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?
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