Name: Vitaly Magerya Date: 03/08/19-04:39:49 PM Z

Hi, folks. If you’ll generate am amplitude involving a sum over
quark flavors in FeynArts, e.g. photon -> q qbar:

    $LoadFeynArts = True;
    «FeynCalc`;
    topologies = CreateTopologies[0, 1 -> 2, ExcludeTopologies -> {Tadpoles}];
    diagrams = InsertFields[topologies,
      {V[1]} -> {F[3], -F[3]},
      InsertionLevel -> {Classes},
      Model -> “SMQCD”
    ];
    amplitude = FCFAConvert[CreateFeynAmp[diagrams],
      IncomingMomenta -> {q},
      OutgoingMomenta -> {k1, k2},
      UndoChiralSplittings -> True,
      ChangeDimension -> d,
      List -> False,
      SMP -> True
    ]/.{MQU[_] -> 0, MQD[_] -> 0, SMP[“m_u”] -> 0}

… then you’ll get these factors in the amplitude:
    SumOver[Index[Generation, 2], 3, External]
    SUNFDelta[SUNFIndex[Index[Generation, 2]], SUNFIndex[Index[Generation, 3]]]

Now, trying to calculate the matrix element as:
    amplitude*ComplexConjugate[FCRenameDummyIndices[amplitude]] // SUNSimplify,

… that factor is immediately turned into CA==SUNN. This would
have made sense, except that this should be the number of
generations, not colors. NF/2, maybe?

A related observation: fermion loops imported from FeynArts don’t
even have SUNFDelta’s related to generation indices at all, they
only have a SumOver.

So, my question is: how exactly do you deal with fermion flavor
sums? I mean it’s easy to fix these two examples manually, but at
e.g. 2 loops, there are more elaborate combinations of SumOver
and SUNFDelta that may appear. Should I try to untangle them
manually?