· FeynCalc

Name: Paulina Knees Date: 07/27/20-09:47:04 PM Z

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Dear Vladyslav,
Since I was not able to reduce significantly the expression of amplitude^2, here I send you the output you asked me for the amplitude (without the ^2).

-(Spinor[Momentum[k2], MassChi[1], 1] . (GA[Lor1] . GA[7]*((-I/2)*CTW*g2*IndexSum[Conjugate[UV[2, j1]]*UV[1, j1], {j1, 3}] -
(I/2)*g1*STW*IndexSum[Conjugate[UV[2, j1]]*UV[1, j1], {j1, 3}] - (I/2)*CTW*g2*Conjugate[UV[2, 6]]*UV[1, 6]

       (I/2)*g1*STW*Conjugate[UV[2, 6]]*UV[1, 6] + (I/2)*CTW*g2*Conjugate[UV[2, 7]]*UV[1, 7] + (I/2)*g1*STW*Conjugate[UV[2, 7]]*UV[1, 7]) +
     GA[Lor1] . GA[6]*((I/2)*CTW*g2*IndexSum[Conjugate[UV[1, j1]]*UV[2, j1], {j1, 3}] +
       (I/2)*g1*STW*IndexSum[Conjugate[UV[1, j1]]*UV[2, j1], {j1, 3}] + (I/2)*CTW*g2*Conjugate[UV[1, 6]]*UV[2, 6]
       (I/2)*g1*STW*Conjugate[UV[1, 6]]*UV[2, 6] - (I/2)*CTW*g2*Conjugate[UV[1, 7]]*UV[2, 7] - (I/2)*g1*STW*Conjugate[UV[1, 7]]*UV[2, 7])) .
    Spinor[-Momentum[k1], MassChi[2], 1]*Spinor[Momentum[k3], MassChi[1], 1] .
    (GA[Lor1] . GA[7]*((-I/2)*CTW*g2*IndexSum[Conjugate[UV[4, j1]]*UV[1, j1], {j1, 3}] -
       (I/2)*g1*STW*IndexSum[Conjugate[UV[4, j1]]*UV[1, j1], {j1, 3}] - (I/2)*CTW*g2*Conjugate[UV[4, 6]]*UV[1, 6]
       (I/2)*g1*STW*Conjugate[UV[4, 6]]*UV[1, 6] + (I/2)*CTW*g2*Conjugate[UV[4, 7]]*UV[1, 7] + (I/2)*g1*STW*Conjugate[UV[4, 7]]*UV[1, 7]) +
     GA[Lor1] . GA[6]*((I/2)*CTW*g2*IndexSum[Conjugate[UV[1, j1]]*UV[4, j1], {j1, 3}] +
       (I/2)*g1*STW*IndexSum[Conjugate[UV[1, j1]]*UV[4, j1], {j1, 3}] + (I/2)*CTW*g2*Conjugate[UV[1, 6]]*UV[4, 6]
       (I/2)*g1*STW*Conjugate[UV[1, 6]]*UV[4, 6] - (I/2)*CTW*g2*Conjugate[UV[1, 7]]*UV[4, 7] - (I/2)*g1*STW*Conjugate[UV[1, 7]]*UV[4, 7])) .
    Spinor[Momentum[p], MassChi[4], 1]*FAD[{k1 + k2, MassVZ}, Dimension -> 4]) +
Spinor[Momentum[k2], MassChi[1], 1] . (GA[Lor2] . GA[7]*((-I/2)*CTW*g2*IndexSum[Conjugate[UV[4, j1]]*UV[1, j1], {j1, 3}] -
      (I/2)*g1*STW*IndexSum[Conjugate[UV[4, j1]]*UV[1, j1], {j1, 3}] - (I/2)*CTW*g2*Conjugate[UV[4, 6]]*UV[1, 6]
      (I/2)*g1*STW*Conjugate[UV[4, 6]]*UV[1, 6] + (I/2)*CTW*g2*Conjugate[UV[4, 7]]*UV[1, 7] + (I/2)*g1*STW*Conjugate[UV[4, 7]]*UV[1, 7]) +
    GA[Lor2] . GA[6]*((I/2)*CTW*g2*IndexSum[Conjugate[UV[1, j1]]*UV[4, j1], {j1, 3}] +
      (I/2)*g1*STW*IndexSum[Conjugate[UV[1, j1]]*UV[4, j1], {j1, 3}] + (I/2)*CTW*g2*Conjugate[UV[1, 6]]*UV[4, 6]
      (I/2)*g1*STW*Conjugate[UV[1, 6]]*UV[4, 6] - (I/2)*CTW*g2*Conjugate[UV[1, 7]]*UV[4, 7] - (I/2)*g1*STW*Conjugate[UV[1, 7]]*UV[4, 7])) .
   Spinor[Momentum[p], MassChi[4], 1]*Spinor[Momentum[k3], MassChi[1], 1] .
   (GA[Lor2] . GA[7]*((-I/2)*CTW*g2*IndexSum[Conjugate[UV[2, j1]]*UV[1, j1], {j1, 3}] -
      (I/2)*g1*STW*IndexSum[Conjugate[UV[2, j1]]*UV[1, j1], {j1, 3}] - (I/2)*CTW*g2*Conjugate[UV[2, 6]]*UV[1, 6]
      (I/2)*g1*STW*Conjugate[UV[2, 6]]*UV[1, 6] + (I/2)*CTW*g2*Conjugate[UV[2, 7]]*UV[1, 7] + (I/2)*g1*STW*Conjugate[UV[2, 7]]*UV[1, 7]) +
    GA[Lor2] . GA[6]*((I/2)*CTW*g2*IndexSum[Conjugate[UV[1, j1]]*UV[2, j1], {j1, 3}] +
      (I/2)*g1*STW*IndexSum[Conjugate[UV[1, j1]]*UV[2, j1], {j1, 3}] + (I/2)*CTW*g2*Conjugate[UV[1, 6]]*UV[2, 6]
      (I/2)*g1*STW*Conjugate[UV[1, 6]]*UV[2, 6] - (I/2)*CTW*g2*Conjugate[UV[1, 7]]*UV[2, 7] - (I/2)*g1*STW*Conjugate[UV[1, 7]]*UV[2, 7])) .
   Spinor[-Momentum[k1], MassChi[2], 1]*FAD[{k1 + k3, MassVZ}, Dimension -> 4] -
Spinor[Momentum[k1], MassChi[2], 1] . (GA[Lor2] . GA[7]*((-I/2)*CTW*g2*IndexSum[Conjugate[UV[4, j1]]*UV[2, j1], {j1, 3}] -
      (I/2)*g1*STW*IndexSum[Conjugate[UV[4, j1]]*UV[2, j1], {j1, 3}] - (I/2)*CTW*g2*Conjugate[UV[4, 6]]*UV[2, 6]
      (I/2)*g1*STW*Conjugate[UV[4, 6]]*UV[2, 6] + (I/2)*CTW*g2*Conjugate[UV[4, 7]]*UV[2, 7] + (I/2)*g1*STW*Conjugate[UV[4, 7]]*UV[2, 7]) +
    GA[Lor2] . GA[6]*((I/2)*CTW*g2*IndexSum[Conjugate[UV[2, j1]]*UV[4, j1], {j1, 3}] +
      (I/2)*g1*STW*IndexSum[Conjugate[UV[2, j1]]*UV[4, j1], {j1, 3}] + (I/2)*CTW*g2*Conjugate[UV[2, 6]]*UV[4, 6]
      (I/2)*g1*STW*Conjugate[UV[2, 6]]*UV[4, 6] - (I/2)*CTW*g2*Conjugate[UV[2, 7]]*UV[4, 7] - (I/2)*g1*STW*Conjugate[UV[2, 7]]*UV[4, 7])) .
   Spinor[Momentum[p], MassChi[4], 1]*Spinor[Momentum[k3], MassChi[1], 1] .
   (GA[Lor2] . GA[6]*((I/2)*CTW*g2*IndexSum[Conjugate[UV[1, j1]]*UV[1, j1], {j1, 3}] +
      (I/2)*g1*STW*IndexSum[Conjugate[UV[1, j1]]*UV[1, j1], {j1, 3}] + (I/2)*CTW*g2*Conjugate[UV[1, 6]]*UV[1, 6]
      (I/2)*g1*STW*Conjugate[UV[1, 6]]*UV[1, 6] - (I/2)*CTW*g2*Conjugate[UV[1, 7]]*UV[1, 7] - (I/2)*g1*STW*Conjugate[UV[1, 7]]*UV[1, 7]) +
    GA[Lor2] . GA[7]*((-I/2)*CTW*g2*IndexSum[Conjugate[UV[1, j1]]*UV[1, j1], {j1, 3}] -
      (I/2)*g1*STW*IndexSum[Conjugate[UV[1, j1]]*UV[1, j1], {j1, 3}] - (I/2)*CTW*g2*Conjugate[UV[1, 6]]*UV[1, 6]
(I/2)*g1*STW*Conjugate[UV[1, 6]]*UV[1, 6] + (I/2)*CTW*g2*Conjugate[UV[1, 7]]*UV[1, 7] + (I/2)*g1*STW*Conjugate[UV[1, 7]]*UV[1, 7])) .
Spinor[-Momentum[k2], MassChi[1], 1]*FAD[{k2 + k3, MassVZ}, Dimension -> 4]

All the UV( , ) terms correspond to a mixing matrix elements.

Thank you very much for your time!

Best,

Paulina

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