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/**
* \authors The HEJ collaboration (see AUTHORS for details)
* \date 2019-2022
* \copyright GPLv2 or later
*/
#include "HEJ/jets.hh"
#include <algorithm>
#include <cassert>
#include <cmath>
#include "HEJ/Constants.hh"
// generated headers
#include "HEJ/currents/j_j.hh"
#include "HEJ/currents/j_jqqbar.hh"
#include "HEJ/currents/j_qqbar_j.hh"
#include "HEJ/currents/juno_j.hh"
namespace {
using COM = std::complex<double>;
} // Anonymous Namespace
namespace HEJ {
namespace currents {
double ME_qq(
HLV const & p1out, HLV const & p1in,
HLV const & p2out, HLV const & p2in
){
using helicity::plus;
using helicity::minus;
// we only have to distinguish between the two possibilities of
// contracting same-helicity or opposite-helicity currents.
COM const Mp = HEJ::j_j<minus, plus>(p1in, p1out, p2in, p2out);
COM const Mm = HEJ::j_j<minus, minus>(p1in, p1out, p2in, p2out);
double const sst = std::norm(Mm) + std::norm(Mp);
// Multiply by factor 2 (helicities)
return 2.*sst;
}
namespace {
template<Helicity h1, Helicity hg>
double amp_juno_j(
HLV const & pa, HLV const & pb,
HLV const & pg, HLV const & p1, HLV const & p2
) {
// TODO: code duplication with Wjets
const COM u1 = U1_j<h1, hg>(pa,p1,pb,p2,pg);
const COM u2 = U2_j<h1, hg>(pa,p1,pb,p2,pg);
const COM l = L_j<h1, hg>(pa,p1,pb,p2,pg);
const COM x = u1 - l;
const COM y = u2 + l;
return C_F*norm(x + y) - C_A*(x*conj(y)).real();
}
} // Anonymous Namespace
double ME_unob_qq(
HLV const & pg,
HLV const & p1out, HLV const & p1in,
HLV const & p2out, HLV const & p2in
){
using helicity::minus;
using helicity::plus;
// only calculate half of the helicity amplitudes,
// the remaining ones follow from CP symmetry
const double amm = amp_juno_j<minus, minus>(p1in, p2in, pg, p1out, p2out);
const double amp = amp_juno_j<minus, plus>(p1in, p2in, pg, p1out, p2out);
const double apm = amp_juno_j< plus, minus>(p1in, p2in, pg, p1out, p2out);
const double app = amp_juno_j< plus, plus>(p1in, p2in, pg, p1out, p2out);
constexpr double hel_fac = 2.;
return hel_fac * (amm + amp + apm + app);
}
namespace {
// helicity amplitudes for j jqqbar contraction
template<Helicity h1, Helicity hg>
double amp_j_jqqbar(
HLV const & pa, HLV const & pb,
HLV const & p1, HLV const & p2, HLV const & p3
) {
// TODO: code duplication with Wjets.cc
// TODO: symbolic colour factors
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 = j_qggm1<h1,hg>(pb,p2,p3,pa,p1);
const COM m2 = j_qggm2<h1,hg>(pb,p2,p3,pa,p1);
const COM m3 = j_qggm3<h1,hg>(pb,p2,p3,pa,p1);
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
double ME_qqbar_qg(
HLV const & pa, HLV const & pb,
HLV const & p1, HLV const & p2, HLV const & p3
){
using helicity::minus;
using helicity::plus;
const double Mmmm = amp_j_jqqbar<minus, minus>(pa, pb, p1, p2, p3);
const double Mmmp = amp_j_jqqbar<minus, plus>(pa, pb, p1, p2, p3);
const double Mpmm = amp_j_jqqbar< plus, minus>(pa, pb, p1, p2, p3);
const double Mpmp = amp_j_jqqbar< plus, plus>(pa, pb, p1, p2, p3);
// Factor of 2 for the helicity for conjugate configurations
return 2.*(Mmmm+Mmmp+Mpmm+Mpmp)/3./C_F;
}
namespace {
// helicity amplitudes for matrix element with central qqbar
// TODO: update to arxiv:2012.10310, around eq. (3.33)
template<Helicity h1a, Helicity h4b>
double amp_Cenqqbar_qq(
HLV const & pa, HLV const & p1,
HLV const & pb, HLV const & p4,
HLV const & pq, HLV const & pqbar,
HLV const & q11, HLV const & q12
){
using std::norm;
const COM sym = M_sym<h1a, h4b>(
pa, p1, pb, p4, pq, pqbar, q11, q12
);
const COM cross = M_cross<h1a, h4b>(
pa, p1, pb, p4, pq, pqbar, q11, q12
);
const COM uncross = M_qbar<h1a, h4b>(
pa, p1, pb, p4, pq, pqbar, 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
double ME_Cenqqbar_qq(
HLV const & pa, HLV const & pb,
std::vector<HLV> const & partons,
const bool qqbarmarker, const std::size_t nabove
){
using helicity::plus;
using helicity::minus;
CLHEP::HepLorentzVector q1 = pa;
for(std::size_t 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 = partons[nabove+1];
HLV pqbar = partons[nabove+2];
if(qqbarmarker) std::swap(pq, pqbar);
const HLV p1 = partons.front();
const HLV pn = partons.back();
// 8 helicity choices, but only 4 independent ones
//(complex conjugation related).
// In principle, the proper helicity labeling depends on
// whether we have antiquark lines (aqlinea and aqlineb).
// However, this only corresponds to a relabeling,
// which doesn't change the sum over all helicities below.
const double amp_mm = amp_Cenqqbar_qq<minus, minus>(
pa, p1, pb, pn, pq, pqbar, qq.first, -qq.second
);
const double amp_mp = amp_Cenqqbar_qq<minus, plus>(
pa, p1, pb, pn, pq, pqbar, qq.first, -qq.second
);
const double amp_pm = amp_Cenqqbar_qq<plus, minus>(
pa, p1, pb, pn, pq, pqbar, qq.first, -qq.second
);
const double amp_pp = amp_Cenqqbar_qq<plus, plus>(
pa, p1, pb, pn, pq, pqbar, qq.first, -qq.second
);
//Result (averaged, without coupling or t-channel props). Factor of
//2 for the 4 helicity configurations I didn't work out explicitly
const HLV q3 = q1 - pq - pqbar;
constexpr double hel_fac = 2.;
// TODO: explain the 1/64
return hel_fac/64.*(amp_mm+amp_mp+amp_pm+amp_pp) / (q1.m2()*q3.m2());
}
} // namespace currents
} // namespace HEJ

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