double Vrel(Vec4D p1,Vec4D& p2)
{
double m21=(p1+p2).Abs2();
double m1=p1.Abs2();
double m2=p2.Abs2();
return sqrt(Lambda(m21,m1,m2))/(m21-m1-m2);
}
Complex W_To_Lepton_Neutrino::InfraredSubtractedME_1_05(unsigned int i) {
m_moms = m_moms1[i]; // set to set of momenta to be used
Vec4C epsW = Polarization_Vector(m_moms[0])[m_spins[0]];
Vec4C epsP = conj(Polarization_Vector(m_moms[3])[m_spins[3]]);
Vec4D q = m_moms[1]+m_moms[3]; // fermion propagator momenta
double q2 = q.Abs2();
Vec4D Q = m_moms[0]-m_moms[3]; // boson propagator momenta
double Q2 = Q.Abs2();
double m = m_masses[1]; // fermion mass/propagator pole
double m2 = sqr(m);
double M = m_masses[0]; // boson mass/propagator pole
double M2 = sqr(M);
m_moms[4] = m_moms[5] = q; // enter those into m_moms
m_flavs[4] = m_flavs[1]; // set to corresponding particle/antiparticle
m_flavs[5] = m_flavs[1].Bar();
XYZFunc XYZ(6,m_moms,m_flavs,false);
m_flavs[4] = m_flavs[5] = Flavour(kf_none);
// two diagrams
// M_1 = -ie^2/(2sqrt(2)sW) * 1/((pl+k)^2-m^2)
// * ubar(l)gamma^mu(-pl-k+m)gamma^nu P_L v(nu) eps_nu^W eps_mu^y*
// M_2 = ie/(2sqrt(2)sW) * 1/(pW-k)^2-M^2)
// * ubar(l)gamma_rho P_L v(nu)
// * [-2g^{rho,nu}pW^mu + g^{rho,mu}pW^nu
// + g^{nu,mu}k^rho + 1/M^2(pW-k)^rho pW^nu pW^mu]
// * eps_nu^W eps_mu^y*
Complex r1 = Complex(0.,0.);
Complex r2 = Complex(0.,0.);
Complex r3 = Complex(0.,0.);
Lorentz_Ten3C ten31,ten32,ten33,ten34;
for (unsigned int s=0; s<=1; s++) {
r1 += XYZ.X(1,m_spins[1],epsP,4,s,1.,1.)
*XYZ.X(4,s,epsW,2,m_spins[2],m_cR,m_cL);
r2 += XYZ.X(1,m_spins[1],epsP,5,s,1.,1.)
*XYZ.X(5,s,epsW,2,m_spins[2],m_cR,m_cL);
}
Vec4D p = m_moms[0];
Vec4D k = m_moms[3];
// index ordering rho(1),nu(2),mu(3)
// -2g^{rho,nu}pW^mu
ten31 = BuildTensor(MetricTensor(),-2.*p);
// g^{rho,mu}pW^nu
ten32 = BuildTensor(MetricTensor(),p).Transpose(2,3);
// g^{nu,mu}k^rho
ten33 = BuildTensor(MetricTensor(),k).Transpose(1,3);
// 1/M^2(pW-k)^rho pW^nu pW^mu
ten34 = -1./M2*BuildTensor(p-k,p,p);
Lorentz_Ten3C ten = ten31+ten32+ten33+ten34;
// v^\sigma = L^\sigma\mu\lambda epsW_\mu epsP_\lambda
Vec4C v3 = Contraction(Contraction(ten,3,epsP),2,epsW);
r3 = XYZ.X(1,m_spins[1],v3,2,m_spins[2],m_cR,m_cL);
r1 *= (1.+m/sqrt(q2))/(q2-m2);
r2 *= (1.-m/sqrt(q2))/(q2-m2);
r3 *= -1./(Q2-M2);
return (m_i*m_e*m_e)/(2.*m_sqrt2*m_sW)*(r1+r2/*+r3*/);
}
LN_Pair PHASIC::GetLN
(const Vec4D &pi,const Vec4D &pk,const int mode)
{
double mi2(pi.Abs2()), mk2(pk.Abs2());
double eps(pi*pk), kap(eps*eps-mi2*mk2);
if (kap<0.0) return LN_Pair();
kap=Sign(eps)*sqrt(kap);
Vec4D l(((eps+kap)*pi-mi2*pk)/(2.0*kap));
Vec4D n(((eps+kap)*pk-mk2*pi)/(2.0*kap));
return LN_Pair(l,n,mode);
}
void Kinematics_Base::SetFixVec(Parton *const p,Vec4D mom,
const Kin_Args <,const int mode) const
{
if (p->GetNext()) SetFixVec(p->GetNext(),mom,lt,mode|4);
if (p->FixSpec()==Vec4D()) return;
Vec4D oldp(p->OldMomentum()), ref(p->FixSpec());
if ((mode&3)==3 || ((mode&1)==1 && lt.m_mode==0)) {
if (mode&4) {
Poincare_Sequence lam(lt.m_lam);
lam.Invert();
mom=lam*mom;
}
else {
oldp=lt.m_lam*oldp;
ref=lt.m_lam*ref;
}
}
if (IsEqual(oldp,mom,rpa->gen.SqrtAccu())) {
p->SetFixSpec(ref);
p->SetOldMomentum(oldp);
return;
}
Vec4D np(0.0,cross(Vec3D(oldp),Vec3D(mom)));
if (np.PSpat2()<=1.0e-6) {
msg_Debugging()<<"Set fixed n_perp\n";
np=Vec4D(0.0,cross(Vec3D(oldp),Vec3D(1.0,1.0,0.0)));
}
np*=1.0/np.PSpat();
Vec4D lp(0.0,cross(Vec3D(oldp),Vec3D(np)));
lp*=1.0/lp.PSpat();
Vec4D pl(0.0,(Vec3D(ref)*Vec3D(lp))*lp);
Vec4D pn(0.0,(Vec3D(ref)*Vec3D(np))*np);
double D(oldp*ref), T(oldp.PSpat()), F(ref[0]);
double Q(mom[0]), P(mom.PSpat()), S(mom.Abs2());
Poincare rot(oldp,mom);
if (oldp.Abs2()>1.0e-3 && mom.Abs2()>1.0e-3) {
Poincare oldcms(oldp), newcms(mom);
oldcms.Boost(ref);
rot.Rotate(ref);
newcms.BoostBack(ref);
}
else {
double E((Q*D+P/T*(F*S-Q*D))/S);
ref=Vec4D(E,Vec3D(mom)*(Q*E-D)/(P*P));
ref+=pn+rot*pl;
}
p->SetFixSpec(ref);
p->SetOldMomentum(mom);
}
double pT2pythia(Cluster_Amplitude* ampl, const Cluster_Leg& RadAfterBranch,
const Cluster_Leg& EmtAfterBranch,
const Cluster_Leg& RecAfterBranch, int ShowerType){
// Save type: 1 = FSR pT definition, else ISR definition
int Type = ShowerType;
// Calculate virtuality of splitting
int sign = (Type==1) ? 1 : -1;
Vec4D Q(RadAfterBranch.Mom() + sign*EmtAfterBranch.Mom());
double Qsq = sign * Q.Abs2();
// Mass term of radiator
DEBUG_VAR(ampl->MS());
double m2Rad = ( abs(RadAfterBranch.Flav().Kfcode()) >= 4
&& abs(RadAfterBranch.Flav().Kfcode()) < 7)
? ampl->MS()->Mass2(RadAfterBranch.Flav())
: 0.;
// Construct 2->3 variables for FSR
Vec4D sum = RadAfterBranch.Mom() + RecAfterBranch.Mom()
+ EmtAfterBranch.Mom();
double m2Dip = sum.Abs2();
double x1 = 2. * (sum * RadAfterBranch.Mom()) / m2Dip;
double x3 = 2. * (sum * EmtAfterBranch.Mom()) / m2Dip;
// Construct momenta of dipole before/after splitting for ISR
Vec4D qBR(RadAfterBranch.Mom() - EmtAfterBranch.Mom() + RecAfterBranch.Mom());
Vec4D qAR(RadAfterBranch.Mom() + RecAfterBranch.Mom());
// Calculate z of splitting, different for FSR and ISR
double z = (Type==1) ? x1/(x1+x3)
: (qBR.Abs2())/( qAR.Abs2());
// Separation of splitting, different for FSR and ISR
double pTpyth = (Type==1) ? z*(1.-z) : (1.-z);
// pT^2 = separation*virtuality
pTpyth *= (Qsq - sign*m2Rad);
if(pTpyth < 0.) pTpyth = 0.;
// Return pT
return pTpyth;
}
PDF::CParam Default_Core_Scale::Calculate(Cluster_Amplitude *const ampl)
{
DEBUG_FUNC("");
msg_Debugging()<<*ampl<<"\n";
if (ampl->Legs().size()==3 && ampl->NIn()==2) {
double kt2cmin(ampl->Leg(2)->Mom().Abs2());
return PDF::CParam(kt2cmin,kt2cmin,0.0,kt2cmin,-1);
}
double muf2(0.0), mur2(0.0), muq2(0.0);
Cluster_Amplitude *campl(Cluster(ampl->Copy()));
if (campl->Legs().size()!=ampl->Legs().size())
msg_Debugging()<<*campl<<"\n";
if (campl->Legs().size()!=4) {
double q2((campl->Leg(0)->Mom()+campl->Leg(1)->Mom()).Abs2());
Vec4D ewsum;
for (size_t i(0);i<campl->Legs().size();++i)
if (!campl->Leg(i)->Flav().Strong()) ewsum+=campl->Leg(i)->Mom();
if (ewsum==Vec4D()) ewsum=campl->Leg(0)->Mom()+campl->Leg(1)->Mom();
if (campl->NIn()==2 &&
campl->Leg(0)->Flav().Strong() &&
campl->Leg(1)->Flav().Strong()) {// HThat'/2
q2=ewsum.PPerp();
for (size_t i(0);i<campl->Legs().size();++i)
if (campl->Leg(i)->Flav().Strong())
q2+=campl->Leg(i)->Mom().PPerp();
q2=sqr(ewsum.Mass()+q2/2.0);
}
campl->Delete();
return PDF::CParam(q2,dabs(ewsum.Abs2()),0.0,q2,-1);
}
Flavour_Vector fl; fl.resize(4);
fl[0]=campl->Leg(0)->Flav();
fl[1]=campl->Leg(1)->Flav();
fl[2]=campl->Leg(2)->Flav();
fl[3]=campl->Leg(3)->Flav();
if (fl[0].Strong() && fl[1].Strong()) {// hh collision
if (fl[2].Strong() && fl[3].Strong()) {
msg_Debugging()<<"pure QCD like\n";
double s(2.0*campl->Leg(0)->Mom()*campl->Leg(1)->Mom());
double t(2.0*campl->Leg(0)->Mom()*campl->Leg(2)->Mom());
double u(2.0*campl->Leg(0)->Mom()*campl->Leg(3)->Mom());
muq2=muf2=mur2=-1.0/(1.0/s+1.0/t+1.0/u)/4.0;
}
else if (!fl[2].Strong() && !fl[3].Strong()) {
msg_Debugging()<<"DY like\n";
muq2=muf2=mur2=(campl->Leg(0)->Mom()+campl->Leg(1)->Mom()).Abs2();
}
else if (fl[2].Strong() && !fl[3].Strong()) {
msg_Debugging()<<"jV like\n";
muq2=muf2=mur2=campl->Leg(3)->Mom().MPerp2()/4.0;
}
else if (!fl[2].Strong() && fl[3].Strong()) {
msg_Debugging()<<"Vj like\n";
muq2=muf2=mur2=campl->Leg(2)->Mom().MPerp2()/4.0;
}
else THROW(fatal_error,"Internal error.");
}
else if (!fl[0].Strong() && !fl[1].Strong()) {// ll collision
if (fl[2].Strong() && fl[3].Strong()) {
msg_Debugging()<<"jets like\n";
muq2=muf2=mur2=(campl->Leg(0)->Mom()+campl->Leg(1)->Mom()).Abs2();
}
}
else {// lh collision
msg_Debugging()<<"DIS like\n";
muq2=muf2=mur2=dabs((campl->Leg(fl[0].Strong()?1:0)->Mom()+
campl->Leg(fl[2].Strong()?3:2)->Mom()).Abs2());
}
campl->Delete();
msg_Debugging()<<"\\mu_f = "<<sqrt(muf2)<<"\n"
<<"\\mu_r = "<<sqrt(mur2)<<"\n"
<<"\\mu_q = "<<sqrt(muq2)<<"\n";
return PDF::CParam(muf2,muq2,0.0,mur2,-1);
}
void II_DipoleSplitting::SetMomenta(const Vec4D *mom)
{
m_mom.clear();
for(int i=0;i<=m_m;i++) m_mom.push_back(mom[i]);
m_pi = mom[m_i];
m_pj = mom[m_j];
m_pk = mom[m_k];
m_xijk = (m_pk*m_pi-m_pi*m_pj-m_pj*m_pk)/(m_pk*m_pi);
m_ptk = m_pk;
m_ptij = m_xijk*m_pi;
Vec4D K = m_pi-m_pj+m_pk;
Vec4D Kt = m_ptij+m_pk;
Vec4D KKt = K+Kt;
for(int i=2;i<=m_m;i++) m_mom[i]-=2.*(m_mom[i]*KKt/KKt.Abs2()*KKt-m_mom[i]*K/K.Abs2()*Kt);
m_vi = (m_pi*m_pj)/(m_pi*m_pk);
m_a = m_vi;
m_Q2 = (-m_pi+m_pj-m_pk).Abs2();
if (m_es==0) {
m_kt2 = m_Q2*(1.-m_xijk)/m_xijk*m_vi;
}
else {
m_kt2 = m_Q2/m_xijk*m_vi;
switch (m_ft) {
case 1:
m_kt2*=(1.-m_xijk);
break;
case 4:
m_kt2*=(1.-m_xijk);
break;
}
}
// m_pt1 = m_pj;
// m_pt2 =-1.*m_vi*m_pk;
m_pt1 = m_pj-m_vi*m_pk;
m_pt2 = m_ptij;
switch (m_ft) {
case 1:
m_sff = 2./(1.-m_xijk)-(1.+m_xijk);
m_av = m_sff;
break;
case 2:
m_sff = 1.-2.*m_xijk*(1.-m_xijk);
m_av = m_sff;
break;
case 3:
m_sff = m_xijk;
m_av = m_sff + 2.0*(1.0-m_xijk)/m_xijk;
break;
case 4:
m_sff = m_xijk/(1.-m_xijk)+m_xijk*(1.-m_xijk);
m_av = m_sff + (1.0-m_xijk)/m_xijk;
}
}