· FeynCalc

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

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Reply: Vladyslav Shtabovenko: “Re: e+e- annihilation’s M squared(calculate with FeynArts and Feyncalc) differ by an overall minus sigh from Peskin\&Schroeder”

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!!!!!!!!!