· FeynCalc

Name: Will Date: 03/28/19-08:52:42 AM Z

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Reply: V. Shtabovenko: “Re: FAPropagatorDenominator”

Hi Vladyslav,

Thanks for your reply.

I send you what I get

FAFeynAmpList[Process -> {{F[3, {1, Index[Colour, 1]}], FourMomentum[Incoming, 1],
      FCGV[“MU”], {(2*Charge)/3, (2*ColorCharge)/Sqrt[3]}},
     {-F[3, {1, Index[Colour, 2]}], FourMomentum[Incoming, 2], FCGV[“MU”],
      {(-2*Charge)/3, (-2*ColorCharge)/Sqrt[3]}}} ->
    {{V[5, {Index[Gluon, 3]}], FourMomentum[Outgoing, 1], 0, {Sqrt[3]*ColorCharge}},
     {S[1], FourMomentum[Outgoing, 2], FCGV[“MH”], {}}}, Model -> {“SMQCD”},
  GenericModel -> {“Lorentz”}, AmplitudeLevel -> {Particles},
  ExcludeParticles -> {S, -F[4], F[4], -F[3, {2, _}], F[3, {2, _}], -F[3, {3, _}],
    F[3, {3, _}], -F[4, {1, _}], F[4, {1, _}], -F[4, {2, _}], F[4, {2, _}],
    -F[4, {3, _}], F[4, {3, _}], S[1], S[2], -S[3], S[3], -V[3], V[3], V[5], V[5, {_}]},
  ExcludeFieldPoints -> {FieldPoint[0][S[1], V[2], V[2]],
    FieldPoint[0][S[1], -V[3], V[3]], FieldPoint[0][-S[3], V[1], V[3]],
    FieldPoint[0][-S[3], V[2], V[3]], FieldPoint[0][S[3], V[1], -V[3]],
    FieldPoint[0][S[3], V[2], -V[3]], FieldPoint[1][S[1], V[1], V[2]],
    FieldPoint[1][S[1], V[2], V[2]], FieldPoint[1][S[1], -V[3], V[3]],
    FieldPoint[1][-S[3], V[1], V[3]], FieldPoint[1][-S[3], V[2], V[3]],
    FieldPoint[1][S[3], V[1], -V[3]], FieldPoint[1][S[3], V[2], -V[3]]},
  LastSelections -> {}][FAFeynAmp[GraphID[Topology == 1, Generic == 1, Particles == 1,
   Number == 1], Integral[FourMomentum[Internal, 1]],
  ((I/16)*FAFeynAmpDenominator[FAPropagatorDenominator[FourMomentum[Internal, 1],
      FCGV[“MU”]], FAPropagatorDenominator[FourMomentum[Incoming, 2] +
       FourMomentum[Internal, 1] - FourMomentum[Outgoing, 1], FCGV[“MZ”]]]*
    FAMetricTensor[Index[Lorentz, 2], Index[Lorentz, 3]]*
    FAPropagatorDenominator[FourMomentum[Incoming, 2] - FourMomentum[Outgoing, 1],
     FCGV[“MU”], 2]*FermionChain[FANonCommutative[FADiracSpinor[
       -FourMomentum[Incoming, 2], FCGV[“MU”]]],
     (-I)*FAGS*FANonCommutative[FADiracMatrix[Index[Lorentz, 1]],
        FAChiralityProjector[-1]]*FASUNT[Index[Gluon, 3], Index[Colour, 2],
        Index[Colour, 1]] - I*FAGS*FANonCommutative[FADiracMatrix[Index[Lorentz, 1]],
        FAChiralityProjector[1]]*FASUNT[Index[Gluon, 3], Index[Colour, 2],
        Index[Colour, 1]], FANonCommutative[
      FADiracSlash[-FourMomentum[Incoming, 2] + FourMomentum[Outgoing, 1]] +
       FCGV[“MU”]], (((-2*I)/3)*FANonCommutative[FADiracMatrix[Index[Lorentz, 3]],
         FAChiralityProjector[1]]*FCGV[“EL”]*FCGV[“SW”])/FCGV[“CW”]

      (I*FANonCommutative[FADiracMatrix[Index[Lorentz, 3]], FAChiralityProjector[-1]]*
        FCGV[“EL”]*(1/2 - (2*FCGV[“SW”]^2)/3))/(FCGV[“CW”]*FCGV[“SW”]),
     FANonCommutative[FADiracSlash[FourMomentum[Internal, 1]] + FCGV[“MU”]],
     (((-2*I)/3)*FANonCommutative[FADiracMatrix[Index[Lorentz, 2]],
         FAChiralityProjector[1]]*FCGV[“EL”]*FCGV[“SW”])/FCGV[“CW”]
      (I*FANonCommutative[FADiracMatrix[Index[Lorentz, 2]], FAChiralityProjector[-1]]*
        FCGV[“EL”]*(1/2 - (2*FCGV[“SW”]^2)/3))/(FCGV[“CW”]*FCGV[“SW”]),
     FANonCommutative[FADiracSlash[-FourMomentum[Incoming, 2] + FourMomentum[Outgoing,
          1]] + FCGV[“MU”]], ((-I/2)*FANonCommutative[FAChiralityProjector[-1]]*
        FCGV[“EL”]*FCGV[“MU”])/(FCGV[“MW”]*FCGV[“SW”])
      ((I/2)*FANonCommutative[FAChiralityProjector[1]]*FCGV[“EL”]*FCGV[“MU”])/
       (FCGV[“MW”]*FCGV[“SW”]), FANonCommutative[FADiracSpinor[
       FourMomentum[Incoming, 1], FCGV[“MU”]]]]*SumOver[Index[Colour, 1], 3, External]*
    SumOver[Index[Colour, 2], 3, External]*SumOver[Index[Gluon, 3], 8, External]*
    Conjugate[FAPolarizationVector][V[5, {Index[Gluon, 3]}], FourMomentum[Outgoing, 1],
     Index[Lorentz, 1]])/Pi^4]]

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