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/**
* \authors The HEJ collaboration (see AUTHORS for details)
* \date 2020
* \copyright GPLv2 or later
*/
#include "HEJ/Wjets.hh"
#include <algorithm>
#include <array>
#include <cassert>
#include <cmath>
#include <iostream>
#include "HEJ/Constants.hh"
#include "HEJ/EWConstants.hh"
#include "HEJ/LorentzVector.hh"
#include "HEJ/exceptions.hh"
#include "HEJ/jets.hh"
// generated headers
#include "HEJ/currents/jV_j.hh"
#include "HEJ/currents/jV_juno.hh"
#include "HEJ/currents/jVuno_j.hh"
#include "HEJ/currents/jW_jqqbar.hh"
#include "HEJ/currents/jW_qqbar_j.hh"
#include "HEJ/currents/jWqqbar_j.hh"
#include "HEJ/currents/j_Wqqbar_j.hh"
namespace HEJ {
namespace currents {
namespace {
using COM = std::complex<double>;
// --- 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;
}
/**
* @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 helicity::minus;
const COM u1 = U1<h1, minus, h2, pol>(p1, p2, pa, pb, pg, pl, plbar);
const COM u2 = U2<h1, minus, h2, pol>(p1, p2, pa, pb, pg, pl, plbar);
const COM l = L<h1, minus, 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)) - 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
){
const COM u1Xcontr = U1X<h1, h2, hg>(pg, pq, plbar, pl, pqbar, p3, pb);
const COM u2Xcontr = U2X<h1, h2, hg>(pg, pq, plbar, pl, pqbar, p3, pb);
const COM lXcontr = 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)) - C_F/2.*(x*conj(y)).real();
amp *= WProp(plbar, pl, wprop);
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 const & p1out, HLV plbar, HLV pl,
HLV const & p1in, HLV const & p2out, HLV const & 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);
// 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(aqlineb) std::swap(pl, plbar);
const COM ampm = jV_j<minus, minus, minus>(p1in,p1out,p2in,p2out,pl,plbar);
const COM ampp = jV_j<minus, minus, plus>(p1in,p1out,p2in,p2out,pl,plbar);
const double Msqr = std::norm(ampm) + std::norm(ampp);
// Division by colour and Helicity average (Nc2-1)(4)
// Multiply by Cf^2
return C_F*C_F*wPropfact*Msqr/(q1.m2()*q2.m2()*(N_C*N_C - 1)*4);
}
} // Anonymous Namespace
double ME_W_qQ(
HLV const & p1out,
HLV const & plbar, HLV const & pl,
HLV const & p1in,
HLV const & p2out, HLV const & p2in,
ParticleProperties const & wprop
){
return jW_j(p1out, plbar, pl, p1in, p2out, p2in, false, false, wprop);
}
double ME_W_qQbar(
HLV const & p1out,
HLV const & plbar, HLV const & pl,
HLV const & p1in,
HLV const & p2out, HLV const & p2in,
ParticleProperties const & wprop
){
return jW_j(p1out, plbar, pl, p1in, p2out, p2in, false, true, wprop);
}
double ME_W_qbarQ(
HLV const & p1out,
HLV const & plbar, HLV const & pl,
HLV const & p1in,
HLV const & p2out, HLV const & p2in,
ParticleProperties const & wprop
){
return jW_j(p1out, plbar, pl, p1in, p2out, p2in, true, false, wprop);
}
double ME_W_qbarQbar(
HLV const & p1out,
HLV const & plbar, HLV const & pl,
HLV const & p1in,
HLV const & p2out, HLV const & p2in,
ParticleProperties const & wprop
){
return jW_j(p1out, plbar, pl, p1in, p2out, p2in, true, true, wprop);
}
double ME_W_qg(
HLV const & p1out,
HLV const & plbar, HLV const & pl,
HLV const & p1in,
HLV const & p2out, HLV const & p2in,
ParticleProperties const & wprop
){
return jW_j(p1out, plbar, pl, p1in, p2out, p2in, false, false, wprop)
*K_g(p2out, p2in)/C_F;
}
double ME_W_qbarg(
HLV const & p1out,
HLV const & plbar, HLV const & pl,
HLV const & p1in,
HLV const & p2out, HLV const & p2in,
ParticleProperties const & wprop
){
return jW_j(p1out, plbar, pl, p1in, p2out, p2in, true, false, wprop)
*K_g(p2out, p2in)/C_F;
}
namespace {
// helicity amplitude squares for contraction of W current with unordered
// current
template<Helicity h2, Helicity hg>
double ampsq_jW_juno(
HLV const & pa, HLV const & p1,
HLV const & pb, HLV const & p2,
HLV const & pg,
HLV const & pl, HLV const & plbar
){
using helicity::minus;
const COM u1 = U1_jV<minus, minus, h2, hg>(pa,p1,pb,p2,pg,pl,plbar);
const COM u2 = U2_jV<minus, minus, h2, hg>(pa,p1,pb,p2,pg,pl,plbar);
const COM l = L_jV<minus, minus, h2, hg>(pa,p1,pb,p2,pg,pl,plbar);
return 2.*C_F*std::real((l-u1)*std::conj(l+u2))
+ 2.*C_F*C_F/3.*std::norm(u1+u2)
;
}
/**
* @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.
*
* @TODO use const & for pl plbar
*/
double jW_juno(
HLV const & p1out, HLV plbar, HLV pl, HLV const & p1in,
HLV const & p2out, HLV const & p2in, HLV const & pg, bool aqlineb,
bool /* aqlinef */,
ParticleProperties const & wprop
){
using helicity::minus;
using helicity::plus;
// 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(aqlineb) std::swap(pl, plbar);
// helicity assignments assume aqlinef == false
// in the end, this is irrelevant since we sum over all helicities
const double ampsq =
+ ampsq_jW_juno<minus, minus>(p1in,p1out,p2in,p2out,pg,pl,plbar)
+ ampsq_jW_juno<minus, plus>(p1in,p1out,p2in,p2out,pg,pl,plbar)
+ ampsq_jW_juno<plus, minus>(p1in,p1out,p2in,p2out,pg,pl,plbar)
+ ampsq_jW_juno<plus, plus>(p1in,p1out,p2in,p2out,pg,pl,plbar)
;
const HLV q1=p1in-p1out-plbar-pl;
const HLV q2=-(p2in-p2out-pg);
//! @TODO explain magic 16
return WProp(plbar, pl, wprop)*ampsq/(16.*q2.m2()*q1.m2());
}
} // Anonymous Namespace
double ME_W_unob_qQ(
HLV const & p1out, HLV const & p1in, HLV const & p2out, HLV const & p2in,
HLV const & pg, HLV const & plbar, HLV const & pl, ParticleProperties
const & wprop
){
return jW_juno(p2out, plbar, pl, p2in, p1out, p1in, pg, false, false, wprop);
}
double ME_W_unob_qQbar(
HLV const & p1out, HLV const & p1in, HLV const & p2out, HLV const & p2in,
HLV const & pg, HLV const & plbar, HLV const & pl,
ParticleProperties const & wprop
){
return jW_juno(p2out, plbar, pl, p2in, p1out, p1in, pg, false, true, wprop);
}
double ME_W_unob_qbarQ(
HLV const & p1out, HLV const & p1in, HLV const & p2out, HLV const & p2in,
HLV const & pg, HLV const & plbar, HLV const & pl,
ParticleProperties const & wprop
){
return jW_juno(p2out, plbar, pl, p2in, p1out, p1in, pg, true, false, wprop);
}
double ME_W_unob_qbarQbar(
HLV const & p1out, HLV const & p1in, HLV const & p2out, HLV const & p2in,
HLV const & pg, HLV const & plbar, HLV const & 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 const & pg, HLV const & p1out, HLV const & plbar, HLV const & pl,
HLV const & p1in, HLV const & p2out, HLV const & 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.*C_A*C_A);
}
} // Anonymous Namespace
double ME_Wuno_qQ(
HLV const & p1out, HLV const & p1in, HLV const & p2out, HLV const & p2in,
HLV const & pg, HLV const & plbar, HLV const & pl,
ParticleProperties const & wprop
){
return jWuno_j(pg, p1out, plbar, pl, p1in, p2out, p2in, false, wprop);
}
double ME_Wuno_qQbar(
HLV const & p1out, HLV const & p1in, HLV const & p2out, HLV const & p2in,
HLV const & pg, HLV const & plbar, HLV const & pl,
ParticleProperties const & wprop
){
return jWuno_j(pg, p1out, plbar, pl, p1in, p2out, p2in, false, wprop);
}
double ME_Wuno_qbarQ(
HLV const & p1out, HLV const & p1in, HLV const & p2out, HLV const & p2in,
HLV const & pg, HLV const & plbar, HLV const & pl,
ParticleProperties const & wprop
){
return jWuno_j(pg, p1out, plbar, pl, p1in, p2out, p2in, true, wprop);
}
double ME_Wuno_qbarQbar(
HLV const & p1out, HLV const & p1in, HLV const & p2out, HLV const & p2in,
HLV const & pg, HLV const & plbar, HLV const & pl,
ParticleProperties const & wprop
){
return jWuno_j(pg, p1out, plbar, pl, p1in, p2out, p2in, true, wprop);
}
double ME_Wuno_qg(
HLV const & p1out, HLV const & p1in, HLV const & p2out, HLV const & p2in,
HLV const & pg, HLV const & plbar, HLV const & pl,
ParticleProperties const & wprop
){
return jWuno_j(pg, p1out, plbar, pl, p1in, p2out, p2in, false, wprop)
*K_g(p2out, p2in)/C_F;
}
double ME_Wuno_qbarg(
HLV const & p1out, HLV const & p1in, HLV const & p2out, HLV const & p2in,
HLV const & pg, HLV const & plbar, HLV const & pl,
ParticleProperties const & wprop
){
return jWuno_j(pg, p1out, plbar, pl, p1in, p2out, p2in, true, wprop)
*K_g(p2out, p2in)/C_F;
}
// helicity sum helper for jWqqbar_j(...)
template<Helicity h1>
double jWqqbar_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 amp_h1pp = jM2_W_extremal_qqbar<h1, plus, plus>(
pg, pq, plbar, pl, pqbar, p3, pb, wprop
);
const double amp_h1pm = jM2_W_extremal_qqbar<h1, plus, minus>(
pg, pq, plbar, pl, pqbar, p3, pb, wprop
);
const double amp_h1mp = jM2_W_extremal_qqbar<h1, minus, plus>(
pg, pq, plbar, pl, pqbar, p3, pb, wprop
);
const double amp_h1mm = jM2_W_extremal_qqbar<h1, minus, minus>(
pg, pq, plbar, pl, pqbar, p3, pb, wprop
);
return amp_h1pp + amp_h1pm + amp_h1mp + amp_h1mm;
}
/**
* @brief W+Jets Extremal qqbar Contributions, function to handle all incoming
* @types.
* @param pgin Incoming gluon which will split into qqbar.
* @param pqout Quark of extremal qqbar outgoing (W-Emission).
* @param plbar Outgoing anti-lepton momenta
* @param pl Outgoing lepton momenta
* @param pqbarout Anti-quark of extremal qqbar 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_{qqbar} ^\mu j_\mu. Ie, Ex-QQbar with W emission same side.
* Handles all possible incoming states. Calculated via crossing symmetry from
* jWuno_j.
*/
double jWqqbar_j(
HLV const & pgin, HLV const & pqout, HLV const & plbar, HLV const & pl,
HLV const & pqbarout, HLV const & p2out, HLV const & p2in, bool aqlinef,
ParticleProperties const & wprop
){
const auto helsum = aqlinef?
jWqqbar_j_helsum<helicity::plus>:
jWqqbar_j_helsum<helicity::minus>;
//Helicity sum and average over initial states.
double ME2 = helsum(pgin, pqout, plbar, pl, pqbarout, p2out, p2in, wprop)/
(4.*C_A*C_A);
//Correct colour averaging after crossing:
ME2*=(3.0/8.0);
return ME2;
}
double ME_WExqqbar_qbarqQ(
HLV const & pgin, HLV const & pqout, HLV const & plbar, HLV const & pl,
HLV const & pqbarout, HLV const & p2out, HLV const & p2in,
ParticleProperties const & wprop
){
return jWqqbar_j(pgin, pqout, plbar, pl, pqbarout, p2out, p2in, false, wprop);
}
double ME_WExqqbar_qqbarQ(
HLV const & pgin, HLV const & pqbarout, HLV const & plbar, HLV const & pl,
HLV const & pqout, HLV const & p2out, HLV const & p2in,
ParticleProperties const & wprop
){
return jWqqbar_j(pgin, pqbarout, plbar, pl, pqout, p2out, p2in, true, wprop);
}
double ME_WExqqbar_qbarqg(
HLV const & pgin, HLV const & pqout, HLV const & plbar, HLV const & pl,
HLV const & pqbarout, HLV const & p2out, HLV const & p2in,
ParticleProperties const & wprop
){
return jWqqbar_j(pgin, pqout, plbar, pl, pqbarout, p2out, p2in, false, wprop)
*K_g(p2out,p2in)/C_F;
}
double ME_WExqqbar_qqbarg(
HLV const & pgin, HLV const & pqbarout, HLV const & plbar, HLV const & pl,
HLV const & pqout, HLV const & p2out, HLV const & p2in,
ParticleProperties const & wprop
){
return jWqqbar_j(pgin, pqbarout, plbar, pl, pqout, p2out, p2in, true, wprop)
*K_g(p2out,p2in)/C_F;
}
namespace {
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 std::norm;
static constexpr double cm1m1 = 8./3.;
static constexpr double cm2m2 = 8./3.;
static constexpr double cm3m3 = 6.;
static constexpr double cm1m2 =-1./3.;
static constexpr COM cm1m3 = COM{0.,-3.};
static constexpr COM cm2m3 = COM{0.,3.};
const COM m1 = jW_qggm1<h1,hg>(pb,p2,p3,pa,p1,pl,plbar);
const COM m2 = jW_qggm2<h1,hg>(pb,p2,p3,pa,p1,pl,plbar);
const COM m3 = jW_qggm3<h1,hg>(pb,p2,p3,pa,p1,pl,plbar);
return
+ cm1m1*norm(m1)
+ cm2m2*norm(m2)
+ cm3m3*norm(m3)
+ 2.*real(cm1m2*m1*conj(m2))
+ 2.*real(cm1m3*m1*conj(m3))
+ 2.*real(cm2m3*m2*conj(m3)) ;
}
} // Anonymous Namespace
// contraction of W current with extremal qqbar on the other side
double ME_W_Exqqbar_QQq(
HLV const & pa, HLV const & pb,
HLV const & p1, HLV const & p2,
HLV const & p3, HLV const & plbar, HLV const & pl, bool aqlinepa,
ParticleProperties const & wprop
){
using helicity::minus;
using helicity::plus;
const double wPropfact = WProp(plbar, pl, wprop);
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<Helicity h1a, Helicity h4b>
double amp_WCenqqbar_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
){
using std::norm;
const COM sym = M_sym_W<h1a, h4b>(
pa, p1, pb, p4, pq, pqbar, pl, plbar, q11, q12
);
const COM cross = M_cross_W<h1a, h4b>(
pa, p1, pb, p4, pq, pqbar, pl, plbar, q11, q12
);
const COM uncross = M_uncross_W<h1a, h4b>(
pa, p1, pb, p4, pq, pqbar, pl, plbar, q11, q12
);
// Colour factors
static constexpr double cmsms = 3.;
static constexpr double cmumu = 4./3.;
static constexpr double cmcmc = 4./3.;
static constexpr COM cmsmu = COM{0., 3./2.};
static constexpr COM cmsmc = COM{0.,-3./2.};
static constexpr double cmumc = -1./6.;
return
+cmsms*norm(sym)
+cmumu*norm(uncross)
+cmcmc*norm(cross)
+2.*real(cmsmu*sym*conj(uncross))
+2.*real(cmsmc*sym*conj(cross))
+2.*real(cmumc*uncross*conj(cross))
;
}
} // Anonymous Namespace
// matrix element for W + Jets with W emission off central qqbar
double ME_WCenqqbar_qq(
HLV const & pa, HLV const & pb, HLV const & pl, HLV const & plbar,
std::vector<HLV> const & partons, bool /* aqlinepa */, bool /* aqlinepb */,
bool qqbar_marker, 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 = 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;
HLV pqbar;
if (qqbar_marker){
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_WCenqqbar_qq<minus, minus>(
pa, p1, pb, p4, pq, pqbar, pl, plbar, qq.first, -qq.second
);
const double amp_mp = amp_WCenqqbar_qq<minus, plus>(
pa, p1, pb, p4, pq, pqbar, pl, plbar, qq.first, -qq.second
);
const double amp_pm = amp_WCenqqbar_qq<plus, minus>(
pa, p1, pb, p4, pq, pqbar, pl, plbar, qq.first, -qq.second
);
const double amp_pp = amp_WCenqqbar_qq<plus, plus>(
pa, p1, pb, p4, pq, pqbar, pl, plbar, qq.first, -qq.second
);
// Divide by t channels, extremal + adjacent central vertex
const double ta = (pa-p1).m2();
const double t1 = q1.m2();
const double t3 = (q1-pl-plbar-pq-pqbar).m2();
const double tb = (p4-pb).m2();
const double amp = WProp(plbar, pl, wprop)*(
amp_mm+amp_mp+amp_pm+amp_pp
)/(9.*4.*ta*t1*t3*tb);
return amp;
}
// helper function for matrix element for W + Jets with central qqbar
// W emitted off extremal parton
// @TODO: code duplication with amp_WCenqqbar_qq
template<Helicity h1a, Helicity hqqbar>
double amp_W_Cenqqbar_qq(
HLV const & pa, HLV const & p1,
HLV const & pb, HLV const & pn,
HLV const & pq, HLV const & pqbar,
HLV const & pl, HLV const & plbar,
HLV const & q11, HLV const & q12
){
using std::norm;
const COM crossed = M_cross<h1a, hqqbar>(
pa, p1, pb, pn, pq, pqbar, pl, plbar, q11, q12
);
const COM uncrossed = M_qbar<h1a, hqqbar>(
pa, p1, pb, pn, pq, pqbar, pl, plbar, q11, q12
);
const COM sym = M_sym<h1a, hqqbar>(
pa, p1, pb, pn, pq, pqbar, pl, plbar, q11, q12
);
//Colour factors:
static constexpr double cmsms = 3.;
static constexpr double cmumu = 4./3.;
static constexpr double cmcmc = 4./3.;
static constexpr COM cmsmu = COM{0.,3./2.};
static constexpr COM cmsmc = COM{0.,-3./2.};
static constexpr double cmumc = -1./6.;
return
+cmsms*norm(sym)
+cmumu*norm(uncrossed)
+cmcmc*norm(crossed)
+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_Cenqqbar_qq(
HLV pa, HLV pb, HLV pl,HLV plbar,
std::vector<HLV> partons, bool aqlinepa, bool aqlinepb,
bool qqbar_marker, 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);
qqbar_marker = !qqbar_marker;
std::swap(nabove,nbelow);
}
HLV q1=pa;
for(int i=0;i<nabove+1;++i){
q1-=partons.at(i);
}
const auto qq = split_into_lightlike(q1);
HLV pq;
HLV pqbar;
if (qqbar_marker){
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 pn = 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_Cenqqbar_qq<minus, minus>(
pa, p1, pb, pn, pq, pqbar, pl, plbar, qq.first, -qq.second
);
const double amp_mp = amp_W_Cenqqbar_qq<minus, plus>(
pa, p1, pb, pn, pq, pqbar, pl, plbar, qq.first, -qq.second
);
const double amp_pm = amp_W_Cenqqbar_qq<plus, minus>(
pa, p1, pb, pn, pq, pqbar, pl, plbar, qq.first, -qq.second
);
const double amp_pp = amp_W_Cenqqbar_qq<plus, plus>(
pa, p1, pb, pn, pq, pqbar, pl, plbar, qq.first, -qq.second
);
// Divide by t channels, extremal + adjacent central vertex
const double ta = (pa-p1).m2();
const double t1 = q1.m2();
const double t3 = (q1 - pq - pqbar).m2();
const double tb = (pn+pl+plbar-pb).m2();
const double amp= WProp(plbar, pl, wprop)*(
amp_mm+amp_mp+amp_pm+amp_pp
)/(9.*4.*ta*t1*t3*tb);
return amp;
}
} // namespace currents
} // namespace HEJ

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