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I want to calculate the squared amplitude of the Feynman diagram of double-pion photoproduction using FeynCalc package. Here is the code I created:

x[1, 2] = s;
x[4, 5] = Subscript[x, 1];
x[2, 3] = Subscript[x, 2];
x[3, 4] = Subscript[x, 3];
x[1, 5] = Subscript[x, 4];

SetMandelstam[x, {k, Subscript[p, 1], -Subscript[p, 2], -Subscript[q, 1], -Subscript[q, 2]}, {0, M, M, Subscript[m, \[Pi]], Subscript[m, \[Pi]]}];

Mt1 = SpinorUBar[Subscript[p, 2], M] . Subscript[g, 1] . GA5 . GS[Subscript[q, 2]] . ((I (GS[Subscript[q, 2] + Subscript[p, 2]] + M))/(SP[Subscript[q, 2] + Subscript[p, 2]] - M^2)) . Subscript[g, 2] . GA5 . GS[Subscript[q, 1]] . (I/(SP[k - Subscript[q, 1]] - Subscript[m, \[Pi]]^2)) . (-I . Subscript[Q, 1]) . FV[2 Subscript[q, 1] - k, \[Mu]] . SpinorU[Subscript[p, 1], M]

Mt1C = ComplexConjugate[Mt1] /. {\[Mu] -> \[Mu]'}

Mt2 = SpinorUBar[Subscript[p, 2], M] . Subscript[g, 1] . GA5 . GS[Subscript[q, 2]] . (I/(SP[k - Subscript[q, 2]] - Subscript[m, \[Pi]]^2)) . (-I . Subscript[Q, 2]) . FV[2 Subscript[q, 2] - k, \[Mu]] . ((I (GS[Subscript[p, 1] - Subscript[q, 1]] + M))/(SP[Subscript[p, 1] - Subscript[q, 1]] - M^2)) . Subscript[g, 2] . GA5 . GS[Subscript[q, 1]] . SpinorU[Subscript[p, 1], M]

Mt2C = ComplexConjugate[Mt2] /. {\[Mu] -> \[Mu]'}

M2 = FermionSpinSum[(Mt1 + Mt2)*(Mt1C + Mt2C)]*(-MT[\[Mu],\[Mu]']) // Contract

DiracSimplify[1/4 M2, DiracTraceEvaluate -> True, Expanding -> False]

FullSimplify[%]

Here is the final result I got:

enter image description here

But why is the result of the squared amplitude calculation that I get still quite long, even after I use the "FullSimplify" function? Is there a way to get simpler results?

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  • $\begingroup$ Do you have reason to believe that it should simplify further? $\endgroup$
    – Ghoster
    Commented May 2 at 0:07
  • $\begingroup$ It is the result of the squared amplitude of the two diagrams on the t-channel. Actually I had to calculate about 7 diagrams at once, which would have been much longer than that. Is that OK? @Ghoster $\endgroup$
    – Albert Copperfield
    Commented May 2 at 1:11

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