Name: Lingxiao Xu Date: 11/24/14-09:31:23 AM Z

Hi developers,

   I’m calculating the process “e-(R),e+(L)->w+w-“, the mass of electron and anitelectron is neglected, “R” and “L” represent helicity.
   The square of reduced matrix element obtained just cantain the contraction of LeviCivita tensor and momentums, how can I simplify the result further to get rid of the LeviCivita tensor in the final results ?
Thanks for help.
Cheers!

Lingxiao

     Here is part of my code, it might be helpful to solve my problem. “fnuL,faL,fzL” represent the amplitudes of t-channel diagram with neutino propagator, s-channel diagram with photon propagator, s-channel diagram with Z propagator respectively.

flistL = List[fnuL, faL, fzL]
fliststarL = {fnuLs, faLs, fzLs} =
  ComplexConjugate /@ {fnuL, faL,
      fzL} /. {\[Mu] -> \[Mu]s, \[Nu] -> \[Nu]s, \[Epsilon] -> \
\[Epsilon]s, \[Omega] -> \[Omega]s} // Explicit
Lsq = Table[0, {i, 1, 3}, {j, 1, 3}];
 
Do[
 Lsq[[i, j]] =
  1/4 FermionSpinSum[
       PolarizationSum[\[Mu], \[Mu]s,
          p3] PolarizationSum[\[Nu], \[Nu]s, p4] flistL[[
          i]] fliststarL[[j]] // Expand] /. DiracTrace -> TR //
    Contract // Simplify;
 Print[i, j, “: “, Lsq[[i, j]]], {i, 1, 3}, {j, 1, 3}
 ]