· FeynCalc

Name: hanif_at_HIDDEN-E-MAIL Date: 05/26/14-12:07:07 PM Z

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Dear Professor Mertig,

My question is related with two cases which are written below (The cases
are in InputForm, this is why they are looking so long, I am sorry, for
this, however in standard form they are simple in fact.). Our aim is to
obtain corresponding matrix elements from amplitude.

In first case, the first matrix element in A.3. is in contradiction with
the fermion currents of the diagram which is taken from A.1.Topology and
insertion and A.2.Corresponding Feynman amplitude.

In second case, the all matrix elements in B.3. is compatible with the
fermion currents of the diagram which is taken from B.1.Topology and
insertion and B.2.Corresponding Feynman amplitude.

The question is: How in the first case does the contradiction appear?

Thank you for your kind considerations.

A.First case: (below; A.1.Topology and insertion, A.2.Corresponding
Feynman amplitude and A.3.Matrix elements)

A.1.Topology and insertion:

dia1 = TopologyList[
   Process -> {F[3, {2, c1}], -F[3, {1, c2}]} -> {-F[3, {2, c1}],
      F[3, {1, c2}]}, Model -> {“SMQCD”}, GenericModel -> {“Lorentz”},
    InsertionLevel -> {Generic, Classes}, ExcludeParticles -> {},
   ExcludeFieldPoints -> {}, LastSelections -> {}][
  Topology[1][
    Propagator[Incoming][Vertex[1][1], Vertex[3][5], Field[1]],
    Propagator[Incoming][Vertex[1][2], Vertex[3][6], Field[2]],
    Propagator[Outgoing][Vertex[1][3], Vertex[3][7], Field[3]],
    Propagator[Outgoing][Vertex[1][4], Vertex[3][8], Field[4]],
    Propagator[Loop[1]][Vertex[3][5], Vertex[3][6], Field[5]],
    Propagator[Loop[1]][Vertex[3][5], Vertex[3][8], Field[6]],
    Propagator[Loop[1]][Vertex[3][6], Vertex[3][7], Field[7]],
    Propagator[Loop[1]][Vertex[3][7], Vertex[3][8], Field[8]]] ->
   Insertions[Generic][
    FeynmanGraph[1, Generic == 7][Field[1] -> F[3, {2, c1}],
      Field[2] -> -F[3, {1, c2}], Field[3] -> F[3, {2, c1}],
      Field[4] -> -F[3, {1, c2}], Field[5] -> F, Field[6] -> V,
      Field[7] -> V, Field[8] -> F] ->
     Insertions[Classes][
      FeynmanGraph[1, Classes == 1][Field[1] -> F[3, {2, c1}],
       Field[2] -> -F[3, {1, c2}], Field[3] -> F[3, {2, c1}],
       Field[4] -> -F[3, {1, c2}],
       Field[5] -> F[4, {Index[Generation, 5], c1}],
       Field[6] -> -V[3], Field[7] -> V[3],
       Field[8] -> F[4, {Index[Generation, 6], c1}]]]]]

A.2.Corresponding Feynman amplitude:

FeynAmpList[Process -> {{F[3, {2, c1}], FourMomentum[Incoming, 1], MC},
     {-F[3, {1, c2}], FourMomentum[Incoming, 2], MU}} ->
    {{-F[3, {2, c1}], FourMomentum[Outgoing, 1], MC},
     {F[3, {1, c2}], FourMomentum[Outgoing, 2], MU}}, Model -> {“SMQCD”},
  GenericModel -> {“Lorentz”}, AmplitudeLevel -> {Generic, Classes},
ExcludeParticles -> {}, ExcludeFieldPoints -> {}, LastSelections -> {}][
FeynAmp[GraphID[Topology == 1, Generic == 1],
Integral[FourMomentum[Internal, 1]],
  ((-I/16)*RelativeCF*FermionChain[NonCommutative[
      Spinor[-Momentum[FourMomentum[Incoming, 2]], MU, 1]],
     NonCommutative[DiracGamma[LorentzIndex[Index[Lorentz, 3]]],
DiracGamma[6]]*
       G[-1][0][-F[3, {1, c2}], F[Index[Generic, 5]], -V[Index[Generic,
7]]][
        NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[6]]] +

      NonCommutative[DiracGamma[LorentzIndex[Index[Lorentz, 3]]],
DiracGamma[7]]*
       G[-1][0][-F[3, {1, c2}], F[Index[Generic, 5]], -V[Index[Generic,
7]]][
        NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[7]]],
     NonCommutative[DiracSlash[FourMomentum[Internal, 1]] +
Mass[F[Index[Generic, 5]],
        Loop]], NonCommutative[DiracGamma[LorentzIndex[Index[Lorentz,
1]]],
        DiracGamma[6]]*G[-1][0][-F[Index[Generic, 5]], F[3, {2, c1}],
         -V[Index[Generic,
6]]][NonCommutative[DiracGamma[LorentzIndex[KI1[3]]],
         DiracGamma[6]]] +
NonCommutative[DiracGamma[LorentzIndex[Index[Lorentz, 1]]],
        DiracGamma[7]]*G[-1][0][-F[Index[Generic, 5]], F[3, {2, c1}],
         -V[Index[Generic,
6]]][NonCommutative[DiracGamma[LorentzIndex[KI1[3]]],
         DiracGamma[7]]],
NonCommutative[Spinor[Momentum[FourMomentum[Incoming, 1]],
       MC, 1]]]*FermionChain[NonCommutative[
      Spinor[Momentum[FourMomentum[Outgoing, 2]], MU, 1]],
     NonCommutative[DiracGamma[LorentzIndex[Index[Lorentz, 2]]],
DiracGamma[6]]*
       G[-1][0][-F[3, {1, c2}], F[Index[Generic, 8]], V[Index[Generic,
6]]][
        NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[6]]] +

      NonCommutative[DiracGamma[LorentzIndex[Index[Lorentz, 2]]],
DiracGamma[7]]*
       G[-1][0][-F[3, {1, c2}], F[Index[Generic, 8]], V[Index[Generic,
6]]][
        NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[7]]],
     NonCommutative[DiracSlash[FourMomentum[Incoming, 2]

FourMomentum[Internal, 1] -
         FourMomentum[Outgoing, 1]] + Mass[F[Index[Generic, 8]], Loop]],
     NonCommutative[DiracGamma[LorentzIndex[Index[Lorentz, 4]]],
DiracGamma[6]]*
       G[-1][0][-F[Index[Generic, 8]], F[3, {2, c1}], V[Index[Generic,
7]]][
        NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[6]]] +

      NonCommutative[DiracGamma[LorentzIndex[Index[Lorentz, 4]]],
DiracGamma[7]]*
       G[-1][0][-F[Index[Generic, 8]], F[3, {2, c1}], V[Index[Generic,
7]]][
        NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[7]]],
     NonCommutative[Spinor[-Momentum[FourMomentum[Outgoing, 1]], MC, 1]]]*
    FeynAmpDenominator[PropagatorDenominator[FourMomentum[Internal, 1],
      Mass[F[Index[Generic, 5]], Loop]], PropagatorDenominator[
      FourMomentum[Incoming, 2] + FourMomentum[Internal, 1],
      Mass[V[Index[Generic, 7]], Loop]], PropagatorDenominator[
      FourMomentum[Incoming, 2] + FourMomentum[Internal, 1] -
       FourMomentum[Outgoing, 1], Mass[F[Index[Generic, 8]], Loop]],
     PropagatorDenominator[FourMomentum[Incoming, 2] +
FourMomentum[Internal, 1] -
       FourMomentum[Outgoing, 1] - FourMomentum[Outgoing, 2],
      Mass[V[Index[Generic, 6]], Loop]]]*MetricTensor[Index[Lorentz, 1],
     Index[Lorentz, 2]]*MetricTensor[Index[Lorentz, 3], Index[Lorentz,
4]])/Pi^4,
  {Mass[F[Index[Generic, 5]], Loop], Mass[F[Index[Generic, 8]], Loop],
    Mass[V[Index[Generic, 6]], Loop], Mass[V[Index[Generic, 7]], Loop],
G[-1][0][-F[Index[Generic, 5]], F[3, {2, c1}], -V[Index[Generic, 6]]][
     NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[6]]],
    G[-1][0][-F[Index[Generic, 5]], F[3, {2, c1}], -V[Index[Generic, 6]]][
     NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[7]]],
    G[-1][0][-F[Index[Generic, 8]], F[3, {2, c1}], V[Index[Generic, 7]]][
     NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[6]]],
    G[-1][0][-F[Index[Generic, 8]], F[3, {2, c1}], V[Index[Generic, 7]]][
     NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[7]]],
    G[-1][0][-F[3, {1, c2}], F[Index[Generic, 5]], -V[Index[Generic, 7]]][
     NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[6]]],
    G[-1][0][-F[3, {1, c2}], F[Index[Generic, 5]], -V[Index[Generic, 7]]][
     NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[7]]],
    G[-1][0][-F[3, {1, c2}], F[Index[Generic, 8]], V[Index[Generic, 6]]][
     NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[6]]],
    G[-1][0][-F[3, {1, c2}], F[Index[Generic, 8]], V[Index[Generic, 6]]][
     NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[7]]],
RelativeCF} ->
   Insertions[Classes][{MQD[Index[Generation, 5]], MQD[Index[Generation,
6]], MW, MW,
     0, (I*EL*Conjugate[CKM[2, Index[Generation, 5]]])/(Sqrt[2]*SW), 0,
(I*EL*Conjugate[CKM[2, Index[Generation, 6]]])/(Sqrt[2]*SW), 0,
(I*EL*CKM[1, Index[Generation, 5]])/(Sqrt[2]*SW), 0,
     (I*EL*CKM[1, Index[Generation, 6]])/(Sqrt[2]*SW), IndexDelta[c1, c2]*
      SumOver[Index[Generation, 5], 3]*SumOver[Index[Generation, 6],
3]}]]]

A.3.Matrix elements (only the elements that include p^0):

{StandardMatrixElement[Spinor[Momentum[p3], MC, 1] . DiracGamma[7] .
    Spinor[Momentum[p1], MC, 1]*Spinor[-Momentum[p4], MU, 1] .
DiracGamma[6] .
    Spinor[-Momentum[p2], MU, 1]], StandardMatrixElement[
  Spinor[-Momentum[p2], MU, 1] . DiracGamma[6] . Spinor[Momentum[p1], MC,
1]*
   Spinor[-Momentum[p4], MU, 1] . DiracGamma[6] . Spinor[Momentum[p3], MC,
1]],
StandardMatrixElement[Spinor[-Momentum[p2], MU, 1] . DiracGamma[7] .
    Spinor[Momentum[p1], MC, 1]*Spinor[-Momentum[p4], MU, 1] .
DiracGamma[6] .
    Spinor[Momentum[p3], MC, 1]], StandardMatrixElement[
  Spinor[-Momentum[p2], MU, 1] . DiracGamma[6] . Spinor[Momentum[p1], MC,
1]*
   Spinor[-Momentum[p4], MU, 1] . DiracGamma[7] . Spinor[Momentum[p3], MC,
1]],
StandardMatrixElement[Spinor[-Momentum[p2], MU, 1] . DiracGamma[7] .
    Spinor[Momentum[p1], MC, 1]*Spinor[-Momentum[p4], MU, 1] .
DiracGamma[7] .
    Spinor[Momentum[p3], MC, 1]], StandardMatrixElement[
  Spinor[-Momentum[p2], MU, 1] . DiracGamma[LorentzIndex[$MU[1]]] .
DiracGamma[6] .
    Spinor[Momentum[p1], MC, 1]*Spinor[-Momentum[p4], MU, 1] .
    DiracGamma[LorentzIndex[$MU[1]]] . DiracGamma[6] .
Spinor[Momentum[p3], MC, 1]],
StandardMatrixElement[Spinor[-Momentum[p2], MU, 1] .
    DiracGamma[LorentzIndex[$MU[1]]] . DiracGamma[7] .
Spinor[Momentum[p1], MC, 1]*
   Spinor[-Momentum[p4], MU, 1] . DiracGamma[LorentzIndex[$MU[1]]] .
DiracGamma[6] .
    Spinor[Momentum[p3], MC, 1]], StandardMatrixElement[
  Spinor[-Momentum[p2], MU, 1] . DiracGamma[LorentzIndex[$MU[1]]] .
DiracGamma[6] .
    Spinor[Momentum[p1], MC, 1]*Spinor[-Momentum[p4], MU, 1] .
    DiracGamma[LorentzIndex[$MU[1]]] . DiracGamma[7] .
Spinor[Momentum[p3], MC, 1]],
StandardMatrixElement[Spinor[-Momentum[p2], MU, 1] .
    DiracGamma[LorentzIndex[$MU[1]]] . DiracGamma[7] .
Spinor[Momentum[p1], MC, 1]*
   Spinor[-Momentum[p4], MU, 1] . DiracGamma[LorentzIndex[$MU[1]]] .
DiracGamma[7] .
    Spinor[Momentum[p3], MC, 1]], StandardMatrixElement[
  Spinor[-Momentum[p2], MU, 1] . DiracGamma[LorentzIndex[$MU[1]]] .
    DiracGamma[LorentzIndex[$MU[2]]] . DiracGamma[6] .
Spinor[Momentum[p1], MC, 1]*
   Spinor[-Momentum[p4], MU, 1] . DiracGamma[LorentzIndex[$MU[1]]] .
    DiracGamma[LorentzIndex[$MU[2]]] . DiracGamma[6] .
Spinor[Momentum[p3], MC, 1]],
StandardMatrixElement[Spinor[-Momentum[p2], MU, 1] .
    DiracGamma[LorentzIndex[$MU[1]]] . DiracGamma[LorentzIndex[$MU[2]]] .
DiracGamma[7] . Spinor[Momentum[p1], MC, 1]*Spinor[-Momentum[p4], MU, 1] .

DiracGamma[LorentzIndex[$MU[1]]] . DiracGamma[LorentzIndex[$MU[2]]] .
DiracGamma[7] . Spinor[Momentum[p3], MC, 1]]}

B.Second case (below; B.1.Topology and insertion, B.2.Corresponding
Feynman amplitude and B.3.Matrix elements)

B.1.Topology and insertion:

dia2 = TopologyList[Process -> {F, F} -> {F, F}, Model -> {“SMQCD”},
   GenericModel -> {“Lorentz”}, InsertionLevel -> {Generic, Classes},
ExcludeParticles -> {}, ExcludeFieldPoints -> {},
   LastSelections -> {}][
  Topology[1][
    Propagator[Incoming][Vertex[1][1], Vertex[3][5], Field[1]],
    Propagator[Incoming][Vertex[1][2], Vertex[3][6], Field[2]],
    Propagator[Outgoing][Vertex[1][3], Vertex[3][7], Field[3]],
    Propagator[Outgoing][Vertex[1][4], Vertex[3][8], Field[4]],
    Propagator[Loop[1]][Vertex[3][5], Vertex[3][6], Field[5]],
    Propagator[Loop[1]][Vertex[3][5], Vertex[3][8], Field[6]],
    Propagator[Loop[1]][Vertex[3][6], Vertex[3][7], Field[7]],
    Propagator[Loop[1]][Vertex[3][7], Vertex[3][8], Field[8]]] ->
   Insertions[Generic][
    FeynmanGraph[1, Generic == 7][Field[1] -> F, Field[2] -> F,
      Field[3] -> F, Field[4] -> F, Field[5] -> F, Field[6] -> V,
Field[7] -> V, Field[8] -> F] -> Insertions[Classes][
       FeynmanGraph[1, Classes == 8][
       Field[1] -> F[3, {Index[Generation, 1], Index[Colour, 1]}],
Field[2] -> -F[3, {Index[Generation, 2], Index[Colour, 2]}],
Field[3] -> F[3, {Index[Generation, 3], Index[Colour, 3]}],
Field[4] -> -F[3, {Index[Generation, 4], Index[Colour, 4]}],
Field[5] -> F[4, {Index[Generation, 5], Index[Colour, 1]}],
Field[6] -> -V[3], Field[7] -> V[3],
       Field[8] -> F[4, {Index[Generation, 6], Index[Colour, 3]}]]]]]
{% enfraw %} B.2.Corresponding Feynman amplitude:
{% raw %} FeynAmpList[Process -> {{F, FourMomentum[Incoming, 1], Mass[F, External]},

     {F, FourMomentum[Incoming, 2], Mass[F, External]}} ->
    {{F, FourMomentum[Outgoing, 1], Mass[F, External]}, {F,
FourMomentum[Outgoing, 2],
      Mass[F, External]}}, Model -> {“SMQCD”}, GenericModel ->
{“Lorentz”},
  AmplitudeLevel -> {Generic, Classes}, ExcludeParticles -> {},
  ExcludeFieldPoints -> {}, LastSelections -> {}][
FeynAmp[GraphID[Topology == 1, Generic == 1],
Integral[FourMomentum[Internal, 1]],
  ((-I/16)*RelativeCF*FermionChain[NonCommutative[SpinorType[Index[Generic,
2]][
       -FourMomentum[Incoming, 2], Mass[F[Index[Generic, 2]], External]]],

     NonCommutative[DiracGamma[LorentzIndex[Index[Lorentz, 3]]],
DiracGamma[6]]*
       G[-1][0][F[Index[Generic, 2]], F[Index[Generic, 5]],
-V[Index[Generic, 7]]][
        NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[6]]] +

      NonCommutative[DiracGamma[LorentzIndex[Index[Lorentz, 3]]],
DiracGamma[7]]*
       G[-1][0][F[Index[Generic, 2]], F[Index[Generic, 5]],
-V[Index[Generic, 7]]][
        NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[7]]],
     NonCommutative[DiracSlash[FourMomentum[Internal, 1]] +
Mass[F[Index[Generic, 5]],
        Loop]], NonCommutative[DiracGamma[LorentzIndex[Index[Lorentz,
1]]],
        DiracGamma[6]]*G[-1][0][-F[Index[Generic, 5]], F[Index[Generic,
1]],
         -V[Index[Generic,
6]]][NonCommutative[DiracGamma[LorentzIndex[KI1[3]]],
         DiracGamma[6]]] +
NonCommutative[DiracGamma[LorentzIndex[Index[Lorentz, 1]]],
        DiracGamma[7]]*G[-1][0][-F[Index[Generic, 5]], F[Index[Generic,
1]],
         -V[Index[Generic,
6]]][NonCommutative[DiracGamma[LorentzIndex[KI1[3]]],
         DiracGamma[7]]], NonCommutative[SpinorType[Index[Generic, 1]][
       FourMomentum[Incoming, 1], Mass[F[Index[Generic, 1]], External]]]]*
    FermionChain[NonCommutative[SpinorType[Index[Generic, 4]][
       FourMomentum[Outgoing, 2], Mass[F[Index[Generic, 4]], External]]],
     NonCommutative[DiracGamma[LorentzIndex[Index[Lorentz, 2]]],
DiracGamma[6]]*
       G[-1][0][F[Index[Generic, 4]], F[Index[Generic, 8]],
V[Index[Generic, 6]]][
        NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[6]]] +

      NonCommutative[DiracGamma[LorentzIndex[Index[Lorentz, 2]]],
DiracGamma[7]]*
       G[-1][0][F[Index[Generic, 4]], F[Index[Generic, 8]],
V[Index[Generic, 6]]][
        NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[7]]],
     NonCommutative[DiracSlash[FourMomentum[Incoming, 2]

FourMomentum[Internal, 1] -
         FourMomentum[Outgoing, 1]] + Mass[F[Index[Generic, 8]], Loop]],
     NonCommutative[DiracGamma[LorentzIndex[Index[Lorentz, 4]]],
DiracGamma[6]]*
       G[-1][0][-F[Index[Generic, 8]], F[Index[Generic, 3]],
V[Index[Generic, 7]]][
        NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[6]]] +

      NonCommutative[DiracGamma[LorentzIndex[Index[Lorentz, 4]]],
DiracGamma[7]]*
       G[-1][0][-F[Index[Generic, 8]], F[Index[Generic, 3]],
V[Index[Generic, 7]]][
        NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[7]]],
     NonCommutative[SpinorType[Index[Generic, 3]][-FourMomentum[Outgoing,
1],
       Mass[F[Index[Generic, 3]], External]]]]*FeynAmpDenominator[
     PropagatorDenominator[FourMomentum[Internal, 1],
Mass[F[Index[Generic, 5]],
       Loop]], PropagatorDenominator[FourMomentum[Incoming, 2] +
       FourMomentum[Internal, 1], Mass[V[Index[Generic, 7]], Loop]],
     PropagatorDenominator[FourMomentum[Incoming, 2] +
FourMomentum[Internal, 1] -
       FourMomentum[Outgoing, 1], Mass[F[Index[Generic, 8]], Loop]],
     PropagatorDenominator[FourMomentum[Incoming, 2] +
FourMomentum[Internal, 1] -
       FourMomentum[Outgoing, 1] - FourMomentum[Outgoing, 2],
      Mass[V[Index[Generic, 6]], Loop]]]*MetricTensor[Index[Lorentz, 1],
     Index[Lorentz, 2]]*MetricTensor[Index[Lorentz, 3], Index[Lorentz,
4]])/Pi^4,
  {Mass[F[Index[Generic, 1]], External], Mass[F[Index[Generic, 2]],
External],
    Mass[F[Index[Generic, 3]], External], Mass[F[Index[Generic, 4]],
External],
    Mass[F[Index[Generic, 5]], Loop], Mass[F[Index[Generic, 8]], Loop],
Mass[V[Index[Generic, 6]], Loop], Mass[V[Index[Generic, 7]], Loop],
G[-1][0][F[Index[Generic, 2]], F[Index[Generic, 5]], -V[Index[Generic,
7]]][
     NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[6]]],
    G[-1][0][F[Index[Generic, 2]], F[Index[Generic, 5]], -V[Index[Generic,
7]]][
     NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[7]]],
    G[-1][0][F[Index[Generic, 4]], F[Index[Generic, 8]], V[Index[Generic,
6]]][
     NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[6]]],
    G[-1][0][F[Index[Generic, 4]], F[Index[Generic, 8]], V[Index[Generic,
6]]][
     NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[7]]],
    G[-1][0][-F[Index[Generic, 5]], F[Index[Generic, 1]],
-V[Index[Generic, 6]]][
     NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[6]]],
    G[-1][0][-F[Index[Generic, 5]], F[Index[Generic, 1]],
-V[Index[Generic, 6]]][
     NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[7]]],
    G[-1][0][-F[Index[Generic, 8]], F[Index[Generic, 3]], V[Index[Generic,
7]]][
     NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[6]]],
    G[-1][0][-F[Index[Generic, 8]], F[Index[Generic, 3]], V[Index[Generic,
7]]][
     NonCommutative[DiracGamma[LorentzIndex[KI1[3]]], DiracGamma[7]]],
RelativeCF} ->
   Insertions[Classes][{MQU[Index[Generation, 1]], MQU[Index[Generation,
2]],
     MQU[Index[Generation, 3]], MQU[Index[Generation, 4]],
MQD[Index[Generation, 5]],
     MQD[Index[Generation, 6]], MW, MW, 0,
     (I*EL*CKM[Index[Generation, 2], Index[Generation, 5]])/(Sqrt[2]*SW),
0,
     (I*EL*CKM[Index[Generation, 4], Index[Generation, 6]])/(Sqrt[2]*SW),
0,
     (I*EL*Conjugate[CKM[Index[Generation, 1], Index[Generation,
5]]])/(Sqrt[2]*SW),
     0, (I*EL*Conjugate[CKM[Index[Generation, 3], Index[Generation, 6]]])/
      (Sqrt[2]*SW), IndexDelta[Index[Colour, 1], Index[Colour, 2]]*
IndexDelta[Index[Colour, 3], Index[Colour,
4]]*SumOver[Index[Generation, 5], 3]*
      SumOver[Index[Generation, 6], 3]*SumOver[Index[Colour, 1], 3,
External]*
      SumOver[Index[Colour, 2], 3, External]*SumOver[Index[Colour, 3], 3,
External]*
      SumOver[Index[Colour, 4], 3, External]*SumOver[Index[Generation, 1],
3,
       External]*SumOver[Index[Generation, 2], 3, External]*
      SumOver[Index[Generation, 3], 3, External]*SumOver[Index[Generation,
4], 3,
       External]}]]]

B.3.Matrix elements (only the elements that include p^0):

{StandardMatrixElement[Spinor[Momentum[Index[Generic, 2]], 0,
1][-Momentum[p2],
     ”Mass[F[Index[Generic, 2]], External]”] . DiracGamma[6] .
    Spinor[Momentum[Index[Generic, 1]], 0, 1][Momentum[p1],
     ”Mass[F[Index[Generic, 1]], External]”]*
   Spinor[Momentum[Index[Generic, 4]], 0, 1][-Momentum[p4],
     ”Mass[F[Index[Generic, 4]], External]”] . DiracGamma[6] .
    Spinor[Momentum[Index[Generic, 3]], 0, 1][Momentum[p3],
     ”Mass[F[Index[Generic, 3]], External]”]], StandardMatrixElement[
  Spinor[Momentum[Index[Generic, 2]], 0, 1][-Momentum[p2],
     ”Mass[F[Index[Generic, 2]], External]”] . DiracGamma[7] .
    Spinor[Momentum[Index[Generic, 1]], 0, 1][Momentum[p1],
     ”Mass[F[Index[Generic, 1]], External]”]*
   Spinor[Momentum[Index[Generic, 4]], 0, 1][-Momentum[p4],
     ”Mass[F[Index[Generic, 4]], External]”] . DiracGamma[6] .
    Spinor[Momentum[Index[Generic, 3]], 0, 1][Momentum[p3],
     ”Mass[F[Index[Generic, 3]], External]”]], StandardMatrixElement[
  Spinor[Momentum[Index[Generic, 2]], 0, 1][-Momentum[p2],
     ”Mass[F[Index[Generic, 2]], External]”] . DiracGamma[6] .
    Spinor[Momentum[Index[Generic, 1]], 0, 1][Momentum[p1],
     ”Mass[F[Index[Generic, 1]], External]”]*
   Spinor[Momentum[Index[Generic, 4]], 0, 1][-Momentum[p4],
     ”Mass[F[Index[Generic, 4]], External]”] . DiracGamma[7] .
    Spinor[Momentum[Index[Generic, 3]], 0, 1][Momentum[p3],
     ”Mass[F[Index[Generic, 3]], External]”]], StandardMatrixElement[
  Spinor[Momentum[Index[Generic, 2]], 0, 1][-Momentum[p2],
     ”Mass[F[Index[Generic, 2]], External]”] . DiracGamma[7] .
    Spinor[Momentum[Index[Generic, 1]], 0, 1][Momentum[p1],
     ”Mass[F[Index[Generic, 1]], External]”]*
   Spinor[Momentum[Index[Generic, 4]], 0, 1][-Momentum[p4],
     ”Mass[F[Index[Generic, 4]], External]”] . DiracGamma[7] .
    Spinor[Momentum[Index[Generic, 3]], 0, 1][Momentum[p3],
     ”Mass[F[Index[Generic, 3]], External]”]], StandardMatrixElement[
  Spinor[Momentum[Index[Generic, 2]], 0, 1][-Momentum[p2],
     ”Mass[F[Index[Generic, 2]], External]”] .
DiracGamma[LorentzIndex[\[Mu]2]] .
    DiracGamma[6] . Spinor[Momentum[Index[Generic, 1]], 0,
1][Momentum[p1],
     ”Mass[F[Index[Generic, 1]], External]”]*
   Spinor[Momentum[Index[Generic, 4]], 0, 1][-Momentum[p4],
     ”Mass[F[Index[Generic, 4]], External]”] .
DiracGamma[LorentzIndex[\[Mu]2]] .
    DiracGamma[6] . Spinor[Momentum[Index[Generic, 3]], 0,
1][Momentum[p3],
     ”Mass[F[Index[Generic, 3]], External]”]], StandardMatrixElement[
  Spinor[Momentum[Index[Generic, 2]], 0, 1][-Momentum[p2],
     ”Mass[F[Index[Generic, 2]], External]”] .
DiracGamma[LorentzIndex[\[Mu]2]] .
    DiracGamma[7] . Spinor[Momentum[Index[Generic, 1]], 0,
1][Momentum[p1],
     ”Mass[F[Index[Generic, 1]], External]”]*
   Spinor[Momentum[Index[Generic, 4]], 0, 1][-Momentum[p4],
     ”Mass[F[Index[Generic, 4]], External]”] .
DiracGamma[LorentzIndex[\[Mu]2]] .
    DiracGamma[6] . Spinor[Momentum[Index[Generic, 3]], 0,
1][Momentum[p3],
     ”Mass[F[Index[Generic, 3]], External]”]], StandardMatrixElement[
  Spinor[Momentum[Index[Generic, 2]], 0, 1][-Momentum[p2],
     ”Mass[F[Index[Generic, 2]], External]”] .
DiracGamma[LorentzIndex[\[Mu]2]] .
    DiracGamma[6] . Spinor[Momentum[Index[Generic, 1]], 0,
1][Momentum[p1],
     ”Mass[F[Index[Generic, 1]], External]”]*
   Spinor[Momentum[Index[Generic, 4]], 0, 1][-Momentum[p4],
     ”Mass[F[Index[Generic, 4]], External]”] .
DiracGamma[LorentzIndex[\[Mu]2]] .
    DiracGamma[7] . Spinor[Momentum[Index[Generic, 3]], 0,
1][Momentum[p3],
     ”Mass[F[Index[Generic, 3]], External]”]], StandardMatrixElement[
  Spinor[Momentum[Index[Generic, 2]], 0, 1][-Momentum[p2],
     ”Mass[F[Index[Generic, 2]], External]”] .
DiracGamma[LorentzIndex[\[Mu]2]] .
    DiracGamma[7] . Spinor[Momentum[Index[Generic, 1]], 0,
1][Momentum[p1],
     ”Mass[F[Index[Generic, 1]], External]”]*
   Spinor[Momentum[Index[Generic, 4]], 0, 1][-Momentum[p4],
     ”Mass[F[Index[Generic, 4]], External]”] .
DiracGamma[LorentzIndex[\[Mu]2]] .
    DiracGamma[7] . Spinor[Momentum[Index[Generic, 3]], 0,
1][Momentum[p3],
     ”Mass[F[Index[Generic, 3]], External]”]], StandardMatrixElement[
  Spinor[Momentum[Index[Generic, 2]], 0, 1][-Momentum[p2],
     ”Mass[F[Index[Generic, 2]], External]”] .
DiracGamma[LorentzIndex[\[Mu]4]] .
    DiracGamma[6] . Spinor[Momentum[Index[Generic, 1]], 0,
1][Momentum[p1],
     ”Mass[F[Index[Generic, 1]], External]”]*
   Spinor[Momentum[Index[Generic, 4]], 0, 1][-Momentum[p4],
     ”Mass[F[Index[Generic, 4]], External]”] .
DiracGamma[LorentzIndex[\[Mu]4]] .
    DiracGamma[6] . Spinor[Momentum[Index[Generic, 3]], 0,
1][Momentum[p3],
     ”Mass[F[Index[Generic, 3]], External]”]], StandardMatrixElement[
  Spinor[Momentum[Index[Generic, 2]], 0, 1][-Momentum[p2],
     ”Mass[F[Index[Generic, 2]], External]”] .
DiracGamma[LorentzIndex[\[Mu]4]] .
    DiracGamma[7] . Spinor[Momentum[Index[Generic, 1]], 0,
1][Momentum[p1],
     ”Mass[F[Index[Generic, 1]], External]”]*
   Spinor[Momentum[Index[Generic, 4]], 0, 1][-Momentum[p4],
     ”Mass[F[Index[Generic, 4]], External]”] .
DiracGamma[LorentzIndex[\[Mu]4]] .
    DiracGamma[6] . Spinor[Momentum[Index[Generic, 3]], 0,
1][Momentum[p3],
     ”Mass[F[Index[Generic, 3]], External]”]], StandardMatrixElement[
  Spinor[Momentum[Index[Generic, 2]], 0, 1][-Momentum[p2],
     ”Mass[F[Index[Generic, 2]], External]”] .
DiracGamma[LorentzIndex[\[Mu]4]] .
    DiracGamma[6] . Spinor[Momentum[Index[Generic, 1]], 0,
1][Momentum[p1],
     ”Mass[F[Index[Generic, 1]], External]”]*
   Spinor[Momentum[Index[Generic, 4]], 0, 1][-Momentum[p4],
     ”Mass[F[Index[Generic, 4]], External]”] .
DiracGamma[LorentzIndex[\[Mu]4]] .
    DiracGamma[7] . Spinor[Momentum[Index[Generic, 3]], 0,
1][Momentum[p3],
     ”Mass[F[Index[Generic, 3]], External]”]], StandardMatrixElement[
  Spinor[Momentum[Index[Generic, 2]], 0, 1][-Momentum[p2],
     ”Mass[F[Index[Generic, 2]], External]”] .
DiracGamma[LorentzIndex[\[Mu]4]] .
    DiracGamma[7] . Spinor[Momentum[Index[Generic, 1]], 0,
1][Momentum[p1],
     ”Mass[F[Index[Generic, 1]], External]”]*
   Spinor[Momentum[Index[Generic, 4]], 0, 1][-Momentum[p4],
     ”Mass[F[Index[Generic, 4]], External]”] .
DiracGamma[LorentzIndex[\[Mu]4]] .
    DiracGamma[7] . Spinor[Momentum[Index[Generic, 3]], 0,
1][Momentum[p3],
     ”Mass[F[Index[Generic, 3]], External]”]], StandardMatrixElement[
  Spinor[Momentum[Index[Generic, 2]], 0, 1][-Momentum[p2],
     ”Mass[F[Index[Generic, 2]], External]”] .
DiracGamma[LorentzIndex[\[Mu]2]] .
    DiracGamma[LorentzIndex[\[Mu]4]] . DiracGamma[6] .
    Spinor[Momentum[Index[Generic, 1]], 0, 1][Momentum[p1],
     ”Mass[F[Index[Generic, 1]], External]”]*
   Spinor[Momentum[Index[Generic, 4]], 0, 1][-Momentum[p4],
     ”Mass[F[Index[Generic, 4]], External]”] .
DiracGamma[LorentzIndex[\[Mu]2]] .
    DiracGamma[LorentzIndex[\[Mu]4]] . DiracGamma[6] .
    Spinor[Momentum[Index[Generic, 3]], 0, 1][Momentum[p3],
     ”Mass[F[Index[Generic, 3]], External]”]], StandardMatrixElement[
  Spinor[Momentum[Index[Generic, 2]], 0, 1][-Momentum[p2],
     ”Mass[F[Index[Generic, 2]], External]”] .
DiracGamma[LorentzIndex[\[Mu]2]] .
    DiracGamma[LorentzIndex[\[Mu]4]] . DiracGamma[7] .
    Spinor[Momentum[Index[Generic, 1]], 0, 1][Momentum[p1],
     ”Mass[F[Index[Generic, 1]], External]”]*
   Spinor[Momentum[Index[Generic, 4]], 0, 1][-Momentum[p4],
     ”Mass[F[Index[Generic, 4]], External]”] .
DiracGamma[LorentzIndex[\[Mu]2]] .
    DiracGamma[LorentzIndex[\[Mu]4]] . DiracGamma[6] .
    Spinor[Momentum[Index[Generic, 3]], 0, 1][Momentum[p3],
     ”Mass[F[Index[Generic, 3]], External]”]], StandardMatrixElement[
  Spinor[Momentum[Index[Generic, 2]], 0, 1][-Momentum[p2],
     ”Mass[F[Index[Generic, 2]], External]”] .
DiracGamma[LorentzIndex[\[Mu]2]] .
    DiracGamma[LorentzIndex[\[Mu]4]] . DiracGamma[6] .
    Spinor[Momentum[Index[Generic, 1]], 0, 1][Momentum[p1],
     ”Mass[F[Index[Generic, 1]], External]”]*
   Spinor[Momentum[Index[Generic, 4]], 0, 1][-Momentum[p4],
     ”Mass[F[Index[Generic, 4]], External]”] .
DiracGamma[LorentzIndex[\[Mu]2]] .
    DiracGamma[LorentzIndex[\[Mu]4]] . DiracGamma[7] .
    Spinor[Momentum[Index[Generic, 3]], 0, 1][Momentum[p3],
     ”Mass[F[Index[Generic, 3]], External]”]], StandardMatrixElement[
  Spinor[Momentum[Index[Generic, 2]], 0, 1][-Momentum[p2],
     ”Mass[F[Index[Generic, 2]], External]”] .
DiracGamma[LorentzIndex[\[Mu]2]] .
    DiracGamma[LorentzIndex[\[Mu]4]] . DiracGamma[7] .
    Spinor[Momentum[Index[Generic, 1]], 0, 1][Momentum[p1],
     ”Mass[F[Index[Generic, 1]], External]”]*
   Spinor[Momentum[Index[Generic, 4]], 0, 1][-Momentum[p4],
     ”Mass[F[Index[Generic, 4]], External]”] .
DiracGamma[LorentzIndex[\[Mu]2]] .
    DiracGamma[LorentzIndex[\[Mu]4]] . DiracGamma[7] .
    Spinor[Momentum[Index[Generic, 3]], 0, 1][Momentum[p3],
     ”Mass[F[Index[Generic, 3]], External]”]]}

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