diff --git a/src/jets.cc b/src/jets.cc index 4d41515..2ec1465 100644 --- a/src/jets.cc +++ b/src/jets.cc @@ -1,842 +1,830 @@ /** * \authors The HEJ collaboration (see AUTHORS for details) * \date 2019 * \copyright GPLv2 or later */ #include "HEJ/jets.hh" #include "HEJ/Tensor.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(std::abs(pout.plus())); const double sqpom = sqrt(std::abs(pout.minus())); // Allow for "jii" format const COM poperp = (pout.x()==0 && pout.y() ==0) ? -1 : 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(std::abs(pin.plus())); cur[0] = sqpop * sqpip; cur[1] = sqpom * sqpip * poperp / std::abs(poperp); cur[2] = -COM(0,1) * cur[1]; cur[3] = cur[0]; } else { // if backward const double sqpim = sqrt(std::abs(pin.minus())); cur[0] = -sqpom * sqpim * poperp / std::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(std::abs(pin.plus())); cur[0] = sqpop * sqpip; cur[1] = sqpom * sqpip * conj(poperp) / std::abs(poperp); cur[2] = COM(0,1) * cur[1]; cur[3] = cur[0]; } else { // if backward double sqpim = sqrt(std::abs(pin.minus())); cur[0] = -sqpom * sqpim * conj(poperp) / std::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(std::abs(pj.plus() )); const double sqpjm = sqrt(std::abs(pj.minus())); const double sqpip = sqrt(std::abs(pi.plus() )); const double sqpim = sqrt(std::abs(pi.minus())); // Allow for "jii" format const COM piperp = (pi.x()==0 && pi.y() ==0) ? -1 : pi.x()+COM(0,1)*pi.y(); const COM pjperp = (pj.x()==0 && pj.y() ==0) ? -1 : pj.x()+COM(0,1)*pj.y(); const COM phasei = piperp / std::abs(piperp); const COM phasej = pjperp / std::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; } namespace { void eps(HLV refmom, HLV kb, bool hel, current &ep){ //Positive helicity eps has negative helicity choices for spinors and vice versa joi(refmom,hel,kb,hel,ep); double norm; if(kb.z()<0.) norm = sqrt(2.*refmom.plus()*kb.minus()); else norm = sqrt(2.*refmom.minus()*kb.plus()); // Normalise std::for_each(begin(ep), end(ep), [&,norm](auto & val){val/=norm;}); } COM qggm1(HLV pa, HLV pb, HLV p1, HLV p2, HLV p3, bool helchain, bool heltop, bool helb,HLV refmom){ // 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); joi(p1, heltop, pa, heltop,cur1a); const double t2 = (p3-pb)*(p3-pb); //Calculate Term 1 in Equation 3.23 in James Cockburn's Thesis. 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 auto eta = HEJ::metric(); //eps eps(refmom,pb,helb, ep); COM M1=0.; // Perform Contraction: g^{ik} j_{1a}_k * v1_i^j eps^l g_lj for(int i=0;i<4;++i){ for(int j=0;j<4;++j){ M1+= eta(i,i) *cur1a[i]*(v1[i][j])*ep[j]*eta(j,j); } } return M1; } COM qggm2(HLV pa, HLV pb, HLV p1, HLV p2, HLV p3, bool helchain, bool heltop, bool helb,HLV refmom){ // 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); joi(p1, heltop, pa, heltop, cur1a); const double t2t = (p2-pb)*(p2-pb); //Calculate Term 2 in Equation 3.23 in James Cockburn's Thesis. 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 auto eta=HEJ::metric(); //eps eps(refmom,pb,helb, ep); COM M2=0.; // Perform Contraction: g^{ik} j_{1a}_k * v2_i^j eps^l g_lj for(int i=0;i<4;++i){ for(int j=0;j<4;++j){ M2+= eta(i,i)*cur1a[i]*(v2[i][j])*ep[j]*eta(j,j); } } return M2; } COM qggm3(HLV pa, HLV pb, HLV p1, HLV p2, HLV p3, bool helchain, bool heltop, bool helb,HLV refmom){ current qqcur,ep,cur1a; const double s23 = (p2+p3)*(p2+p3); joo(p2,helchain,p3,helchain,qqcur); joi(p1, heltop, pa, heltop,cur1a); //Redefine relevant momenta as currents - for ease of calling correct part of vector const current kb{pb.e(), pb.x(), pb.y(), pb.z()}; const current k2{p2.e(), p2.x(), p2.y(), p2.z()}; const current k3{p3.e(), p3.x(), p3.y(), p3.z()}; auto eta=HEJ::metric(); //Calculate Term 3 in Equation 3.23 in James Cockburn's Thesis. COM V3g[4][4]={}; const COM kbqq=kb[0]*qqcur[0] -kb[1]*qqcur[1] -kb[2]*qqcur[2] -kb[3]*qqcur[3]; for(int u=0;u<4;++u){ for(int v=0;v<4;++v){ V3g[u][v] += 2.*COM(0.,1.)*(((k2[v]+k3[v])*qqcur[u] - (kb[u])*qqcur[v])+ kbqq*eta(u,v))/s23; } } eps(refmom,pb,helb, ep); COM M3=0.; // Perform Contraction: g^{ik} j_{1a}_k * (v2_i^j) eps^l g_lj for(int i=0;i<4;++i){ for(int j=0;j<4;++j){ M3+= eta(i,i)*cur1a[i]*(V3g[i][j])*ep[j]*eta(j,j); } } return M3; } //Now the function to give helicity/colour sum/average double MqgtqQQ(HLV pa, HLV pb, HLV p1, HLV p2, HLV p3){ // 4 indepedent helicity choices (complex conjugation related). //Need to evalute each independent hel configuration and store that result somewhere const COM Mmmm1 = qggm1(pa,pb,p1,p2,p3,false,false,false, pa); const COM Mmmm2 = qggm2(pa,pb,p1,p2,p3,false,false,false, pa); const COM Mmmm3 = qggm3(pa,pb,p1,p2,p3,false,false,false, pa); const COM Mmmp1 = qggm1(pa,pb,p1,p2,p3,false,true, false, pa); const COM Mmmp2 = qggm2(pa,pb,p1,p2,p3,false,true, false, pa); const COM Mmmp3 = qggm3(pa,pb,p1,p2,p3,false,true, false, pa); const COM Mpmm1 = qggm1(pa,pb,p1,p2,p3,false,false,true, pa); const COM Mpmm2 = qggm2(pa,pb,p1,p2,p3,false,false,true, pa); const COM Mpmm3 = qggm3(pa,pb,p1,p2,p3,false,false,true, pa); const COM Mpmp1 = qggm1(pa,pb,p1,p2,p3,false,true, true, pa); const COM Mpmp2 = qggm2(pa,pb,p1,p2,p3,false,true, true, pa); const COM Mpmp3 = qggm3(pa,pb,p1,p2,p3,false,true, true, pa); //Colour factors: const COM cm1m1 = 8./3.; const COM cm2m2 = 8./3.; const COM cm3m3 = 6.; const COM cm1m2 = -1./3.; const COM cm1m3 = -3.*COM(0.,1.); const COM cm2m3 = 3.*COM(0.,1.); //Sqaure and sum for each helicity config: const 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))); const double 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))); const 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))); const double 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))); // Factor of 2 for the helicity for conjugate configurations return (2.*(Mmmm+Mmmp+Mpmm+Mpmp)/3.)/(pa-p1).m2()/(p2+p3-pb).m2(); } } // Extremal qqx double ME_Exqqx_qbarqQ(HLV pgin, HLV pqout, HLV pqbarout, HLV p2out, HLV p2in){ return MqgtqQQ(p2in, pgin, p2out, pqout, pqbarout); } double ME_Exqqx_qqbarQ(HLV pgin, HLV pqout, HLV pqbarout, HLV p2out, HLV p2in){ return MqgtqQQ(p2in, pgin, p2out, pqbarout, pqout); } double ME_Exqqx_qbarqg(HLV pgin, HLV pqout, HLV pqbarout, HLV p2out, HLV p2in){ return MqgtqQQ(p2in, pgin, p2out, pqout, pqbarout)*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, pqbarout, pqout)*K_g(p2out,p2in)/HEJ::C_F; } namespace { void CurrentMatrix(current j1, current j2, COM array[4][4]){ for(int i=0;i<4;i++){ for(int j=0;j<4;j++){ array[i][j]=j1[i]*j2[j]; } } } //qqbar produced in the middle COM m1(current jtop, current jbot, bool hel2, HLV ka, HLV kb, HLV k2, HLV k3, std::vector<HLV> partons, unsigned int nabove){ //Define a load of invaraints I need const double s23 = 2.*(k2*k3); const double sa2 = 2.*(ka*k2); const double sa3 = 2.*(ka*k3); const double s12 = 2.*(partons.front()*k2); const double s13 = 2.*(partons.front()*k3); const double sb2 = 2.*(kb*k2); const double sb3 = 2.*(kb*k3); const double s42 = 2.*(partons.back()*k2); const double s43 = 2.*(partons.back()*k3); HLV q1=ka-partons.front(); for(unsigned int i=1;i<nabove+1;i++) q1-=partons.at(i); const HLV q2=q1-partons.at(nabove+2)-partons.at(nabove+1); const double t1 = q1.m2(); const double t3 = q2.m2(); //Easier to have everything in terms of 'currents' //(E,px,py,pz). To make the distinction between actual currents of //the form ubar gamma u and 4-vectors being placed under the //'current' class (to make dot products work out), all actual //currents will have either a j or 'cur' in their variable name. current cur23,curka,curkb,curk1,curk2,curk3,curk4,qc1,qc2; //From what I gather, joo is what I use for two outgoing momenta, //jio with one outgoing and one incoming (in that order) and j for //lines when pa,pb are on the right of the spinor product joo(k2,hel2,k3,hel2,cur23); curka[0]=ka.e(); curka[1]=ka.px(); curka[2]=ka.py(); curka[3]=ka.pz(); curkb[0]=kb.e(); curkb[1]=kb.px(); curkb[2]=kb.py(); curkb[3]=kb.pz(); curk1[0]=partons.front().e(); curk1[1]=partons.front().px(); curk1[2]=partons.front().py(); curk1[3]=partons.front().pz(); curk2[0]=k2.e(); curk2[1]=k2.px(); curk2[2]=k2.py(); curk2[3]=k2.pz(); curk3[0]=k3.e(); curk3[1]=k3.px(); curk3[2]=k3.py(); curk3[3]=k3.pz(); curk4[0]=partons.back().e(); curk4[1]=partons.back().px(); curk4[2]=partons.back().py(); curk4[3]=partons.back().pz(); qc1[0]=q1.e(); qc1[1]=q1.px(); qc1[2]=q1.py(); qc1[3]=q1.pz(); qc2[0]=q2.e(); qc2[1]=q2.px(); qc2[2]=q2.py(); qc2[3]=q2.pz(); //Metric tensor auto eta=HEJ::metric(); //Create the two bits of this vertex COM veik[4][4],v3g[4][4]; for(int i=0;i<4;i++) { for(int j=0;j<4;j++){ veik[i][j] = (cdot(cur23,curka)*(t1/(sa2+sa3))+cdot(cur23,curk1)* (t1/(s12+s13))-cdot(cur23,curkb)*(t3/(sb2+sb3))- cdot(cur23,curk4)*(t3/(s42+s43)))*eta(i,j); } } for(int i=0;i<4;i++){ for(int j=0;j<4;j++){ v3g[i][j] = qc1[j]*cur23[i]+curk2[j]*cur23[i]+curk3[j]*cur23[i]+ qc2[i]*cur23[j]-curk2[i]*cur23[j]-curk3[i]*cur23[j]- (cdot(qc1,cur23)+cdot(qc2,cur23))*eta(i,j); } } //Now dot in the currents - potential problem here with Lorentz //indicies, so check this 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)*jtop[k]*(veik[i][j]+v3g[i][j])*jbot[l]*eta(l,j); - } - } + M1+= eta(i,i)*jtop[i]*(veik[i][j]+v3g[i][j])*jbot[j]*eta(j,j); } } M1/=s23; return M1; } COM m2 (current jtop, current jbot, bool hel2, HLV ka, HLV k2, HLV k3, std::vector<HLV> partons, unsigned int nabove){ //In order to get correct momentum dependence in the vertex, forst //have to work with CCurrent objects and then convert to 'current' current cur22,cur23,cur2q,curq3; COM qarray[4][4]={}; COM temp[4][4]={}; joo(k2,hel2,k2,hel2,cur22); joo(k2,hel2,k3,hel2,cur23); joi(k2,hel2,ka,hel2,cur2q); jio(ka,hel2,k3,hel2,curq3); CurrentMatrix(cur2q, curq3, qarray); for(unsigned int i =0; i<nabove+1; i++){ joo(k2,hel2,partons.at(i),hel2,cur2q); joo(partons.at(i),hel2,k3,hel2,curq3); CurrentMatrix(cur2q, curq3, temp); for(int ii=0;ii<4;ii++){ for(int jj=0;jj<4;jj++){ qarray[ii][jj]=qarray[ii][jj]-temp[ii][jj]; } } } HLV qt=ka-k2; for(unsigned int i=0; i<nabove+1;i++){ qt-=partons.at(i); } const double t2=qt*qt; //Metric tensor auto eta=HEJ::metric(); COM tempv[4][4]; for(int i=0; i<4;i++){ for(int j=0;j<4;j++){ tempv[i][j] = COM(0.,1.)*(qarray[i][j]-cur22[i]*cur23[j]); } } 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)*jtop[k]*(tempv[i][j])*jbot[l]*eta(l,j); - } - } + M2+= eta(i,i)*jtop[i]*(tempv[i][j])*jbot[j]*eta(j,j); } } M2/=t2; return M2; } COM m3 (current jtop, current jbot, bool hel2, HLV ka, HLV k2, HLV k3, std::vector<HLV> partons, unsigned int nabove){ COM M3=0.; current cur23,cur33,cur2q,curq3; COM qarray[4][4]={}; COM temp[4][4]={}; joo(k3,hel2,k3,hel2,cur33); joo(k2,hel2,k3,hel2,cur23); joi(k2,hel2,ka,hel2,cur2q); jio(ka,hel2,k3,hel2,curq3); CurrentMatrix(cur2q, curq3, qarray); for(unsigned int i =0; i<nabove+1; i++){ joo(k2,hel2,partons.at(i),hel2,cur2q); joo(partons.at(i),hel2,k3,hel2,curq3); CurrentMatrix(cur2q, curq3, temp); for(int ii=0;ii<4;ii++){ for(int jj=0;jj<4;jj++){ qarray[ii][jj]=qarray[ii][jj]-temp[ii][jj]; } } } HLV qt=ka-k3; for(unsigned int i=0; i<nabove+1;i++){ qt-=partons.at(i); } const double t2t=qt*qt; //Metric tensor auto eta=HEJ::metric(); COM tempv[4][4]; for(int i=0; i<4;i++){ for(int j=0;j<4;j++){ tempv[i][j] = COM(0.,-1.)*(qarray[j][i]-cur23[j]*cur33[i]); } } 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)*jtop[k]*(tempv[i][j])*jbot[l]*eta(l,j); - } - } + M3+= eta(i,i)*jtop[i]*(tempv[i][j])*jbot[j]*eta(j,j); } } M3/= t2t; return M3; } } double ME_Cenqqx_qq(HLV ka, HLV kb, std::vector<HLV> partons, bool aqlinepa, bool aqlinepb, bool qqxmarker, int nabove){ //Partons in the 'wrong' ordering, so reverse it. Just put ka = //forward and kb = backward into the function call std::reverse(partons.begin(),partons.end()); //Get all the possible outer currents current j1p,j1m,j4p,j4m; if(!(aqlinepa)){ joi(partons.front(),true,ka,true,j1p); joi(partons.front(),false,ka,false,j1m); } if(aqlinepa){ jio(ka,true,partons.front(),true,j1p); jio(ka,false,partons.front(),false,j1m); } if(!(aqlinepb)){ joi(partons.back(),true,kb,true,j4p); joi(partons.back(),false,kb,false,j4m); } if(aqlinepb){ jio(kb,true,partons.back(),true,j4p); jio(kb,false,partons.back(),false,j4m); } HLV k2,k3; if(!(qqxmarker)){ k2=partons.at(nabove+1); k3=partons.at(nabove+2); } else{ k2=partons.at(nabove+2); k3=partons.at(nabove+1); } //8 helicity choices we can make, but only 4 indepedent ones //(complex conjugation related). const COM Mmmm1 = m1(j1m,j4m,false,ka,kb,k2,k3,partons,nabove); const COM Mmmm2 = m2(j1m,j4m,false,ka, k2,k3,partons,nabove); const COM Mmmm3 = m3(j1m,j4m,false,ka, k2,k3,partons,nabove); const COM Mmmp1 = m1(j1m,j4m,true, ka,kb,k2,k3,partons,nabove); const COM Mmmp2 = m2(j1m,j4m,true, ka, k2,k3,partons,nabove); const COM Mmmp3 = m3(j1m,j4m,true, ka, k2,k3,partons,nabove); const COM Mpmm1 = m1(j1p,j4m,false,ka,kb,k2,k3,partons,nabove); const COM Mpmm2 = m2(j1p,j4m,false,ka, k2,k3,partons,nabove); const COM Mpmm3 = m3(j1p,j4m,false,ka, k2,k3,partons,nabove); const COM Mpmp1 = m1(j1p,j4m,true, ka,kb,k2,k3,partons,nabove); const COM Mpmp2 = m2(j1p,j4m,true, ka, k2,k3,partons,nabove); const COM Mpmp3 = m3(j1p,j4m,true, ka, k2,k3,partons,nabove); //Colour factors: const COM cm1m1=3.; const COM cm2m2=4./3.; const COM cm3m3=4./3.; const COM cm1m2 =3./2.*COM(0.,1.); const COM cm1m3 = -3./2.*COM(0.,1.); const COM cm2m3 = -1./6.; //Square and sum for each helicity config: const 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))); const double 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))); const 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))); const double 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 or t-channel props). Factor of //2 for the 4 helicity configurations I didn't work out explicitly HLV prop1 = ka; for(int i=0; i<=nabove; i++){ prop1 -= partons[i]; } const HLV prop2 = prop1 - k2 - k3; return (2.*(Mmmm+Mmmp+Mpmm+Mpmp)/9./4.) / ((ka-partons.front()).m2()*(kb-partons.back()).m2()*prop1.m2()*prop2.m2()); }