•Calculation of the amplitude

Calculation of the amplitude:

amplFC0 = Expand[CreateFCAmp[mesontreeinsert, AmplitudeLevel -> Classes, EqualMasses -> False, Sum -> True]] // Contract // SUNReduce // Simplify

{(8 C^( ) (e^( ))^2 - (f _ π^(ó  ))^2 (-(m _ π^0^(ó  ))^2 + p _ 1 · p _ 2 + p _ 1 · p _ 3 - 2 p _ 1 · p _ 4 - 2 p _ 2 · p _ 3 + p _ 2 · p _ 4 + p _ 3 · p _ 4))/(3 (f _ π^(ó  ))^4), ((e^( ))^2 (p _ 1 · p _ 3 - p _ 1 · p _ 4 - p _ 2 · p _ 3 + p _ 2 · p _ 4))/((-p _ 3 - p _ 4)^2 - (m _ γ^(ó  ))^2), ((e^( ))^2 (p _ 1 · p _ 2 - p _ 1 · p _ 4 - p _ 2 · p _ 3 + p _ 3 · p _ 4))/((-p _ 2 - p _ 4)^2 - (m _ γ^(ó  ))^2), 0}

lowestamp = If[opi, Expand[Plus @@ amplFC0] /. ParticleMass[Vector[1], RenormalizationState[0]] -> 0 // PropagatorDenominatorExplicit // manred[MandelstamU] // FullSimplify, Expand[amplFC0[[1]]] /. ParticleMass[Vector[1], RenormalizationState[0]] -> 0 /. ren4Rule // PropagatorDenominatorExplicit // manred[MandelstamU] // FullSimplify]

(8 C^( ) (e^(r ))^2 + (f _ π^(ó  ))^2 (-4 (m _ π^+^(ó  r ))^2 + (m _ π^0^(ó  r ))^2 + 3 t))/(3 (f _ π^(ó  ))^4)

amplFC = Expand[CreateFCAmp[mesontreeinsert, AmplitudeLevel -> Classes, EqualMasses -> False, Sum -> True, WFRenormalize -> True]] // Contract // SUNReduce // Simplify ;

ampl2mult = Plus @@ ((((# // ChargeEliminate // PMRenormalize) /. ren4Rule // PropagatorDenominatorExplicit // DiscardOrders[#, PerturbationOrder -> 4] & // ChargedMassesEliminate // Expand) /. eDrop // ChargeEliminate // manred[None] // Simplify // ChargedNeutralMassesCancel) & /@ If[opi, Plus @@ amplFC, {amplFC [[1]]}])

1/(864 π^2 (C^( ))^2 (f _ π^(ó  ))^4) (-1280 π^2 (C^( ))^2 (e^(r ))^4 (k _ 13^(r ) + 2 k _ 14^(r )) (f _ π^(ó  ))^4 + 8 (C^( ))^2 (e^(r ))^2 (-288 π^2 λ (m _ π^+^(ó  r ))^2 - 9 log((m _ π^+^(ó  r ))^2/μ^2) (m _ π^+^(ó  r ))^2 - 36 log((m _ γ^(ó  r ))^2/(m _ π^+^(ó  r ))^2) (m _ π^+^(ó  r ))^2 + 432 π^2 k _ 3^(r ) (m _ π^0^(ó  r ))^2 - 216 π^2 k _ 4^(r ) (m _ π^0^(ó  r ))^2 - 80 π^2 k _ 5^(r ) (m _ π^0^(ó  r ))^2 - 1232 π^2 k _ 6^(r ) (m _ π^0^(ó  r ))^2 - 16 π^2 k _ 7^(r ) (m _ π^0^(ó  r ))^2 - 1152 π^2 k _ 8^(r ) (m _ π^0^(ó  r ))^2 + 216 π^2 λ (m _ π^0^(ó  r ))^2 + 27 log((m _ π^+^(ó  r ))^2/μ^2) (m _ π^0^(ó  r ))^2 + 27 log((m _ γ^(ó  r ))^2/(m _ π^+^(ó  r ))^2) (m _ π^0^(ó  r ))^2 - 27 (m _ π^0^(ó  r ))^2 - 9 s + 18 t - 9 u + 72 s π^2 λ - 144 t π^2 λ + 72 u π^2 λ + 9 s log((m _ π^+^(ó  r ))^2/μ^2) - 18 t log((m _ π^+^(ó  r ))^2/μ^2) + 9 u log((m _ π^+^(ó  r ))^2/μ^2) + 9 s log((m _ γ^(ó  r ))^2/(m _ π^+^(ó  r ))^2) - 18 t log((m _ γ^(ó  r ))^2/(m _ π^+^(ó  r ))^2) + 9 u log((m _ γ^(ó  r ))^2/(m _ π^+^(ó  r ))^2) + 80 π^2 k _ 1^(r ) (-4 (m _ π^+^(ó  r ))^2 + 3 (m _ π^0^(ó  r ))^2 + 2 (s - 2 t + u)) + 80 π^2 k _ 2^(r ) (-4 (m _ π^+^(ó  r ))^2 + 3 (m _ π^0^(ó  r ))^2 + 2 (s - 2 t + u))) (f _ π^(ó  ))^2 - 3 (C^( ))^2 (64 (16 π^2 λ - log((m _ π^+^(ó  r ))^2/μ^2)) (m _ π^+^(ó  r ))^4 - 2 ((8 (176 π^2 λ + log((m _ π^0^(ó  r ))^2/μ^2)) - 21 log((m _ π^+^(ó  r ))^2/μ^2)) (m _ π^0^(ó  r ))^2 + 2 (s - 2 t + u) (64 π^2 λ - log((m _ π^+^(ó  r ))^2/μ^2))) (m _ π^+^(ó  r ))^2 + 96 π^2 (f _ π^(ó  ))^2 (-4 (m _ π^+^(ó  r ))^2 + 3 (m _ π^0^(ó  r ))^2 + s - 2 t + u) + (m _ π^0^(ó  r ))^2 (192 π^2 l _ 3^(r ) (m _ π^0^(ó  r ))^2 + 3 (512 π^2 λ + 11 log((m _ π^0^(ó  r ))^2/μ^2)) (m _ π^0^(ó  r ))^2 + 4 (s - 2 t + u) (128 π^2 λ + log((m _ π^0^(ó  r ))^2/μ^2)))))

Converted by Mathematica  (July 10, 2003)