p2i*MWmm)/(p2in-pg).m2();
const auto U2mp=((-1.)*COM{j2gp.dot(j_W)}*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.*abs2(U1mm+U2mm);
amp=HEJ::C_F*(2.*vre(Lmp-U1mp,Lmp+U2mp))+2.*HEJ::C_F*HEJ::C_F/3.*abs2(U1mp+U2mp);
double ampsq=-(amm+amp);
//Divide by WProp
ampsq*=WProp(plbar, pl, wprop);
return ampsq/((16)*(q2.m2()*q1.m2()));
}
}
double ME_W_unob_qQ(HLV p1out, HLV p1in, HLV p2out, HLV p2in,
HLV pg, HLV plbar, HLV pl,
ParticleProperties const & wprop
){
return jW_juno(p2out, plbar, pl, p2in, p1out, p1in, pg, false, false, wprop);
}
double ME_W_unob_qQbar(HLV p1out, HLV p1in, HLV p2out, HLV p2in,
HLV pg, HLV plbar, HLV pl,
ParticleProperties const & wprop
){
return jW_juno(p2out, plbar, pl, p2in, p1out, p1in, pg, false, true, wprop);
}
double ME_W_unob_qbarQ(HLV p1out, HLV p1in, HLV p2out, HLV p2in,
HLV pg, HLV plbar, HLV pl,
ParticleProperties const & wprop
){
return jW_juno(p2out, plbar, pl, p2in, p1out, p1in, pg, true, false, wprop);
}
double ME_W_unob_qbarQbar(HLV p1out, HLV p1in, HLV p2out, HLV p2in,
HLV pg, HLV plbar, HLV pl,
ParticleProperties const & wprop
){
return jW_juno(p2out, plbar, pl, p2in, p1out, p1in, pg, true, true, wprop);
}
namespace{
// helicity sum helper for jWuno_j(...)
template<Helicity h1>
double jWuno_j_helsum(
HLV const & pg, HLV const & p1, HLV const & plbar, HLV const & pl,
HLV const & pa, HLV const & p2, HLV const & pb,
ParticleProperties const & wprop
){
using helicity::minus;
using helicity::plus;
const double ME2h1pp = jM2Wuno<h1, plus, plus>(
pg, p1, plbar, pl, pa, p2, pb, wprop
);
const double ME2h1pm = jM2Wuno<h1, plus, minus>(
pg, p1, plbar, pl, pa, p2, pb, wprop
);
const double ME2h1mp = jM2Wuno<h1, minus, plus>(
pg, p1, plbar, pl, pa, p2, pb, wprop
);
const double ME2h1mm = jM2Wuno<h1, minus, minus>(
pg, p1, plbar, pl, pa, p2, pb, wprop
);
return ME2h1pp + ME2h1pm + ME2h1mp + ME2h1mm;
}
/**
* @brief W+Jets Unordered Contributions, function to handle all incoming types.
* @param pg Unordered Gluon momenta
* @param p1out Outgoing Particle 1. (Quark - W and Uno emission)
* @param plbar Outgoing election momenta
* @param pl Outgoing neutrino momenta
* @param p1in Incoming Particle 1. (Quark - W and Uno emission)
* @param p2out Outgoing Particle 2
* @param p2in Incoming Particle 2
* @param aqlineb Bool. Is Backwards quark line an anti-quark line?
*
* Calculates j_W_{uno} ^\mu j_\mu. Ie, unordered with W emission same side.
* Handles all possible incoming states. Note this handles both forward and back-
* -ward Wuno emission. For forward, ensure p1out is the uno and W emission parton.
* @TODO: Include separate wrapper functions for forward and backward to clean up
* ME_W_unof_current in `MatrixElement.cc`.
*/
double jWuno_j(HLV pg, HLV p1out, HLV plbar, HLV pl, HLV p1in,
HLV p2out, HLV p2in, bool aqlineb,
ParticleProperties const & wprop
){
const auto helsum = aqlineb?
jWuno_j_helsum<helicity::plus>:
jWuno_j_helsum<helicity::minus>;
//Helicity sum and average over initial states
return helsum(pg, p1out,plbar,pl,p1in,p2out,p2in, wprop)/(4.*HEJ::C_A*HEJ::C_A);
}
}
double ME_Wuno_qQ(HLV p1out, HLV p1in, HLV p2out, HLV p2in,
HLV pg, HLV plbar, HLV pl, ParticleProperties const & wprop
){
return jWuno_j(pg, p1out, plbar, pl, p1in, p2out, p2in, false, wprop);
}
double ME_Wuno_qQbar(HLV p1out, HLV p1in, HLV p2out, HLV p2in,
HLV pg, HLV plbar, HLV pl,
ParticleProperties const & wprop
){
return jWuno_j(pg, p1out, plbar, pl, p1in, p2out, p2in, false, wprop);
}
double ME_Wuno_qbarQ(HLV p1out, HLV p1in, HLV p2out, HLV p2in,
HLV pg, HLV plbar, HLV pl,
ParticleProperties const & wprop
){
return jWuno_j(pg, p1out, plbar, pl, p1in, p2out, p2in, true, wprop);
}
double ME_Wuno_qbarQbar(HLV p1out, HLV p1in, HLV p2out, HLV p2in,
HLV pg, HLV plbar, HLV pl,
ParticleProperties const & wprop
){
return jWuno_j(pg, p1out, plbar, pl, p1in, p2out, p2in, true, wprop);
}
double ME_Wuno_qg(HLV p1out, HLV p1in, HLV p2out, HLV p2in,
HLV pg, HLV plbar, HLV pl, ParticleProperties const & wprop
){
return jWuno_j(pg, p1out, plbar, pl, p1in, p2out, p2in, false, wprop)
*K_g(p2out, p2in)/HEJ::C_F;
}
double ME_Wuno_qbarg(HLV p1out, HLV p1in, HLV p2out, HLV p2in,
HLV pg, HLV plbar, HLV pl,
ParticleProperties const & wprop
){
return jWuno_j(pg, p1out, plbar, pl, p1in, p2out, p2in, true, wprop)
*K_g(p2out, p2in)/HEJ::C_F;
}
// helicity sum helper for jWqqx_j(...)
template<Helicity h1>
double jWqqx_j_helsum(
HLV const & pg, HLV const & pq, HLV const & plbar, HLV const & pl,
HLV const & pqbar, HLV const & p3, HLV const & pb,
ParticleProperties const & wprop
){
using helicity::minus;
using helicity::plus;
const double ME2h1pp = jM2_W_extremal_qqbar<h1, plus, plus>(
pg, pq, plbar, pl, pqbar, p3, pb, wprop
);
const double ME2h1pm = jM2_W_extremal_qqbar<h1, plus, minus>(
pg, pq, plbar, pl, pqbar, p3, pb, wprop
);
const double ME2h1mp = jM2_W_extremal_qqbar<h1, minus, plus>(
pg, pq, plbar, pl, pqbar, p3, pb, wprop
);
const double ME2h1mm = jM2_W_extremal_qqbar<h1, minus, minus>(
pg, pq, plbar, pl, pqbar, p3, pb, wprop
);
return ME2h1pp + ME2h1pm + ME2h1mp + ME2h1mm;
}
/**
* @brief W+Jets Extremal qqx Contributions, function to handle all incoming types.
* @param pgin Incoming gluon which will split into qqx.
* @param pqout Quark of extremal qqx outgoing (W-Emission).
* @param plbar Outgoing anti-lepton momenta
* @param pl Outgoing lepton momenta
* @param pqbarout Anti-quark of extremal qqx pair. (W-Emission)
* @param pout Outgoing Particle 2 (end of FKL chain)
* @param p2in Incoming Particle 2
* @param aqlinef Bool. Is Forwards quark line an anti-quark line?
*
* Calculates j_W_{qqx} ^\mu j_\mu. Ie, Ex-QQX with W emission same side.
* Handles all possible incoming states. Calculated via crossing symmetry from jWuno_j.
*/
double jWqqx_j(HLV pgin, HLV pqout, HLV plbar, HLV pl,
HLV pqbarout, HLV p2out, HLV p2in, bool aqlinef,
ParticleProperties const & wprop
){
const auto helsum = aqlinef?
jWqqx_j_helsum<helicity::plus>:
jWqqx_j_helsum<helicity::minus>;
//Helicity sum and average over initial states.
double ME2 = helsum(pgin, pqout, plbar, pl, pqbarout, p2out, p2in, wprop)/
(4.*HEJ::C_A*HEJ::C_A);
//Correct colour averaging after crossing:
ME2*=(3.0/8.0);
return ME2;
}
double ME_WExqqx_qbarqQ(HLV pgin, HLV pqout, HLV plbar, HLV pl,
HLV pqbarout, HLV p2out, HLV p2in,
ParticleProperties const & wprop
){
return jWqqx_j(pgin, pqout, plbar, pl, pqbarout, p2out, p2in, false, wprop);
}
double ME_WExqqx_qqbarQ(HLV pgin, HLV pqbarout, HLV plbar, HLV pl,
HLV pqout, HLV p2out, HLV p2in,
ParticleProperties const & wprop
){
return jWqqx_j(pgin, pqbarout, plbar, pl, pqout, p2out, p2in, true, wprop);
}
double ME_WExqqx_qbarqg(HLV pgin, HLV pqout, HLV plbar, HLV pl,
HLV pqbarout, HLV p2out, HLV p2in,
ParticleProperties const & wprop
){
return jWqqx_j(pgin, pqout, plbar, pl, pqbarout, p2out, p2in, false, wprop)
*K_g(p2out,p2in)/HEJ::C_F;
}
double ME_WExqqx_qqbarg(HLV pgin, HLV pqbarout, HLV plbar, HLV pl,
HLV pqout, HLV p2out, HLV p2in,
ParticleProperties const & wprop
){
return jWqqx_j(pgin, pqbarout, plbar, pl, pqout, p2out, p2in, true, wprop)
*K_g(p2out,p2in)/HEJ::C_F;
}
namespace {
-//Function to calculate Term 1 in Equation 3.23 in James Cockburn's Thesis.
- Tensor<1> qggm1(HLV pb, HLV p2, HLV p3, Helicity hel2, Helicity helg, HLV refmom){
- //@TODO Simplify the calculation below. (Less Tensor class use?)
- double t1 = (p3-pb)*(p3-pb);
- // Gauge choice in polarisation tensor. (see JC's Thesis)
- Tensor<1> epsg = eps(pb, refmom, helg);
- Tensor<3> qqCurBlank = rank3_current(p2,p3,hel2);
- Tensor<2> qqCur = qqCurBlank.contract(p3-pb,2);
- Tensor<1> gqqCur = qqCur.contract(epsg,2)/t1;
-
- return gqqCur*(-1);
- }
+ template<Helicity h1, Helicity hg>
+ double jW_jqqbar(
+ HLV const & pb,
+ HLV const & p2,
+ HLV const & p3,
+ HLV const & pa,
+ HLV const & p1,
+ HLV const & pl,
+ HLV const & plbar
+ ) {
+ using helicity::minus;
+ using helicity::plus;
-//Function to calculate Term 2 in Equation 3.23 in James Cockburn's Thesis.
- Tensor<1> qggm2(HLV pb, HLV p2, HLV p3, Helicity hel2, Helicity helg, HLV refmom){
- //@TODO Simplify the calculation below (Less Tensor class use?)
- double t1 = (p2-pb)*(p2-pb);
- // Gauge choice in polarisation tensor. (see JC's Thesis)
- Tensor<1> epsg = eps(pb,refmom, helg);
- Tensor<3> qqCurBlank = rank3_current(p2,p3,hel2);
- Tensor<2> qqCur = qqCurBlank.contract(p2-pb,2);
- Tensor<1> gqqCur = qqCur.contract(epsg,1)/t1;
-
- return gqqCur;
- }
+ static constexpr COM cm1m1 = 8./3.;
+ static constexpr COM cm2m2 = 8./3.;
+ static constexpr COM cm3m3 = 6.;
+ static constexpr COM cm1m2 =-1./3.;
+ static constexpr COM cm1m3 = COM{0.,-3.};
+ static constexpr COM cm2m3 = COM{0.,3.};
+
+ const COM m1 = HEJ::jW_qggm1<h1,hg>(pb,p2,p3,pa,p1,pl,plbar);
+ const COM m2 = HEJ::jW_qggm2<h1,hg>(pb,p2,p3,pa,p1,pl,plbar);
+ const COM m3 = HEJ::jW_qggm3<h1,hg>(pb,p2,p3,pa,p1,pl,plbar);
-//Function to calculate Term 3 in Equation 3.23 in James Cockburn's Thesis.
- Tensor<1> qggm3(HLV pb, HLV p2, HLV p3, Helicity hel2, Helicity helg, HLV refmom){
- //@TODO Simplify the calculation below (Less Tensor class use?)
- double s23 = (p2+p3)*(p2+p3);
- // Gauge choice in polarisation tensor. (see JC's Thesis)
- Tensor<1> epsg = eps(pb, refmom, helg);
- Tensor<3> qqCurBlank1 = outer(p2+p3, metric())/s23;
- Tensor<3> qqCurBlank2 = outer(pb, metric())/s23;
- Tensor<1> Cur23 = HEJ::current(p2, 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;
+ return real(
+ cm1m1*pow(abs(m1),2) + cm2m2*pow(abs(m2),2)
+ + cm3m3*pow(abs(m3),2) + 2.*real(cm1m2*m1*conj(m2))
+ )
+ + 2.*real(cm1m3*m1*conj(m3))
+ + 2.*real(cm2m3*m2*conj(m3)) ;
}
}
-// no wqq emission
-double ME_W_Exqqx_QQq(HLV pa, HLV pb, HLV p1, HLV p2,
- HLV p3,HLV plbar, HLV pl, bool aqlinepa,
- ParticleProperties const & wprop
+// contraction of W current with extremal qqbar on the other side
+double ME_W_Exqqx_QQq(
+ HLV pa, HLV pb,
+ HLV p1, HLV p2,
+ HLV p3, HLV plbar, HLV pl, bool aqlinepa,
+ ParticleProperties const & wprop
){
using helicity::minus;
using helicity::plus;
- init_sigma_index();
-
- // 2 independent helicity choices (complex conjugation related).
- Tensor<1> TMmmm1 = qggm1(pb,p2,p3,minus,minus, pa);
- Tensor<1> TMmmm2 = qggm2(pb,p2,p3,minus,minus, pa);
- Tensor<1> TMmmm3 = qggm3(pb,p2,p3,minus,minus, pa);
- Tensor<1> TMpmm1 = qggm1(pb,p2,p3,minus,plus, pa);
- Tensor<1> TMpmm2 = qggm2(pb,p2,p3,minus,plus, pa);
- Tensor<1> TMpmm3 = qggm3(pb,p2,p3,minus,plus, pa);
-
- // Build the external quark line W Emmision
- Tensor<1> cur1a = jW(pa,p1,plbar,pl, aqlinepa?plus:minus);
-
- //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
const double WPropfact = WProp(plbar, pl, wprop);
- return (2*WPropfact*(Mmmm+Mpmm)/24./4.)/(pa-p1-pl-plbar).m2()/(p2+p3-pb).m2();
+ const double prefactor = 2.*WPropfact/24./4./(
+ (pa-p1-pl-plbar).m2()*(p2+p3-pb).m2()
+ );
+ if(aqlinepa) {
+ return prefactor*(
+ jW_jqqbar<plus, minus>(pb,p2,p3,pa,p1,pl,plbar)
+ + jW_jqqbar<plus, plus>(pb,p2,p3,pa,p1,pl,plbar)
+ );
+ }
+ return prefactor*(
+ jW_jqqbar<minus, minus>(pb,p2,p3,pa,p1,pl,plbar)
+ + jW_jqqbar<minus, plus>(pb,p2,p3,pa,p1,pl,plbar)
+ );
}
namespace {
// helper function for matrix element for W + Jets with central qqbar
template<HEJ::Helicity h1a, HEJ::Helicity h4b>
double amp_WCenqqx_qq(
HLV const & pa, HLV const & p1,
HLV const & pb, HLV const & p4,
HLV const & pq, HLV const & pqbar,
HLV const & pl, HLV const & plbar,
HLV const & q11, HLV const & q12
) {
const COM sym = HEJ::M_sym_W<h1a, h4b>(
pa, p1, pb, p4, pq, pqbar, pl, plbar, q11, q12
);
const COM cross = HEJ::M_cross_W<h1a, h4b>(
pa, p1, pb, p4, pq, pqbar, pl, plbar, q11, q12
);
const COM uncross = HEJ::M_uncross_W<h1a, h4b>(
pa, p1, pb, p4, pq, pqbar, pl, plbar, q11, q12
);
// Colour factors
static constexpr COM cmsms = 3.;
static constexpr COM cmumu = 4./3.;
static constexpr COM cmcmc = 4./3.;
static constexpr COM cmsmu = COM{0., 3./2.};
static constexpr COM cmsmc = COM{0.,-3./2.};
static constexpr COM cmumc = -1./6.;
return real(
cmsms*pow(abs(sym),2)
+cmumu*pow(abs(uncross),2)
+cmcmc*pow(abs(cross),2)
)
+2.*real(cmsmu*sym*conj(uncross))
+2.*real(cmsmc*sym*conj(cross))
+2.*real(cmumc*uncross*conj(cross))
;
}
}
// matrix element for W + Jets with W emission off central qqbar
double ME_WCenqqx_qq(
HLV pa, HLV pb, HLV pl, HLV plbar, std::vector<HLV> partons,
bool /* aqlinepa */, bool /* aqlinepb */, bool qqxmarker, int nabove,
ParticleProperties const & wprop
) {
using helicity::plus;
using helicity::minus;
CLHEP::HepLorentzVector q1 = pa;
for(int i = 0; i <= nabove; ++i){
q1 -= partons[i];
}
const auto qq = HEJ::split_into_lightlike(q1);
// since q1.m2() < 0 the following assertion is always true
// see documentation for split_into_lightlike
assert(qq.second.e() < 0);
HLV pq, pqbar;
if (qqxmarker){
pqbar = partons[nabove+1];
pq = partons[nabove+2];}
else{
pq = partons[nabove+1];
pqbar = partons[nabove+2];
}
const HLV p1 = partons.front();
const HLV p4 = partons.back();
// 4 Different Helicity Choices (Differs from Pure Jet Case, where there is
// also the choice in qqbar helicity.
// the first helicity label is for aqlinepa == true,
// the second one for aqlinepb == true
// In principle the corresponding helicity should be flipped
// if either of them is false, but we sum up all helicities,
// so this has no effect in the end.
const double amp_mm = amp_WCenqqx_qq<minus, minus>(
pa, p1, pb, p4, pq, pqbar, pl, plbar, qq.first, -qq.second
);
const double amp_mp = amp_WCenqqx_qq<minus, plus>(
pa, p1, pb, p4, pq, pqbar, pl, plbar, qq.first, -qq.second
);
const double amp_pm = amp_WCenqqx_qq<plus, minus>(
pa, p1, pb, p4, pq, pqbar, pl, plbar, qq.first, -qq.second
);
const double amp_pp = amp_WCenqqx_qq<plus, plus>(
pa, p1, pb, p4, pq, pqbar, pl, plbar, qq.first, -qq.second
);
const double t1 = q1.m2();
const double t3 = (q1-pl-plbar-pq-pqbar).m2();
const double amp = WProp(plbar, pl, wprop)*(
amp_mm+amp_mp+amp_pm+amp_pp
)/(9.*4.*t1*t1*t3*t3);
return amp;
}
// helper function for matrix element for W + Jets with central qqbar
// W emitted off extremal parton
// @TODO: code duplication with amp_WCenqqx_qq
template<HEJ::Helicity h1a, HEJ::Helicity hqqbar>
double amp_W_Cenqqx_qq(
HLV const & pa, HLV const & p1,
HLV const & pb, HLV const & p4,
HLV const & pq, HLV const & pqbar,
HLV const & pl, HLV const & plbar,
HLV const & q11, HLV const & q12
) {
const COM crossed = HEJ::M_cross<h1a, hqqbar>(
pa, p1, pb, p4, pq, pqbar, pl, plbar, q11, q12
);
const COM uncrossed = HEJ::M_qbar<h1a, hqqbar>(
pa, p1, pb, p4, pq, pqbar, pl, plbar, q11, q12
);
const COM sym = HEJ::M_sym<h1a, hqqbar>(
pa, p1, pb, p4, pq, pqbar, pl, plbar, q11, q12
);
//Colour factors:
static constexpr COM cmsms = 3.;
static constexpr COM cmumu = 4./3.;
static constexpr COM cmcmc = 4./3.;
static constexpr COM cmsmu = COM{0.,3./2.};
static constexpr COM cmsmc = COM{0.,-3./2.};
static constexpr COM cmumc = -1./6.;
return real(
cmsms*pow(abs(sym),2)
+cmumu*pow(abs(uncrossed),2)
+cmcmc*pow(abs(crossed),2)
)
+2.*real(cmsmu*sym*conj(uncrossed))
+2.*real(cmsmc*sym*conj(crossed))
+2.*real(cmumc*uncrossed*conj(crossed))
;
}
// matrix element for W + Jets with W emission *not* off central qqbar
double ME_W_Cenqqx_qq(
HLV pa, HLV pb,HLV pl,HLV plbar, std::vector<HLV> partons,
bool aqlinepa, bool aqlinepb, bool qqxmarker, int nabove,
int nbelow, bool forwards, ParticleProperties const & wprop
){
using helicity::minus;
using helicity::plus;
if (!forwards){ //If Emission from Leg a instead, flip process.
std::swap(pa, pb);
std::reverse(partons.begin(),partons.end());
std::swap(aqlinepa, aqlinepb);
qqxmarker = !qqxmarker;
std::swap(nabove,nbelow);
}
HLV q1=pa;
for(int i=0;i<nabove+1;++i){
q1-=partons.at(i);
}
const auto qq = HEJ::split_into_lightlike(q1);
HLV pq, pqbar;
if (qqxmarker){
pqbar = partons[nabove+1];
pq = partons[nabove+2];}
else{
pq = partons[nabove+1];
pqbar = partons[nabove+2];}
// we assume that the W is emitted off a quark line
// if this is not the case, we have to apply CP conjugation,
// which is equivalent to swapping lepton and antilepton momenta
if(aqlinepb) std::swap(pl, plbar);
const HLV p1 = partons.front();
const HLV p4 = partons.back();
// helicity labels are for aqlinepa == aqlineb == false,
// In principle the helicities should be flipped
// if either of them is true, but we sum up all helicities,
// so this has no effect in the end.
const double amp_mm = amp_W_Cenqqx_qq<minus, minus>(
pa, p1, pb, p4, pq, pqbar, pl, plbar, qq.first, -qq.second
);
const double amp_mp = amp_W_Cenqqx_qq<minus, plus>(
pa, p1, pb, p4, pq, pqbar, pl, plbar, qq.first, -qq.second
);
const double amp_pm = amp_W_Cenqqx_qq<plus, minus>(
pa, p1, pb, p4, pq, pqbar, pl, plbar, qq.first, -qq.second
);
const double amp_pp = amp_W_Cenqqx_qq<plus, plus>(
pa, p1, pb, p4, pq, pqbar, pl, plbar, qq.first, -qq.second
);
const double t1 = q1.m2();
const double t3 = (q1 - pq - pqbar).m2();
const double amp= WProp(plbar, pl, wprop)*(
amp_mm+amp_mp+amp_pm+amp_pp
)/(9.*4.*t1*t1*t3*t3);
return amp;
}
diff --git a/t/ME_data/ME_Wp.dat b/t/ME_data/ME_Wp.dat
index 21d025b..bc2417a 100644
--- a/t/ME_data/ME_Wp.dat
+++ b/t/ME_data/ME_Wp.dat
@@ -1,9517 +1,9517 @@
8.260048810e-11
5.469891741e-14
1.192453510e-13
3.824158135e-11
2.764420182e-10
1.856558271e-10
1.755866646e-08
6.565387692e-05
9.622995901e-08
1.928598102e-11
1.226291593e-10
5.432088384e-10
2.853465399e-10
6.551510279e-11
8.988447022e-12
3.230211223e-15
8.677438755e-11
9.352689977e-11
1.982414034e-15
4.578280600e-11
2.750042768e-08
1.711771844e-12
3.008414565e-10
1.526877992e-10
4.991816140e-14
3.532550758e-12
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1.533615934e-13
3.095682964e-11
1.506784776e-09
6.557924854e-07
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6.138303610e-11
1.262734891e-14
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1.749652043e-13
1.699911990e-11
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1.643649041e-14
4.482336528e-14
5.783400774e-17
1.793864686e-12
6.404740116e-10
1.902651375e-10
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2.255639166e-17
1.267602042e-19
5.726070605e-16
3.036365136e-19
4.655693619e-13
4.166042416e-13
6.433132242e-22
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3.179587261e-11
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1.469624766e-10
1.750815635e-10
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3.289892028e-12
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1.490810182e-15
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5.584132251e-09
1.354596481e-11
1.804238531e-05
2.610832978e-09
1.425690400e-10
3.993672540e-10
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1.229708950e-08
1.697500888e-08
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1.926261824e-16
3.003272402e-17
4.112179935e-15
4.930558855e-15
5.897378897e-09
4.009641672e-11
1.036139947e-11
6.904861881e-14
8.323716307e-14
1.495283429e-13
3.007511843e-15
3.007511843e-15
1.611730319e-09
1.546544705e-10
1.153295210e-12
2.646751897e-11
2.646751897e-11
2.735914721e-12
1.327921238e-08
8.189911859e-12
3.050998283e-16
2.505873168e-14
1.404304315e-16
1.047884247e-09
2.902799873e-10
2.703371098e-11
6.717286156e-11
1.449556420e-10
1.097125020e-07
1.150131521e-12
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2.200825894e-18
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2.553961370e-11
3.553171647e-09
3.637895246e-09
6.273840781e-08
3.160500833e-15
4.534211952e-09
1.994820773e-16
2.799642278e-12
5.633227882e-11
1.825052638e-18
5.830077500e-20
1.323403136e-08
2.784275986e-07
5.000067138e-09
2.791543682e-10
7.114652207e-12
4.319031885e-14
2.743604190e-12
3.394491837e-18
3.297799681e-12
8.867542559e-17
3.334338483e-16
1.014767913e-15
4.771269265e-15
1.090221195e-16
6.325484210e-15
5.787026279e-16
2.473604060e-11
5.391522870e-11
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1.563249129e-12
1.910758007e-11
7.949523788e-12
1.477282689e-12
6.530282360e-07
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1.328393047e-15
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2.453282188e-08
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1.762415995e-11
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1.456727889e-10
3.475420737e-09
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1.837550428e-12
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4.939746214e-15
1.709995352e-15
1.129152376e-12
1.670363997e-11
1.933897190e-10
3.839284419e-11
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1.124049763e-14
6.330268263e-14
8.870816093e-13
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2.982725847e-12
8.252905630e-11
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3.132789543e-09
3.684641602e-13
1.336685602e-17
9.866834122e-17
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2.873117620e-14
2.065699998e-13
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2.084591739e-16
5.104966270e-17
1.556813840e-13
4.636813042e-17
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3.051892715e-11
3.450971445e-11
4.568377078e-10
1.265235455e-13
1.759916583e-11
3.926586066e-17
2.331638310e-19
5.562789275e-17
3.926586066e-17
2.284724356e-08
9.043756696e-04
4.769104112e-05
2.304404864e-11
2.906586158e-10
3.760451941e-09
1.439690441e-12
9.140865484e-10
3.420009770e-12
5.964850716e-09
8.754531473e-09
2.691065091e-12
1.713354850e-01
1.889633855e-12
3.980097986e-13
1.025632819e-15
7.487795609e-17
1.683027081e-13
1.313269173e-12
2.883260303e-12
1.038602647e-06
1.677340341e-08
1.244953649e-10
3.280552318e-11
9.610838144e-07
2.541913000e-13
6.295318636e-12
6.640075757e-12
3.363446555e-12
3.158670881e-09
5.848314606e-10
5.368846192e-11
3.467056654e-10
2.381923613e-15
9.768945850e-14
1.000018520e-09
2.385520609e-15
2.521249070e-14
6.667415606e-16
4.160639712e-15
4.350240774e-12
9.326759913e-10
1.587175880e-11
3.056453095e-12
1.431064485e-11
1.740815792e-16
3.625376953e-15
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