hi,
I am using feynarts and feyncalc to calculate the process: e+e-annihilation into a pair of photon. When I am doing the polarization sum of final state photon, I just replace the polarization vector by metric tensor,here is the mathematica code for this process:
Quit[];
$LoadPhi = True;
$LoadFeynArts = True;
$Configuration = "QED";
$Lagrangians = {"QED"[1], "QED"[2]};
<< HighEnergyPhysics`Feyncalc`
SetOptions[FourVector, FeynCalcInternal -> False];
tops = CreateTopologies[0, 2 -> 2];
Paint[tops, AutoEdit -> False, ColumnsXRows -> {4, 1}];
inserttops =
InsertFields[tops, {F[2, {1}], -F[2, {1}]} -> {V[1], V[1]},
InsertionLevel -> {Classes}, LastSelections -> {F[2, {1}]}];
Paint[inserttops, AutoEdit -> False, ColumnsXRows -> {3, 1}];
M20 = CreateFCAmp[inserttops] /. {ME -> me, EL -> e} // Total
M21 = ComplexConjugate[M20] /. {\[Mu]1 -> m1, \[Mu]2 -> m2}
M22 = M20*M21 // Expand
M23 = M22 /.
Pair[LorentzIndex[m1, D], Momentum[Polarization[p3, I], D]] Pair[
LorentzIndex[m2, D], Momentum[Polarization[p4, I], D]] Pair[
LorentzIndex[\[Mu]1, D], Momentum[Polarization[p3, -I], D]] Pair[
LorentzIndex[\[Mu]2, D], Momentum[Polarization[p4, -I], D]] ->
Pair[LorentzIndex[m1, D], LorentzIndex[\[Mu]1, D]] Pair[
LorentzIndex[m2, D], LorentzIndex[\[Mu]2, D]]
M24 = 1/4*FermionSpinSum[M23] // Contract
M25 = M24 /. DiracTrace -> TR // Simplify
M26 = M25 /. {Pair[Momentum[p2], Momentum[p2]] -> me^2,
Pair[Momentum[p3], Momentum[p3]] -> 0,
Pair[Momentum[p4], Momentum[p4]] -> 0,
PropagatorDenominator[Momentum[p2, D] + Momentum[p3, D], me] ->
1/(2 Pair[Momentum[p2], Momentum[p3]]),
PropagatorDenominator[Momentum[p2, D] + Momentum[p4, D], me] ->
1/(2 Pair[Momentum[p2], Momentum[p4]])}
M27 = M26 /. {Pair[Momentum[p2], Momentum[p3]] ->
Pair[Momentum[p1], Momentum[p4]],
Pair[Momentum[p2], Momentum[p4]] ->
Pair[Momentum[p1], Momentum[p3]],
Pair[Momentum[p3], Momentum[p4]] ->
Pair[Momentum[p1], Momentum[p2]] + me^2}
M28 = M27 /.
Pair[Momentum[p1],
Momentum[p2]] -> -Pair[Momentum[p1], Momentum[p4]] -
Pair[Momentum[p1], Momentum[p3]] - me^2 // Expand
M29 = M28 /. {Pair[Momentum[p1],
Momentum[p3]] -> -Pair[Momentum[p1], Momentum[k1]],
Pair[Momentum[p1],
Momentum[p4]] -> -Pair[Momentum[p1], Momentum[k2]]}
I am wondering why the final result differ by an overall minus sign from Peskin and if there are any better way to perform the whole process???
Thanks for Help!!!!!!!!!
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