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diff --git a/include/HEJ/Tensor.hh b/include/HEJ/Tensor.hh
index 256dd9c..a668b7c 100644
--- a/include/HEJ/Tensor.hh
+++ b/include/HEJ/Tensor.hh
@@ -1,177 +1,171 @@
/** \file
* \brief Tensor Template Class declaration.
*
* This file contains the declaration of the Tensor Template class. This
* is used to calculate some of the more complex currents within the
* W+Jets implementation particularly.
*
* \authors The HEJ collaboration (see AUTHORS for details)
* \date 2019
* \copyright GPLv2 or later
*/
#pragma once
#include <array>
#include <complex>
#include <valarray>
namespace CLHEP {
class HepLorentzVector;
}
class CCurrent;
typedef std::complex<double> COM;
///@TODO put in some namespace
namespace detail {
static constexpr std::size_t d = 4;
}
template <unsigned int N>
class Tensor{
public:
static constexpr std::size_t d = detail::d;
//! Constructor
Tensor();
explicit Tensor(COM x);
//! Rank of Tensor
int rank(){
return N;
};
//! total number of entries
int len(){
return size;
};
//! Tensor element with given indices
template<typename... Indices>
COM const & operator()(Indices... i) const;
//! Tensor element with given indices
template<typename... Indices>
COM & operator()(Indices... rest);
//! implicit conversion to complex number for rank 0 tensors (scalars)
operator COM() const;
Tensor<N> & operator*=(COM const & x);
Tensor<N> & operator/=(COM const & x);
Tensor<N> & operator+=(Tensor<N> const & T2);
Tensor<N> & operator-=(Tensor<N> const & T2);
- /**
- * \brief Multiply Tensor from Right: T1^(mu1...mk..mN-1)T2_(muN)
- * @param T2 Tensor of Rank 1 to multiply from right with with.
- * @returns T1.contract(T2,1) -> T1^(mu,nu,rho...)T2^sigma
- */
- Tensor<N+1> rightprod(const Tensor<1> T2);
+ //! Outer product of two tensors
+ template<unsigned M>
+ Tensor<N+M> outer(Tensor<M> const & T2) const;
- /**
- * \brief Multiply Tensor from Left: T2_(muN)T1^(mu1...mk..mN-1)
- * @param T2 Tensor of Rank 1 to multiply from left with with.
- * @returns T1.contract(T2,1) -> T2^sigma T1^(mu,nu,rho...)
- */
- Tensor<N+1> leftprod(const Tensor<1> T2);
+ //! Outer product of two tensors
+ template<unsigned K, unsigned M>
+ friend Tensor<K+M> outer(Tensor<K> const & T1, Tensor<M> const & T2);
/**
* \brief T^(mu1...mk..mN)T2_(muk) contract kth index, where k member of [1,N]
* @param T2 Tensor of Rank 1 to contract with.
* @param k int to contract Tensor T2 with from original Tensor.
* @returns T1.contract(T2,1) -> T1^(mu,nu,rho...)T2_mu
*/
Tensor<N-1> contract(const Tensor<1> T2, int k);
std::valarray<COM> components;
private:
int size;
COM sign(unsigned int i);
};
template<unsigned N>
Tensor<N> operator*(Tensor<N> t, COM const & x);
template<unsigned N>
Tensor<N> operator/(Tensor<N> t, COM const & x);
template<unsigned N>
Tensor<N> operator+(Tensor<N> T1, Tensor<N> const & T2);
template<unsigned N>
Tensor<N> operator-(Tensor<N> T1, Tensor<N> const & T2);
/**
* \brief Returns diag(+---) Metric
* @returns Metric {(1,0,0,0),(0,-1,0,0),(0,0,-1,0),(0,0,0,-1)}
*/
Tensor<2> Metric();
/**
* \brief Calculates current <p1|mu|p2>
* @param p1 Momentum of Particle 1
* @param h1 Helicity of Particle 1 (Boolean, False = -h, True = +h)
* @param p2 Momentum of Particle 2
* @param h2 Helicity of Particle 2 (Boolean, False = -h, True = +h)
* @returns Tensor T^mu = <p1|mu|p2>
*
* @note in/out configuration considered in calculation
*/
Tensor<1> TCurrent(CLHEP::HepLorentzVector p1, bool h1,
CLHEP::HepLorentzVector p2, bool h2);
/**
* \brief Calculates current <p1|mu nu rho|p2>
* @param p1 Momentum of Particle 1
* @param h1 Helicity of Particle 1 (Boolean, False = -h, True = +h)
* @param p2 Momentum of Particle 2
* @param h2 Helicity of Particle 2 (Boolean, False = -h, True = +h)
* @returns Tensor T^mu^nu^rho = <p1|mu nu rho|p2>
*
* @note in/out configuration considered in calculation
*/
Tensor<3> T3Current(CLHEP::HepLorentzVector p1, bool h1,
CLHEP::HepLorentzVector p2, bool h2);
/**
* \brief Calculates current <p1|mu nu rho tau sigma|p2>
* @param p1 Momentum of Particle 1
* @param h1 Helicity of Particle 1 (Boolean, False = -h, True = +h)
* @param p2 Momentum of Particle 2
* @param h2 Helicity of Particle 2 (Boolean, False = -h, True = +h)
* @returns Tensor T^mu^nu^rho = <p1|mu nu rho tau sigma|p2>
*
* @note in/out configuration considered in calculation
*/
Tensor<5> T5Current(CLHEP::HepLorentzVector p1, bool h1,
CLHEP::HepLorentzVector p2, bool h2);
/**
* \brief Convert from CCurrent class
* @param j Current in CCurrent format
* @returns Current in Tensor Format
*/
Tensor<1> Construct1Tensor(CCurrent j);
/**
* \brief Convert from HLV class
* @param p Current in HLV format
* @returns Current in Tensor Format
*/
Tensor<1> Construct1Tensor(CLHEP::HepLorentzVector p);
/**
* \brief Construct Epsilon (Polarisation) Tensor
* @param k Momentum of incoming/outgoing boson
* @param ref Reference momentum for calculation
* @param pol Polarisation of boson
* @returns Polarisation Tensor E^mu
*/
Tensor<1> eps(CLHEP::HepLorentzVector k, CLHEP::HepLorentzVector ref, bool pol);
//! Initialises Tensor values by iterating over permutations of gamma matrices.
bool init_sigma_index();
// implementation of template functions
#include "HEJ/detail/Tensor_impl.hh"
diff --git a/include/HEJ/detail/Tensor_impl.hh b/include/HEJ/detail/Tensor_impl.hh
index f466c91..3dae313 100644
--- a/include/HEJ/detail/Tensor_impl.hh
+++ b/include/HEJ/detail/Tensor_impl.hh
@@ -1,152 +1,152 @@
/** \file
* \brief Tensor Template Class Implementation.
*
* This file contains the implementation of the Tensor Template functions
*
* \authors The HEJ collaboration (see AUTHORS for details)
* \date 2019
* \copyright GPLv2 or later
*/
#pragma once
#include "HEJ/Tensor.hh"
#include <cassert>
+#include <algorithm>
namespace detail {
constexpr std::size_t accumulate_idx(const std::size_t acc) {
return acc;
}
template<typename... Indices>
constexpr std::size_t accumulate_idx(
const std::size_t acc,
const std::size_t idx, Indices... indices
) {
return accumulate_idx(d*acc + idx, indices...);
}
}
template <unsigned int N>
template<typename... Indices>
COM & Tensor<N>::operator()(Indices... i) {
static_assert(
sizeof...(Indices) == N,
"number of indices must match tensor rank"
);
return components[detail::accumulate_idx(0, i...)];
}
template <unsigned int N>
template<typename... Indices>
COM const & Tensor<N>::operator()(Indices... i) const {
static_assert(
sizeof...(Indices) == N,
"number of indices must match tensor rank"
);
return components[detail::accumulate_idx(0, i...)];
}
template <unsigned int N>
Tensor<N>::operator COM() const{
static_assert(N==0, "Can only convert a scalar (rank 0 tensor) to a number");
assert(components.size() == 1);
return components[0];
}
template <unsigned int N>
-Tensor<N>::Tensor(){
+Tensor<N>::Tensor() {
size = pow(4,N);
components.resize(size);
}
template <unsigned int N>
Tensor<N>::Tensor(COM x) {
size = pow(4,N);
components.resize(size, x);
}
template<unsigned N>
Tensor<N> & Tensor<N>::operator*=(COM const & x) {
components *= x;
return *this;
}
template<unsigned N>
Tensor<N> & Tensor<N>::operator/=(COM const & x) {
components /= x;
return *this;
}
template<unsigned N>
Tensor<N> operator*(Tensor<N> t, COM const & x) {
return t *= x;
}
template<unsigned N>
Tensor<N> operator/(Tensor<N> t, COM const & x) {
return t /= x;
}
template <unsigned int N>
Tensor<N> & Tensor<N>::operator+=(Tensor<N> const & T2){
components += T2.components;
return *this;
}
template <unsigned int N>
Tensor<N> & Tensor<N>::operator-=(Tensor<N> const & T2){
components -= T2.components;
return *this;
}
template<unsigned N>
Tensor<N> operator+(Tensor<N> T1, Tensor<N> const & T2) {
return T1 += T2;
}
template<unsigned N>
Tensor<N> operator-(Tensor<N> T1, Tensor<N> const & T2) {
return T1 -= T2;
}
-template <unsigned int N>
-Tensor<N+1> Tensor<N>::rightprod(const Tensor<1> T2){
- Tensor<N+1> newT;
- for(int i=0; i<size;i++){
- for(unsigned int j=0;j<4;j++){
- newT.components[i*4+j]=components[i]*T2.components[j];
- }
+template<unsigned K, unsigned M>
+Tensor<K+M> outer(Tensor<K> const & T1, Tensor<M> const & T2) {
+ Tensor<K+M> product;
+ auto target = begin(product.components);
+ for(auto && t1: T1.components) {
+ std::transform(
+ begin(T2.components), end(T2.components),
+ target,
+ [t1](auto && t2) { return t1*t2; }
+ );
+ std::advance(target, T2.components.size());
}
- return newT;
+ return product;
}
-template <unsigned int N>
-Tensor<N+1> Tensor<N>::leftprod(const Tensor<1> T2){
- Tensor<N+1> newT;
- for(unsigned int j=0;j<4;j++){
- for(int i=0; i<size;i++){
- newT.components[j*size+i]=components[i]*T2.components[j];
- }
- }
- return newT;
+template<unsigned N>
+template<unsigned M>
+Tensor<N+M> Tensor<N>::outer(Tensor<M> const & T2) const {
+ return outer(*this, T2);
}
template <unsigned int N>
Tensor<N-1> Tensor<N>::contract(const Tensor<1> T2, int k){
Tensor<N-1> newT;
for(int j=0; j<newT.len(); j++){
COM temp;
int itemp = pow(4,(N-k));
for (unsigned int i=0; i<4; i++){
int index = 4*itemp*floor(j/itemp) + itemp*i +j%(itemp);
temp+=components[index]*T2.components[i]*sign(i);
}
newT.components[j]=temp;
}
return newT;
}
template <unsigned int N>
COM Tensor<N>::sign(unsigned int i){
if(i==0)
return 1.;
else
return -1.;
}
diff --git a/src/Wjets.cc b/src/Wjets.cc
index 56157d8..350cc5d 100644
--- a/src/Wjets.cc
+++ b/src/Wjets.cc
@@ -1,2068 +1,2068 @@
/**
* \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 =J2_qaW.leftprod(Tq1q2);
- Tensor<3> L1b =J2_p1W.leftprod(Tq1q2);
- Tensor<3> L2a = J2_qaW.leftprod(Tq1g);
- Tensor<3> L2b = J2_p1W.leftprod(Tq1g);
- Tensor<3> L3 = (g.rightprod(J2_qaW.contract(Tq2g,1)+J2_p1W.contract(Tq2g,2)))/taW1;
+ 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 p1, HLV pb, HLV p4, 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> 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();
// 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 p1, HLV pb, HLV p4, 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> 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();
// 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 = g.rightprod( Tp1*(t1/(s12+s13+s1A+s1B))
+ 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 = g.rightprod( Tp4*(t3/(s42+s43+s4A+s4B))
+ 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 = g.leftprod(Tq1+Tpq+Tpqbar+TAB);
- Tensor<3> X3g2 = g.leftprod(Tq3-Tpq-Tpqbar-TAB);
- Tensor<3> X3g3 = g.leftprod((Tq1+Tq3));
+ 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 = g.rightprod(Tp1*(t1/(s12+s13))+Tpa*(t1/(sa2+sa3)));
+ 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 = g.rightprod(Tp4*(t3/(s42+s43)) + Tpb*(t3/(sb2+sb3)));
+ 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 = g.leftprod(Tq1+Tpq+Tpqbar);
- Tensor<3> X3g2 = g.leftprod(Tq3-Tpq-Tpqbar);
- Tensor<3> X3g3 = g.leftprod((Tq1+Tq3));
+ 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);
}
// W+Jets Unordered Contributions
//qQ->qQWg_unob
// Calculates the square of the current contractions for qQ->qenuQ scattering
// p1: quark (with W emittance)
// p2: Quark
double junobMWqQg (HLV p1out, HLV pe, HLV pnu,HLV p1in, HLV p2out, HLV p2in, HLV pg){
CCurrent mj1m,mj2p,mj2m;
HLV q1=p1in-p1out-pe-pnu;
HLV q2=-(p2in-p2out-pg);
HLV q3=-(p2in-p2out);
mj1m=jW(p1out,false,pe,false,pnu,false,p1in,false);
mj2p=joi(p2out,true,p2in,true);
mj2m=joi(p2out,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 jgbm,jgbp,j2gm,j2gp;
j2gp=joo(p2out,true,pg,true);
j2gm=joo(p2out,false,pg,false);
jgbp=joi(pg,true,p2in,true);
jgbm=joi(pg,false,p2in,false);
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
double WPropfact = WProp(pe, pnu);
ampsq*=WPropfact;
// Now add the t-channels
double th=q2.m2()*q1.m2();
ampsq/=th;
ampsq/=16.;
return ampsq;
}
//qQbar->qQbarWg_unob
// Calculates the square of the current contractions for qQ->qenuQ scattering
// p1: quark (with W emittance)
// p2: Quark
double junobMWqQbarg (HLV p1out, HLV pe, HLV pnu,HLV p1in,
HLV p2out, HLV p2in, HLV pg
){
CCurrent mj1m,mj2p,mj2m;
HLV q1=p1in-p1out-pe-pnu;
HLV q2=-(p2in-p2out-pg);
HLV q3=-(p2in-p2out);
mj1m=jW(p1out,false,pe,false,pnu,false,p1in,false);
mj2p=jio(p2in,true,p2out,true);
mj2m=jio(p2in,false,p2out,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 jgbm,jgbp,j2gm,j2gp;
j2gp=joo(pg,true,p2out,true);
j2gm=joo(pg,false,p2out,false);
jgbp=jio(p2in,true,pg,true);
jgbm=jio(p2in,false,pg,false);
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
double WPropfact = WProp(pe, pnu);
ampsq*=WPropfact;
// Now add the t-channels
double th=q2.m2()*q1.m2();
ampsq/=th;
ampsq/=16.;
return ampsq;
}
//qbarQ->qbarQWg_unob
// Calculates the square of the current contractions for qQ->qenuQ scattering
// p1: quark (with W emittance)
// p2: Quark
double junobMWqbarQg (HLV p1out, HLV pe, HLV pnu,HLV p1in,
HLV p2out, HLV p2in, HLV pg
){
CCurrent mj1m,mj2p,mj2m;
HLV q1=p1in-p1out-pe-pnu;
HLV q2=-(p2in-p2out-pg);
HLV q3=-(p2in-p2out);
mj1m=jWbar(p1out,false,pe,false,pnu,false,p1in,false);
mj2p=joi(p2out,true,p2in,true);
mj2m=joi(p2out,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 jgbm,jgbp,j2gm,j2gp;
j2gp=joo(p2out,true,pg,true);
j2gm=joo(p2out,false,pg,false);
jgbp=joi(pg,true,p2in,true);
jgbm=joi(pg,false,p2in,false);
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
double WPropfact = WProp(pe, pnu);
ampsq*=WPropfact;
// Now add the t-channels
double th=q2.m2()*q1.m2();
ampsq/=th;
ampsq/=16.;
return ampsq;
}
//qbarQbar->qbarQbarWg_unob
// Calculates the square of the current contractions for qQ->qenuQ scattering
// p1: quark (with W emittance)
// p2: Quark
double junobMWqbarQbarg (HLV p1out, HLV pe, HLV pnu,HLV p1in,
HLV p2out, HLV p2in, HLV pg
){
CCurrent mj1m,mj2p,mj2m;
HLV q1=p1in-p1out-pe-pnu;
HLV q2=-(p2in-p2out-pg);
HLV q3=-(p2in-p2out);
mj1m=jWbar(p1out,false,pe,false,pnu,false,p1in,false);
mj2p=jio(p2in,true,p2out,true);
mj2m=jio(p2in,false,p2out,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 jgbm,jgbp,j2gm,j2gp;
j2gp=joo(pg,true,p2out,true);
j2gm=joo(pg,false,p2out,false);
jgbp=jio(p2in,true,pg,true);
jgbm=jio(p2in,false,pg,false);
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
double WPropfact = WProp(pe, pnu);
ampsq*=WPropfact;
// Now add the t-channels
double th=q2.m2()*q1.m2();
ampsq/=th;
ampsq/=16.;
return ampsq;
}
////////////////////////////////////////////////////////////////////
//qQ->qQWg_unof
// Calculates the square of the current contractions for qQ->qenuQ scattering
// p1: quark (with W emittance)
// p2: Quark
double junofMWgqQ (HLV pg,HLV p1out,HLV p1in, HLV p2out, HLV pe, HLV pnu, HLV p2in){
CCurrent mj2m,mj1p,mj1m;
HLV q1=p1in-p1out;
HLV qg=p1in-p1out-pg;
HLV q2=-(p2in-p2out-pe-pnu);
mj2m=jW(p2out,false,pe,false,pnu,false,p2in,false);
mj1p=joi(p1out,true,p1in,true);
mj1m=joi(p1out,false,p1in,false);
// Dot products of these which occur again and again
COM MWpm=mj1p.dot(mj2m); // And now for the Higgs ones
COM MWmm=mj1m.dot(mj2m);
CCurrent jgam,jgap,j2gm,j2gp;
j2gp=joo(p1out,true,pg,true);
j2gm=joo(p1out,false,pg,false);
jgap=joi(pg,true,p1in,true);
jgam=joi(pg,false,p1in,false);
CCurrent qsum(q1+qg);
CCurrent Lmp,Lmm,Lpp,Lpm,U1mp,U1mm,U1pp,U1pm,U2mp,U2mm,U2pp,U2pm,p2o(p2out),p2i(p2in);
CCurrent p1o(p1out);
CCurrent p1i(p1in);
Lmm=( qsum*(MWmm) + (-2.*mj2m.dot(pg))*mj1m + 2.*mj1m.dot(pg)*mj2m
+ ( p2o/pg.dot(p2out) + p2i/pg.dot(p2in) )*( qg.m2()*MWmm/2. ) )/q1.m2();
Lpm=( qsum*(MWpm) + (-2.*mj2m.dot(pg))*mj1p + 2.*mj1p.dot(pg)*mj2m
+ ( p2o/pg.dot(p2out) + p2i/pg.dot(p2in) )*( qg.m2()*MWpm/2. ) )/q1.m2();
U1mm=(jgam.dot(mj2m)*j2gm+2.*p1o*MWmm)/(p1out+pg).m2();
U1pm=(jgap.dot(mj2m)*j2gp+2.*p1o*MWpm)/(p1out+pg).m2();
U2mm=((-1.)*j2gm.dot(mj2m)*jgam+2.*p1i*MWmm)/(p1in-pg).m2();
U2pm=((-1.)*j2gp.dot(mj2m)*jgap+2.*p1i*MWpm)/(p1in-pg).m2();
double amm,apm;
amm=HEJ::C_F*(2.*vre(Lmm-U1mm,Lmm+U2mm))+2.*HEJ::C_F*HEJ::C_F/3.*vabs2(U1mm+U2mm);
apm=HEJ::C_F*(2.*vre(Lpm-U1pm,Lpm+U2pm))+2.*HEJ::C_F*HEJ::C_F/3.*vabs2(U1pm+U2pm);
double ampsq=-(apm+amm);
//Divide by WProp
double WPropfact = WProp(pe, pnu);
ampsq*=WPropfact;
// Now add the t-channels
double th=q2.m2()*qg.m2();
ampsq/=th;
ampsq/=16.;
return ampsq;
}
//qQbar->qQbarWg_unof
// Calculates the square of the current contractions for qQ->qenuQ scattering
// p1: quark (with W emittance)
// p2: Quark
double junofMWgqQbar (HLV pg,HLV p1out,HLV p1in, HLV p2out, HLV pe, HLV pnu,
HLV p2in
){
CCurrent mj2m,mj1p,mj1m;
HLV q1=p1in-p1out;
HLV qg=p1in-p1out-pg;
HLV q2=-(p2in-p2out-pe-pnu);
mj2m=jWbar(p2out,false,pe,false,pnu,false,p2in,false);
mj1p=joi(p1out,true,p1in,true);
mj1m=joi(p1out,false,p1in,false);
// Dot products of these which occur again and again
COM MWpm=mj1p.dot(mj2m); // And now for the Higgs ones
COM MWmm=mj1m.dot(mj2m);
CCurrent jgam,jgap,j2gm,j2gp;
j2gp=joo(p1out,true,pg,true);
j2gm=joo(p1out,false,pg,false);
jgap=joi(pg,true,p1in,true);
jgam=joi(pg,false,p1in,false);
CCurrent qsum(q1+qg);
CCurrent Lmp,Lmm,Lpp,Lpm,U1mp,U1mm,U1pp,U1pm,U2mp,U2mm,U2pp,U2pm,p2o(p2out),p2i(p2in);
CCurrent p1o(p1out);
CCurrent p1i(p1in);
Lmm=( qsum*(MWmm) + (-2.*mj2m.dot(pg))*mj1m + 2.*mj1m.dot(pg)*mj2m
+ ( p2o/pg.dot(p2out) + p2i/pg.dot(p2in) )*( qg.m2()*MWmm/2.) )/q1.m2();
Lpm=( qsum*(MWpm) + (-2.*mj2m.dot(pg))*mj1p + 2.*mj1p.dot(pg)*mj2m
+ ( p2o/pg.dot(p2out) + p2i/pg.dot(p2in) )*( qg.m2()*MWpm/2.) )/q1.m2();
U1mm=(jgam.dot(mj2m)*j2gm+2.*p1o*MWmm)/(p1out+pg).m2();
U1pm=(jgap.dot(mj2m)*j2gp+2.*p1o*MWpm)/(p1out+pg).m2();
U2mm=((-1.)*j2gm.dot(mj2m)*jgam+2.*p1i*MWmm)/(p1in-pg).m2();
U2pm=((-1.)*j2gp.dot(mj2m)*jgap+2.*p1i*MWpm)/(p1in-pg).m2();
double amm,apm;
amm=HEJ::C_F*(2.*vre(Lmm-U1mm,Lmm+U2mm))+2.*HEJ::C_F*HEJ::C_F/3.*vabs2(U1mm+U2mm);
apm=HEJ::C_F*(2.*vre(Lpm-U1pm,Lpm+U2pm))+2.*HEJ::C_F*HEJ::C_F/3.*vabs2(U1pm+U2pm);
double ampsq=-(apm+amm);
//Divide by WProp
double WPropfact = WProp(pe, pnu);
ampsq*=WPropfact;
// Now add the t-channels
double th=q2.m2()*qg.m2();
ampsq/=th;
ampsq/=16.;
return ampsq;
}
//qbarQ->qbarQWg_unof
// Calculates the square of the current contractions for qQ->qenuQ scattering
// p1: quark (with W emittance)
// p2: Quark
double junofMWgqbarQ (HLV pg,HLV p1out,HLV p1in, HLV p2out, HLV pe, HLV pnu,
HLV p2in
){
CCurrent mj2m,mj1p,mj1m;
HLV q1=p1in-p1out;
HLV qg=p1in-p1out-pg;
HLV q2=-(p2in-p2out-pe-pnu);
mj2m=jW(p2out,false,pe,false,pnu,false,p2in,false);
mj1p=jio(p1in,true,p1out,true);
mj1m=jio(p1in,false,p1out,false);
// Dot products of these which occur again and again
COM MWpm=mj1p.dot(mj2m); // And now for the Higgs ones
COM MWmm=mj1m.dot(mj2m);
CCurrent jgam,jgap,j2gm,j2gp;
j2gp=joo(pg,true,p1out,true);
j2gm=joo(pg,false,p1out,false);
jgap=jio(p1in,true,pg,true);
jgam=jio(p1in,false,pg,false);
CCurrent qsum(q1+qg);
CCurrent Lmp,Lmm,Lpp,Lpm,U1mp,U1mm,U1pp,U1pm,U2mp,U2mm,U2pp,U2pm,p2o(p2out),p2i(p2in);
CCurrent p1o(p1out);
CCurrent p1i(p1in);
Lmm=(qsum*(MWmm) + (-2.*mj2m.dot(pg))*mj1m + 2.*mj1m.dot(pg)*mj2m
+ ( p2o/pg.dot(p2out) + p2i/pg.dot(p2in) )*( qg.m2()*MWmm/2. ) )/q1.m2();
Lpm=(qsum*(MWpm) + (-2.*mj2m.dot(pg))*mj1p + 2.*mj1p.dot(pg)*mj2m
+ ( p2o/pg.dot(p2out) + p2i/pg.dot(p2in) )*( qg.m2()*MWpm/2. ) )/q1.m2();
U1mm=(jgam.dot(mj2m)*j2gm+2.*p1o*MWmm)/(p1out+pg).m2();
U1pm=(jgap.dot(mj2m)*j2gp+2.*p1o*MWpm)/(p1out+pg).m2();
U2mm=((-1.)*j2gm.dot(mj2m)*jgam+2.*p1i*MWmm)/(p1in-pg).m2();
U2pm=((-1.)*j2gp.dot(mj2m)*jgap+2.*p1i*MWpm)/(p1in-pg).m2();
double amm,apm;
amm=HEJ::C_F*(2.*vre(Lmm-U1mm,Lmm+U2mm))+2.*HEJ::C_F*HEJ::C_F/3.*vabs2(U1mm+U2mm);
apm=HEJ::C_F*(2.*vre(Lpm-U1pm,Lpm+U2pm))+2.*HEJ::C_F*HEJ::C_F/3.*vabs2(U1pm+U2pm);
double ampsq=-(apm+amm);
//Divide by WProp
double WPropfact = WProp(pe, pnu);
ampsq*=WPropfact;
// Now add the t-channels
double th=q2.m2()*qg.m2();
ampsq/=th;
ampsq/=16.;
return ampsq;
}
//qbarQbar->qbarQbarWg_unof
// Calculates the square of the current contractions for qQ->qenuQ scattering
// p1: quark (with W emittance)
// p2: Quark
double junofMWgqbarQbar (HLV pg,HLV p1out,HLV p1in, HLV p2out, HLV pe, HLV pnu,
HLV p2in
){
CCurrent mj2m,mj1p,mj1m;
HLV q1=p1in-p1out;
HLV qg=p1in-p1out-pg;
HLV q2=-(p2in-p2out-pe-pnu);
mj2m=jWbar(p2out,false,pe,false,pnu,false,p2in,false);
mj1p=jio(p1in,true,p1out,true);
mj1m=jio(p1in,false,p1out,false);
// Dot products of these which occur again and again
COM MWpm=mj1p.dot(mj2m); // And now for the Higgs ones
COM MWmm=mj1m.dot(mj2m);
CCurrent jgam,jgap,j2gm,j2gp;
j2gp=joo(pg,true,p1out,true);
j2gm=joo(pg,false,p1out,false);
jgap=jio(p1in,true,pg,true);
jgam=jio(p1in,false,pg,false);
CCurrent qsum(q1+qg);
CCurrent Lmp,Lmm,Lpp,Lpm,U1mp,U1mm,U1pp,U1pm,U2mp,U2mm,U2pp,U2pm,p2o(p2out),p2i(p2in);
CCurrent p1o(p1out);
CCurrent p1i(p1in);
Lmm=(qsum*(MWmm) + (-2.*mj2m.dot(pg))*mj1m + 2.*mj1m.dot(pg)*mj2m
+ ( p2o/pg.dot(p2out) + p2i/pg.dot(p2in) )*( qg.m2()*MWmm/2.) )/q1.m2();
Lpm=(qsum*(MWpm) + (-2.*mj2m.dot(pg))*mj1p + 2.*mj1p.dot(pg)*mj2m
+ ( p2o/pg.dot(p2out) + p2i/pg.dot(p2in) )*( qg.m2()*MWpm/2.) )/q1.m2();
U1mm=(jgam.dot(mj2m)*j2gm+2.*p1o*MWmm)/(p1out+pg).m2();
U1pm=(jgap.dot(mj2m)*j2gp+2.*p1o*MWpm)/(p1out+pg).m2();
U2mm=((-1.)*j2gm.dot(mj2m)*jgam+2.*p1i*MWmm)/(p1in-pg).m2();
U2pm=((-1.)*j2gp.dot(mj2m)*jgap+2.*p1i*MWpm)/(p1in-pg).m2();
double amm,apm;
amm=HEJ::C_F*(2.*vre(Lmm-U1mm,Lmm+U2mm))+2.*HEJ::C_F*HEJ::C_F/3.*vabs2(U1mm+U2mm);
apm=HEJ::C_F*(2.*vre(Lpm-U1pm,Lpm+U2pm))+2.*HEJ::C_F*HEJ::C_F/3.*vabs2(U1pm+U2pm);
double ampsq=-(apm+amm);
//Divide by WProp
double WPropfact = WProp(pe, pnu);
ampsq*=WPropfact;
// Now add the t-channels
double th=q2.m2()*qg.m2();
ampsq/=th;
ampsq/=16.;
return ampsq;
}
///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 = g.leftprod(Tp2+Tp3)/s23;
- Tensor<3> qqCurBlank2 = g.leftprod(Tpb)/s23;
+ 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;
}

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