Name: L.X. Xu (email_not_shown)
Date: 10/12/14-07:45:05 PM Z

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[];

\$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!!!!!!!!!

This archive was generated by hypermail 2b29 : 07/16/18-01:00:02 AM Z CEST