void FullAmplitude_External::BuildColorMatrix
(const size_t &ci,const size_t &cj)
{
m_colfs[ci][cj].
resize(m_amap.size(),std::vector<Complex>
(m_amap.size(),Complex(0.0,0.0)));
for (size_t a=0;a<m_amap.size();++a) {
const std::vector<int> &cp(m_amap[a].m_perm);
int nsuba, psuba, swapa;
Flavour_Vector fla;
std::vector<size_t> ida, perma(cp.begin(),cp.end());
GetPermutation(perma,ida,fla,nsuba,psuba,swapa);
msg_Debugging()<<"A: "<<perma<<ida<<fla<<" sub = -"<<nsuba<<"/+"<<psuba
<<" swap = "<<swapa<<" ( em = "<<ci<<" )\n";
msg_Indent();
for (size_t b=a;b<m_amap.size();++b) {
const std::vector<int> &cp(m_amap[b].m_perm);
int nsubb, psubb, swapb;
Flavour_Vector flb;
std::vector<size_t> idb, permb(cp.begin(),cp.end());
GetPermutation(permb,idb,flb,nsubb,psubb,swapb);
msg_Debugging()<<"B: "<<permb<<idb<<flb<<" sub = -"<<nsubb<<"/+"<<psubb
<<" swap = "<<swapb<<" ( sp = "<<cj<<" )\n";
msg_Indent();
Expression expression(100,100);
expression.pop_back();
expression.SetTR(p_calc->TR());
size_t ad(expression.AIndex()), lf(expression.FIndex()), fl(lf);
for (size_t i=0;i<fla.size();++i) {
if (fla[i].StrongCharge()==3) {
if (i>0) lf=expression.FIndex();
expression.push_back(Delta::New(ida[i]+1,lf));
if (ci!=cj) {
if (ci==ida[i]) {
size_t nlf=expression.FIndex();
expression.push_back(Fundamental::New(ad,lf,nlf));
lf=nlf;
}
}
}
else if (fla[i].StrongCharge()==-3) {
if (ci!=cj) {
if (ci==ida[i]) {
size_t nlf=expression.FIndex();
expression.push_back(Fundamental::New(ad,lf,nlf));
expression.push_back(CNumber::New(Complex(-1.0)));
lf=nlf;
}
}
expression.push_back(Delta::New(lf,ida[i]+1));
}
else {
if (ci==cj) {
size_t nlf=expression.FIndex();
expression.push_back(Fundamental::New(ida[i]+1,lf,nlf));
lf=nlf;
}
else {
if (ci!=ida[i]) {
size_t nlf=expression.FIndex();
expression.push_back(Fundamental::New(ida[i]+1,lf,nlf));
lf=nlf;
}
else {
size_t la=expression.AIndex();
size_t nlf=expression.FIndex();
expression.push_back(Fundamental::New(la,lf,nlf));
expression.push_back(Adjoint::New(ad,ida[i]+1,la));
expression.push_back(CNumber::New(Complex(0.0,-1.0)));
lf=nlf;
}
}
}
}
if (fla.back().StrongCharge()==3 ||
fla.back().StrongCharge()==8)
expression.push_back(Delta::New(lf,fl));
fl=lf=expression.FIndex();
for (size_t i=0;i<flb.size();++i) {
if (flb[i].StrongCharge()==3) {
if (i>0) lf=expression.FIndex();
expression.push_back(Delta::New(lf,idb[i]+1));
if (ci!=cj) {
if (cj==idb[i]) {
size_t nlf=expression.FIndex();
expression.push_back(Fundamental::New(ad,nlf,lf));
lf=nlf;
}
}
}
else if (flb[i].StrongCharge()==-3) {
if (ci!=cj) {
if (cj==idb[i]) {
size_t nlf=expression.FIndex();
expression.push_back(Fundamental::New(ad,nlf,lf));
expression.push_back(CNumber::New(Complex(-1.0)));
lf=nlf;
}
}
expression.push_back(Delta::New(idb[i]+1,lf));
}
else {
if (ci==cj) {
size_t nlf=expression.FIndex();
expression.push_back(Fundamental::New(idb[i]+1,nlf,lf));
lf=nlf;
}
else {
if (cj!=idb[i]) {
size_t nlf=expression.FIndex();
expression.push_back(Fundamental::New(idb[i]+1,nlf,lf));
lf=nlf;
}
else {
size_t la=expression.AIndex();
size_t nlf=expression.FIndex();
expression.push_back(Fundamental::New(la,nlf,lf));
expression.push_back(Adjoint::New(ad,la,idb[i]+1));
expression.push_back(CNumber::New(Complex(0.0,-1.0)));
lf=nlf;
}
}
}
}
if (fla.back().StrongCharge()==3 ||
flb.back().StrongCharge()==8)
expression.push_back(Delta::New(fl,lf));
if (msg_LevelIsDebugging()) expression.Print();
expression.Evaluate();
Complex col=expression.Result();
if (nsuba || nsubb) col/=pow(-expression.NC(),nsuba+nsubb);
if (psuba || psubb) col/=pow(expression.NC(),psuba+psubb);
if ((swapa+swapb)%2) col=-col;
double T2=1.0;
if (ci!=cj) {
if (m_fls[ci].StrongCharge()==8) {
T2=expression.NC()*expression.TR();
T2/=CSC.CA*CSC.TR;
}
else {
T2=expression.TR()*(expression.NC()-1.0/expression.NC());
T2/=CSC.CF;
}
}
msg_Debugging()<<"A B^* = "<<col<<" <- sub = -"<<nsuba+nsubb
<<"/+"<<psuba+psubb<<", swap = "<<swapa+swapb
<<", T2 = "<<T2<<" ("<<a<<","<<b<<")\n";
m_colfs[ci][cj][a][b]=col/T2;
m_colfs[ci][cj][b][a]=conj(col)/T2;
}
}
}
