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diff --git a/src/jets.cc b/src/jets.cc
index ff126b6..1d87e6d 100644
--- a/src/jets.cc
+++ b/src/jets.cc
@@ -1,658 +1,677 @@
/**
* \authors The HEJ collaboration (see AUTHORS for details)
* \date 2019
* \copyright GPLv2 or later
*/
#include "HEJ/jets.hh"
#include "HEJ/Constants.hh"
// Colour acceleration multiplier for gluons see eq. (7) in arXiv:0910.5113
// @TODO: this is not a current and should be moved somewhere else
double K_g(double p1minus, double paminus) {
return 1./2.*(p1minus/paminus + paminus/p1minus)*(HEJ::C_A - 1./HEJ::C_A) + 1./HEJ::C_A;
}
double K_g(
HLV const & pout,
HLV const & pin
) {
if(pin.z() > 0) return K_g(pout.plus(), pin.plus());
return K_g(pout.minus(), pin.minus());
}
CCurrent CCurrent::operator+(const CCurrent& other)
{
COM result_c0=c0 + other.c0;
COM result_c1=c1 + other.c1;
COM result_c2=c2 + other.c2;
COM result_c3=c3 + other.c3;
return CCurrent(result_c0,result_c1,result_c2,result_c3);
}
CCurrent CCurrent::operator-(const CCurrent& other)
{
COM result_c0=c0 - other.c0;
COM result_c1=c1 - other.c1;
COM result_c2=c2 - other.c2;
COM result_c3=c3 - other.c3;
return CCurrent(result_c0,result_c1,result_c2,result_c3);
}
CCurrent CCurrent::operator*(const double x)
{
COM result_c0=x*CCurrent::c0;
COM result_c1=x*CCurrent::c1;
COM result_c2=x*CCurrent::c2;
COM result_c3=x*CCurrent::c3;
return CCurrent(result_c0,result_c1,result_c2,result_c3);
}
CCurrent CCurrent::operator/(const double x)
{
COM result_c0=CCurrent::c0/x;
COM result_c1=CCurrent::c1/x;
COM result_c2=CCurrent::c2/x;
COM result_c3=CCurrent::c3/x;
return CCurrent(result_c0,result_c1,result_c2,result_c3);
}
CCurrent CCurrent::operator*(const COM x)
{
COM result_c0=x*CCurrent::c0;
COM result_c1=x*CCurrent::c1;
COM result_c2=x*CCurrent::c2;
COM result_c3=x*CCurrent::c3;
return CCurrent(result_c0,result_c1,result_c2,result_c3);
}
CCurrent CCurrent::operator/(const COM x)
{
COM result_c0=(CCurrent::c0)/x;
COM result_c1=(CCurrent::c1)/x;
COM result_c2=(CCurrent::c2)/x;
COM result_c3=(CCurrent::c3)/x;
return CCurrent(result_c0,result_c1,result_c2,result_c3);
}
std::ostream& operator <<(std::ostream& os, const CCurrent& cur)
{
os << "("<<cur.c0<< " ; "<<cur.c1<<" , "<<cur.c2<<" , "<<cur.c3<<")";
return os;
}
CCurrent operator * ( double x, CCurrent& m)
{
return m*x;
}
CCurrent operator * ( COM x, CCurrent& m)
{
return m*x;
}
CCurrent operator / ( double x, CCurrent& m)
{
return m/x;
}
CCurrent operator / ( COM x, CCurrent& m)
{
return m/x;
}
COM CCurrent::dot(HLV p1)
{
// Current goes (E,px,py,pz)
// Vector goes (px,py,pz,E)
return p1[3]*c0-p1[0]*c1-p1[1]*c2-p1[2]*c3;
}
COM CCurrent::dot(CCurrent p1)
{
return p1.c0*c0-p1.c1*c1-p1.c2*c2-p1.c3*c3;
}
//Current Functions
void joi(HLV pout, bool helout, HLV pin, bool helin, current &cur) {
cur[0]=0.;
cur[1]=0.;
cur[2]=0.;
cur[3]=0.;
- const double sqpop = sqrt(pout.plus());
- const double sqpom = sqrt(pout.minus());
- COM poperp = pout.x() + COM(0, 1) * pout.y();
+ double sqpop, sqpom;
+ if(pout.plus()>0) sqpop = sqrt(pout.plus());
+ else sqpop = sqrt(abs(pout.plus()));
+ if(pout.minus()>0) sqpom = sqrt(pout.minus());
+ else sqpom = sqrt(abs(pout.minus()));
- //Add here a bit if want to create a jii, in effect
- if(pout.x()==0 && pout.y() ==0){
- poperp = -1.;
- }
- else {
- poperp=pout.x()+COM(0,1)*pout.y();
- }
+ COM poperp;
+ if(pout.x()==0 && pout.y() ==0) poperp = -1.;
+ else poperp=pout.x()+COM(0,1)*pout.y();
if (helout != helin) {
throw std::invalid_argument{"Non-matching helicities"};
} else if (helout == false) { // negative helicity
if (pin.plus() > pin.minus()) { // if forward
- const double sqpip = sqrt(pin.plus());
+ double sqpip;
+ if(pin.plus()>0) sqpip=sqrt(pin.plus());
+ else sqpip=sqrt(abs(pin.plus()));
+
cur[0] = sqpop * sqpip;
cur[1] = sqpom * sqpip * poperp / abs(poperp);
cur[2] = -COM(0,1) * cur[1];
cur[3] = cur[0];
} else { // if backward
- const double sqpim = sqrt(pin.minus());
+ double sqpim;
+ if(pin.minus()>0) sqpim=sqrt(pin.minus());
+ else sqpim=sqrt(abs(pin.minus()));
+
cur[0] = -sqpom * sqpim * poperp / abs(poperp);
cur[1] = -sqpim * sqpop;
cur[2] = COM(0,1) * cur[1];
cur[3] = -cur[0];
}
} else { // positive helicity
if (pin.plus() > pin.minus()) { // if forward
- const double sqpip = sqrt(pin.plus());
+ double sqpip;
+ if(pin.plus()>0) sqpip=sqrt(pin.plus());
+ else sqpip=sqrt(abs(pin.plus()));
+
cur[0] = sqpop * sqpip;
cur[1] = sqpom * sqpip * conj(poperp) / abs(poperp);
cur[2] = COM(0,1) * cur[1];
cur[3] = cur[0];
} else { // if backward
- const double sqpim = sqrt(pin.minus());
+ double sqpim;
+ if(pin.minus()>0) sqpim=sqrt(pin.minus());
+ else sqpim=sqrt(abs(pin.minus()));
+
cur[0] = -sqpom * sqpim * conj(poperp) / abs(poperp);
cur[1] = -sqpim * sqpop;
cur[2] = -COM(0,1) * cur[1];
cur[3] = -cur[0];
}
}
}
CCurrent joi (HLV pout, bool helout, HLV pin, bool helin)
{
current cur;
joi(pout, helout, pin, helin, cur);
return CCurrent(cur[0],cur[1],cur[2],cur[3]);
}
void jio(HLV pin, bool helin, HLV pout, bool helout, current &cur) {
joi(pout, !helout, pin, !helin, cur);
}
CCurrent jio (HLV pin, bool helin, HLV pout, bool helout)
{
current cur;
jio(pin, helin, pout, helout, cur);
return CCurrent(cur[0],cur[1],cur[2],cur[3]);
}
void joo(HLV pi, bool heli, HLV pj, bool helj, current &cur) {
// Zero our current
cur[0] = 0.0;
cur[1] = 0.0;
cur[2] = 0.0;
cur[3] = 0.0;
if (heli!=helj) {
throw std::invalid_argument{"Non-matching helicities"};
} else if ( heli == true ) { // If positive helicity swap momenta
std::swap(pi,pj);
}
- const double sqpjp = sqrt(pj.plus());
- const double sqpjm = sqrt(pj.minus());
- const double sqpip = sqrt(pi.plus());
- const double sqpim = sqrt(pi.minus());
+ double sqpjp, sqpjm, sqpip, sqpim;
+ if( pj.plus() > 0) sqpjp = sqrt(pj.plus());
+ else sqpjp = sqrt(abs(pj.plus()));
+ if( pj.minus() > 0) sqpjm = sqrt(pj.minus());
+ else sqpjm = sqrt(abs(pj.minus()));
+ if( pi.plus() > 0) sqpip = sqrt(pi.plus());
+ else sqpip = sqrt(abs(pi.plus()));
+ if( pi.minus() > 0) sqpim = sqrt(pi.minus());
+ else sqpim = sqrt(abs(pi.minus()));
+
+ COM piperp, pjperp;
+ if(pi.x()==0 && pi.y() ==0) piperp = -1.;
+ else piperp=pi.x()+COM(0,1)*pi.y();
+ if(pj.x()==0 && pj.y() ==0) pjperp = -1.;
+ else pjperp=pj.x()+COM(0,1)*pj.y();
- const COM piperp = pi.x() + COM(0,1) * pi.y();
- const COM pjperp = pj.x() + COM(0,1) * pj.y();
const COM phasei = piperp / abs(piperp);
const COM phasej = pjperp / abs(pjperp);
cur[0] = sqpim * sqpjm * phasei * conj(phasej) + sqpip * sqpjp;
cur[1] = sqpim * sqpjp * phasei + sqpip * sqpjm * conj(phasej);
cur[2] = -COM(0, 1) * (sqpim * sqpjp * phasei - sqpip * sqpjm * conj(phasej));
cur[3] = -sqpim * sqpjm * phasei * conj(phasej) + sqpip * sqpjp;
}
CCurrent joo (HLV pi, bool heli, HLV pj, bool helj)
{
current cur;
joo(pi, heli, pj, helj, cur);
return CCurrent(cur[0],cur[1],cur[2],cur[3]);
}
namespace{
//@{
/**
* @brief Pure Jet FKL Contributions, function to handle all incoming types.
* @param p1out Outgoing Particle 1.
* @param p1in Incoming Particle 1.
* @param p2out Outgoing Particle 2
* @param p2in Incoming Particle 2
*
* Calculates j_\mu j^\mu.
* Handles all possible incoming states. Helicity doesn't matter since we sum
* over all of them.
*/
double j_j(HLV const & p1out, HLV const & p1in,
HLV const & p2out, HLV const & p2in
){
HLV const q1=p1in-p1out;
HLV const q2=-(p2in-p2out);
current mj1m,mj1p,mj2m,mj2p;
// Note need to flip helicities in anti-quark case.
joi(p1out, false, p1in, false, mj1p);
joi(p1out, true, p1in, true, mj1m);
joi(p2out, false, p2in, false, mj2p);
joi(p2out, true, p2in, true, mj2m);
COM const Mmp=cdot(mj1m,mj2p);
COM const Mmm=cdot(mj1m,mj2m);
COM const Mpp=cdot(mj1p,mj2p);
COM const Mpm=cdot(mj1p,mj2m);
double const sst=abs2(Mmm)+abs2(Mmp)+abs2(Mpp)+abs2(Mpm);
// Multiply by Cf^2
return HEJ::C_F*HEJ::C_F*(sst)/(q1.m2()*q2.m2());
}
} //anonymous namespace
double ME_qQ(HLV p1out, HLV p1in, HLV p2out, HLV p2in){
return j_j(p1out, p1in, p2out, p2in);
}
double ME_qQbar(HLV p1out, HLV p1in, HLV p2out, HLV p2in){
return j_j(p1out, p1in, p2out, p2in);
}
double ME_qbarQbar(HLV p1out, HLV p1in, HLV p2out, HLV p2in){
return j_j(p1out, p1in, p2out, p2in);
}
double ME_qg(HLV p1out, HLV p1in, HLV p2out, HLV p2in){
return j_j(p1out, p1in, p2out, p2in)*K_g(p2out, p2in)/HEJ::C_F;
}
double ME_qbarg(HLV p1out, HLV p1in, HLV p2out, HLV p2in){
return j_j(p1out, p1in, p2out, p2in)*K_g(p2out, p2in)/(HEJ::C_F);
}
double ME_gg(HLV p1out, HLV p1in, HLV p2out, HLV p2in){
return j_j(p1out, p1in, p2out, p2in)*K_g(p1out, p1in)*K_g(p2out, p2in)/(HEJ::C_F*HEJ::C_F);
}
//@}
namespace{
double juno_j(HLV const & pg, HLV const & p1out,
HLV const & p1in, HLV const & p2out, HLV const & p2in
){
// This construction is taking rapidity order: pg > p1out >> p2out
HLV q1=p1in-p1out; // Top End
HLV q2=-(p2in-p2out); // Bottom End
HLV qg=p1in-p1out-pg; // Extra bit post-gluon
// Note <p1|eps|pa> current split into two by gauge choice.
// See James C's Thesis (p72). <p1|eps|pa> -> <p1|pg><pg|pa>
CCurrent mj1p=joi(p1out, false, p1in, false);
CCurrent mj1m=joi(p1out, true, p1in, true);
CCurrent jgap=joi(pg, false, p1in, false);
CCurrent jgam=joi(pg, true, p1in, true);
// Note for function joo(): <p1+|pg+> = <pg-|p1->.
CCurrent j2gp=joo(p1out, false, pg, false);
CCurrent j2gm=joo(p1out, true, pg, true);
CCurrent mj2p=joi(p2out, false, p2in, false);
CCurrent mj2m=joi(p2out, true, p2in, true);
// Dot products of these which occur again and again
COM Mmp=mj1m.dot(mj2p);
COM Mmm=mj1m.dot(mj2m);
COM Mpp=mj1p.dot(mj2p);
COM Mpm=mj1p.dot(mj2m);
CCurrent p1o(p1out),p2o(p2out),p2i(p2in),qsum(q1+qg),p1i(p1in);
CCurrent Lmm=(qsum*(Mmm)+(-2.*mj2m.dot(pg))*mj1m+2.*mj1m.dot(pg)*mj2m
+(p2o/pg.dot(p2out) + p2i/pg.dot(p2in))*(qg.m2()*Mmm/2.))/q1.m2();
CCurrent Lmp=(qsum*(Mmp) + (-2.*mj2p.dot(pg))*mj1m+2.*mj1m.dot(pg)*mj2p
+(p2o/pg.dot(p2out) + p2i/pg.dot(p2in))*(qg.m2()*Mmp/2.))/q1.m2();
CCurrent Lpm=(qsum*(Mpm) + (-2.*mj2m.dot(pg))*mj1p+2.*mj1p.dot(pg)*mj2m
+(p2o/pg.dot(p2out) + p2i/pg.dot(p2in))*(qg.m2()*Mpm/2.))/q1.m2();
CCurrent Lpp=(qsum*(Mpp) + (-2.*mj2p.dot(pg))*mj1p+2.*mj1p.dot(pg)*mj2p
+(p2o/pg.dot(p2out) + p2i/pg.dot(p2in))*(qg.m2()*Mpp/2.))/q1.m2();
CCurrent U1mm=(jgam.dot(mj2m)*j2gm+2.*p1o*Mmm)/(p1out+pg).m2();
CCurrent U1mp=(jgam.dot(mj2p)*j2gm+2.*p1o*Mmp)/(p1out+pg).m2();
CCurrent U1pm=(jgap.dot(mj2m)*j2gp+2.*p1o*Mpm)/(p1out+pg).m2();
CCurrent U1pp=(jgap.dot(mj2p)*j2gp+2.*p1o*Mpp)/(p1out+pg).m2();
CCurrent U2mm=((-1.)*j2gm.dot(mj2m)*jgam+2.*p1i*Mmm)/(p1in-pg).m2();
CCurrent U2mp=((-1.)*j2gm.dot(mj2p)*jgam+2.*p1i*Mmp)/(p1in-pg).m2();
CCurrent U2pm=((-1.)*j2gp.dot(mj2m)*jgap+2.*p1i*Mpm)/(p1in-pg).m2();
CCurrent U2pp=((-1.)*j2gp.dot(mj2p)*jgap+2.*p1i*Mpp)/(p1in-pg).m2();
constexpr double cf=HEJ::C_F;
double amm=cf*(2.*vre(Lmm-U1mm,Lmm+U2mm))+2.*cf*cf/3.*vabs2(U1mm+U2mm);
double amp=cf*(2.*vre(Lmp-U1mp,Lmp+U2mp))+2.*cf*cf/3.*vabs2(U1mp+U2mp);
double apm=cf*(2.*vre(Lpm-U1pm,Lpm+U2pm))+2.*cf*cf/3.*vabs2(U1pm+U2pm);
double app=cf*(2.*vre(Lpp-U1pp,Lpp+U2pp))+2.*cf*cf/3.*vabs2(U1pp+U2pp);
double ampsq=-(amm+amp+apm+app);
//Divide by t-channels
ampsq/=q2.m2()*qg.m2();
ampsq/=16.;
// Factor of (Cf/Ca) for each quark to match j_j.
ampsq*=(HEJ::C_F*HEJ::C_F)/(HEJ::C_A*HEJ::C_A);
return ampsq;
}
}
//Unordered bits for pure jet
double ME_unob_qQ (HLV pg, HLV p1out, HLV p1in, HLV p2out, HLV p2in){
return juno_j(pg, p1out, p1in, p2out, p2in);
}
double ME_unob_qbarQ (HLV pg, HLV p1out, HLV p1in, HLV p2out, HLV p2in){
return juno_j(pg, p1out, p1in, p2out, p2in);
}
double ME_unob_qQbar (HLV pg, HLV p1out, HLV p1in, HLV p2out, HLV p2in){
return juno_j(pg, p1out, p1in, p2out, p2in);
}
double ME_unob_qbarQbar (HLV pg, HLV p1out, HLV p1in, HLV p2out, HLV p2in){
return juno_j(pg, p1out, p1in, p2out, p2in);
}
double ME_unob_qg (HLV pg, HLV p1out, HLV p1in, HLV p2out, HLV p2in){
return juno_j(pg, p1out, p1in, p2out, p2in)*K_g(p2out,p2in)/HEJ::C_F;
}
double ME_unob_qbarg (HLV pg, HLV p1out, HLV p1in, HLV p2out, HLV p2in){
return juno_j(pg, p1out, p1in, p2out, p2in)*K_g(p2out,p2in)/HEJ::C_F;
}
// qg -> qQQ~
//First, a function for generating polarisation tensors. Output as 'current'.
//Should be general for any refmom now that I've added a bit to the j function.
void eps(HLV refmom, HLV kb, bool hel, current &ep){
current curm,curp;
//Positive helicity eps has negative helicity choices for spinors and vice versa
joi(refmom,true,kb,true,curm);
joi(refmom,false,kb,false,curp);
double norm=1.;
if(kb.z()<0.)
norm *= sqrt(2.*refmom.plus()*kb.minus());
if(kb.z()>0.)
norm = sqrt(2.*refmom.minus()*kb.plus());
if(hel==false){
ep[0] = curm[0]/norm;
ep[1] = curm[1]/norm;
ep[2] = curm[2]/norm;
ep[3] = curm[3]/norm;
}
if(hel==true){
ep[0] = curp[0]/norm;
ep[1] = curp[1]/norm;
ep[2] = curp[2]/norm;
ep[3] = curp[3]/norm;
}
}
//Now build up each part of the sqaured amplitude
COM qggm1(HLV pa, HLV pb, HLV p1, HLV p2, HLV p3, bool helchain,
bool heltop, bool helb,HLV refmom, bool aqline){
// Since everything is defined with currents, need to use compeleness relation
// to expand p slash. i.e. pslash = |p><p|. Only one helicity 'survives' as
// defined by the helicities of the spinors at the end of the chain.
current cur33, cur23, curb3, cur2b, cur1a, ep;
joo(p3, helchain, p3, helchain,cur33);
joo(p2,helchain,p3,helchain,cur23);
jio(pb,helchain,p3,helchain,curb3);
joi(p2,helchain,pb,helchain,cur2b);
if(aqline==true)
jio(pa, heltop, p1, heltop,cur1a);
if(aqline==false)
joi(p1, heltop, pa, heltop,cur1a);
double t2 = (p3-pb)*(p3-pb);
//Create vertex
COM v1[4][4];
for(int u=0; u<4;u++)
{
for(int v=0; v<4; v++)
{
v1[u][v]=(cur23[u]*cur33[v]-cur2b[u]*curb3[v])/t2*(-1.);
}
}
//Dot in current and eps
//Metric tensor
double eta[4][4]={};
eta[0][0]=1.;
eta[1][1]=-1.;
eta[2][2]=-1.;
eta[3][3]=-1.;
//eps
eps(refmom,pb,helb, ep);
COM M1=0.;
for(int i=0;i<4;i++){
for(int j=0;j<4;j++){
for(int k=0; k<4; k++){
for(int l=0; l<4;l++){
M1+= eta[i][k]*cur1a[k]*(v1[i][j])*ep[l]*eta[l][j];
}
}
}
}
return M1;
}
COM qggm2(HLV pa, HLV pb, HLV p1, HLV p2, HLV p3, bool helchain, bool heltop,
bool helb,HLV refmom, bool aqline){
// Since everything is defined with currents, need to use completeness relation
// to expand p slash. i.e. pslash = |p><p|. Only one helicity 'survives' as
// defined by the helicities of the spinors at the end of the chain.
current cur22, cur23, curb3, cur2b, cur1a, ep;
joo(p2, helchain, p2, helchain,cur22);
joo(p2,helchain,p3,helchain,cur23);
jio(pb,helchain,p3,helchain,curb3);
joi(p2,helchain,pb,helchain,cur2b);
if(aqline==true)
jio(pa, heltop, p1, heltop,cur1a);
if(aqline==false)
joi(p1, heltop, pa, heltop,cur1a);
double t2t = (p2-pb)*(p2-pb);
//Create vertex
COM v2[4][4]={};
for(int u=0; u<4;u++)
{
for(int v=0; v<4; v++)
{
v2[u][v]=(cur22[v]*cur23[u]-cur2b[v]*curb3[u])/t2t;
}
}
//Dot in current and eps
//Metric tensor
double eta[4][4]={};
eta[0][0]=1.;
eta[1][1]=-1.;
eta[2][2]=-1.;
eta[3][3]=-1.;
//eps
eps(refmom,pb,helb, ep);
COM M2=0.;
for(int i=0;i<4;i++){
for(int j=0;j<4;j++){
for(int k=0; k<4; k++){
for(int l=0; l<4;l++){
M2+= eta[i][k]*cur1a[k]*(v2[i][j])*ep[l]*eta[l][j];
}
}
}
}
return M2;
}
COM qggm3(HLV pa, HLV pb, HLV p1, HLV p2, HLV p3, bool helchain, bool heltop,
bool helb,HLV refmom, bool aqline){
//3 gluon vertex bit
//Metric tensor
double eta[4][4]={};
eta[0][0]=1.;
eta[1][1]=-1.;
eta[2][2]=-1.;
eta[3][3]=-1.;
current spincur,ep,cur1a;
double s23 = (p2+p3)*(p2+p3);
joo(p2,helchain,p3,helchain,spincur);
if(aqline==true)
jio(pa, heltop, p1, heltop,cur1a);
if(aqline==false)
joi(p1, heltop, pa, heltop,cur1a);
//Redefine relevant momenta as currents - for ease of calling correct part of vector
current ka,k2,k3,kb;
kb[0]=pb.e();
kb[1]=pb.x();
kb[2]=pb.y();
kb[3]=pb.z();
k2[0]=p2.e();
k2[1]=p2.x();
k2[2]=p2.y();
k2[3]=p2.z();
k3[0]=p3.e();
k3[1]=p3.x();
k3[2]=p3.y();
k3[3]=p3.z();
ka[0]=pa.e();
ka[1]=pa.x();
ka[2]=pa.y();
ka[3]=pa.z();
COM V3g[4][4]={};
for(int u=0;u<4;u++){
for(int v=0;v<4;v++){
for(int p=0;p<4;p++){
for(int r=0; r<4;r++){
V3g[u][v] += COM(0.,1.)*(((2.*k2[v]+2.*k3[v])*eta[u][p] -
(2.*kb[u])*eta[p][v]+2.*kb[p]*eta[u][v])*spincur[r]*eta[r][p])/s23;
}
}
}
}
//Alternative extra bit - I will also choose the gauge such that this part vanishes
COM diffextrabit[4][4]={};
for(int u=0;u<4;u++) {
for(int v=0;v<4;v++) {
diffextrabit[u][v] = 0.;
}
}
//Dot in current and eps
//eps
eps(refmom,pb,helb, ep);
COM M3=0.;
for(int i=0;i<4;i++){
for(int j=0;j<4;j++){
for(int k=0; k<4; k++){
for(int l=0; l<4;l++){
M3+= eta[i][k]*cur1a[k]*(V3g[i][j]+diffextrabit[i][j])*ep[l]*eta[l][j];
}
}
}
}
return M3;
}
//Now the function to give helicity/colour sum/average
double MqgtqQQ(HLV pa, HLV pb, HLV p1, HLV p2, HLV p3, bool aqline, bool qqxmarker){
//If qqxmarker is true, switch the order of quark and anti-quark
HLV ka,kb,k1,k2,k3;
if(qqxmarker==true){
ka=pa;
kb=pb;
k1=p1;
k2=p3;
k3=p2;
} else {
ka=pa;
kb=pb;
k1=p1;
k2=p2;
k3=p3;
}
// 4 indepedent helicity choices (complex conjugation related).
//Need to evalute each independent hel configuration and store that result somewhere
COM Mmmm1 = qggm1(ka,kb,k1,k2,k3,false,false,false, ka, aqline);
COM Mmmm2 = qggm2(ka,kb,k1,k2,k3,false,false,false, ka, aqline);
COM Mmmm3 = qggm3(ka,kb,k1,k2,k3,false,false,false, ka, aqline);
COM Mmmp1 = qggm1(ka,kb,k1,k2,k3,false,true,false, ka, aqline);
COM Mmmp2 = qggm2(ka,kb,k1,k2,k3,false,true,false, ka, aqline);
COM Mmmp3 = qggm3(ka,kb,k1,k2,k3,false,true,false, ka, aqline);
COM Mpmm1 = qggm1(ka,kb,k1,k2,k3,false,false,true, ka, aqline);
COM Mpmm2 = qggm2(ka,kb,k1,k2,k3,false,false,true, ka, aqline);
COM Mpmm3 = qggm3(ka,kb,k1,k2,k3,false,false,true, ka, aqline);
COM Mpmp1 = qggm1(ka,kb,k1,k2,k3,false,true,true, ka, aqline);
COM Mpmp2 = qggm2(ka,kb,k1,k2,k3,false,true,true, ka, aqline);
COM Mpmp3 = qggm3(ka,kb,k1,k2,k3,false,true,true, ka, aqline);
//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,Mmmp,Mpmm,Mpmp;
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)));
Mmmp = real(cm1m1*pow(abs(Mmmp1),2)+cm2m2*pow(abs(Mmmp2),2)+
cm3m3*pow(abs(Mmmp3),2)+2.*real(cm1m2*Mmmp1*conj(Mmmp2))+
2.*real(cm1m3*Mmmp1*conj(Mmmp3))+2.*real(cm2m3*Mmmp2*conj(Mmmp3)));
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)));
Mpmp = real(cm1m1*pow(abs(Mpmp1),2)+cm2m2*pow(abs(Mpmp2),2)+
cm3m3*pow(abs(Mpmp3),2)+2.*real(cm1m2*Mpmp1*conj(Mpmp2))+
2.*real(cm1m3*Mpmp1*conj(Mpmp3))+2.*real(cm2m3*Mpmp2*conj(Mpmp3)));
// Result (averaged, without coupling). Factor of 2 for the helicity
// configurations we didn't need to evalute explicity
return (2.*(Mmmm+Mmmp+Mpmm+Mpmp)/24./4.)/(ka-k1).m2()/(k2+k3-kb).m2();
}
// Extremal qqx
double ME_Exqqx_qbarqQ(HLV pgin, HLV pqout, HLV pqbarout, HLV p2out, HLV p2in){
return MqgtqQQ(p2in, pgin, p2out, pqout, pqbarout, false, false);
}
double ME_Exqqx_qqbarQ(HLV pgin, HLV pqout, HLV pqbarout, HLV p2out, HLV p2in){
return MqgtqQQ(p2in, pgin, p2out, pqout, pqbarout, false, true);
}
double ME_Exqqx_qbarqg(HLV pgin, HLV pqout, HLV pqbarout, HLV p2out, HLV p2in){
return MqgtqQQ(p2in, pgin, p2out, pqout, pqbarout, false, false)*K_g(p2out,p2in)/HEJ::C_F;
}
double ME_Exqqx_qqbarg(HLV pgin, HLV pqout, HLV pqbarout, HLV p2out, HLV p2in){
return MqgtqQQ(p2in, pgin, p2out, pqout, pqbarout, false, true)*K_g(p2out,p2in)/HEJ::C_F;
}

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