•Calculation and reduction of the amplitude

ampp4 = CreateFCAmp[mesontreeinsert, AmplitudeLevel -> Classes, EqualMasses -> False, Sum -> True] // SUNReduce // Simplify

{1/(27 (f _ π^(ó  ))^4) (2 (4 (e^( ))^4 (5 k _ 13^( ) + 37 k _ 14^( )) (f _ π^(ó  ))^4 - (e^( ))^2 (-10 k _ 5^( ) (m _ π^0^(ó  ))^2 - 370 k _ 6^( ) (m _ π^0^(ó  ))^2 - 2 k _ 7^( ) (m _ π^0^(ó  ))^2 - 360 k _ 8^( ) (m _ π^0^(ó  ))^2 + 54 k _ 3^( ) p _ 1 · p _ 2 + 27 k _ 4^( ) p _ 1 · p _ 2 + 54 k _ 3^( ) p _ 1 · p _ 3 + 27 k _ 4^( ) p _ 1 · p _ 3 - 108 k _ 3^( ) p _ 1 · p _ 4 - 54 k _ 4^( ) p _ 1 · p _ 4 - 108 k _ 3^( ) p _ 2 · p _ 3 - 54 k _ 4^( ) p _ 2 · p _ 3 + 54 k _ 3^( ) p _ 2 · p _ 4 + 27 k _ 4^( ) p _ 2 · p _ 4 + 54 k _ 3^( ) p _ 3 · p _ 4 + 27 k _ 4^( ) p _ 3 · p _ 4 + 10 k _ 1^( ) (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) + 2 k _ 2^( ) (5 p _ 1 · p _ 2 + 5 p _ 1 · p _ 3 - 64 p _ 1 · p _ 4 - 64 p _ 2 · p _ 3 + 5 p _ 2 · p _ 4 + 5 p _ 3 · p _ 4)) (f _ π^(ó  ))^2 + 18 (2 l _ 3^( ) (m _ π^0^(ó  ))^4 + 6 l _ 1^( ) p _ 1 · p _ 4 p _ 2 · p _ 3 + 3 l _ 2^( ) (p _ 1 · p _ 3 p _ 2 · p _ 4 + p _ 1 · p _ 2 p _ 3 · p _ 4)))), (2 (e^( ))^2 g^(μ _ 1 μ _ 2) (p _ 1^μ _ 1 - p _ 2^μ _ 1) (10 (e^( ))^2 (k _ 1^( ) + k _ 2^( )) (p _ 3^μ _ 2 - p _ 4^μ _ 2) (f _ π^(ó  ))^2 + 9 l _ 6^( ) (p _ 4^μ _ 2 (p _ 3 + p _ 4) . (p _ 3) - p _ 3^μ _ 2 (p _ 3 + p _ 4) . (p _ 4))))/(9 (f _ π^(ó  ))^2 ((-p _ 3 - p _ 4)^2 - (m _ γ^(ó  ))^2)), (2 (e^( ))^2 g^(μ _ 1 μ _ 2) (p _ 1^μ _ 1 - p _ 3^μ _ 1) (10 (e^( ))^2 (k _ 1^( ) + k _ 2^( )) (p _ 2^μ _ 2 - p _ 4^μ _ 2) (f _ π^(ó  ))^2 + 9 l _ 6^( ) (p _ 4^μ _ 2 (p _ 2 + p _ 4) . (p _ 2) - p _ 2^μ _ 2 (p _ 2 + p _ 4) . (p _ 4))))/(9 (f _ π^(ó  ))^2 ((-p _ 2 - p _ 4)^2 - (m _ γ^(ó  ))^2)), 0, 0, (2 (e^( ))^2 g^(μ _ 1 μ _ 2) (p _ 2^μ _ 2 - p _ 4^μ _ 2) (10 (e^( ))^2 (k _ 1^( ) + k _ 2^( )) (p _ 1^μ _ 1 - p _ 3^μ _ 1) (f _ π^(ó  ))^2 + 9 l _ 6^( ) (p _ 1^μ _ 1 (p _ 2 + p _ 4) . (p _ 3) - p _ 3^μ _ 1 (p _ 2 + p _ 4) . (p _ 1))))/(9 (f _ π^(ó  ))^2 ((-p _ 2 - p _ 4)^2 - (m _ γ^(ó  ))^2)), (2 (e^( ))^2 g^(μ _ 1 μ _ 2) (p _ 3^μ _ 2 - p _ 4^μ _ 2) (10 (e^( ))^2 (k _ 1^( ) + k _ 2^( )) (p _ 1^μ _ 1 - p _ 2^μ _ 1) (f _ π^(ó  ))^2 + 9 l _ 6^( ) (p _ 1^μ _ 1 (p _ 3 + p _ 4) . (p _ 2) - p _ 2^μ _ 1 (p _ 3 + p _ 4) . (p _ 1))))/(9 (f _ π^(ó  ))^2 ((-p _ 3 - p _ 4)^2 - (m _ γ^(ó  ))^2))}

amps4 = If[opi, ampp4, Take[ampp4, {1, 1}]] ;

ampl4 = (Simplify /@ Collect[Contract[PropagatorDenominatorExplicit[Plus @@ amps4]] // manred[None] // Expand, _DecayConstant]) /. eDrop /. ren4Rule // FullSimplify

1/27 (40 k _ 13^( ) (e^(r ))^4 + 296 k _ 14^( ) (e^(r ))^4 + (2 (2 (5 k _ 5^( ) + 185 k _ 6^( ) + k _ 7^( ) + 180 k _ 8^( )) (m _ π^0^(ó  r ))^2 - 10 (s - 2 t + u) k _ 1^( ) + (-64 s + 74 t - 64 u) k _ 2^( ) - 27 (s - 2 t + u) (2 k _ 3^( ) + k _ 4^( ))) (e^(r ))^2)/(f _ π^(ó  ))^2 + (9 (8 l _ 3^( ) (m _ π^0^(ó  r ))^4 - 6 l _ 1^( ) (t - 2 (m _ π^+^(ó  r ))^2) (-2 (m _ π^+^(ó  r ))^2 + s + u) - 3 l _ 2^( ) (8 (m _ π^+^(ó  r ))^4 - 4 (s + t + u) (m _ π^+^(ó  r ))^2 + t u + s (t + 2 u))))/(f _ π^(ó  ))^4)

Converted by Mathematica  (July 10, 2003)