•Calculation and reduction of the amplitude

ampp4 = (CreateFCAmp[mesontreeinsert, EqualMasses -> False, Sum -> True] // SUNReduce) /. D -> Sequence[] ;

ampp4 // Simplify

{1/(9 (f _ π^(ó  ))^4) (4 (288 L _ 6^( ) (m _ π^(ó  ))^4 + 144 L _ 8^( ) (m _ π^(ó  ))^4 + 5 (e^( ))^2 k _ 7^( ) (f _ π^(ó  ))^2 (m _ π^(ó  ))^2 + 5 (e^( ))^2 k _ 11^( ) (f _ π^(ó  ))^2 (m _ π^(ó  ))^2 + 36 L _ 4^( ) p _ 1 · p _ 2 (m _ π^(ó  ))^2 + 18 L _ 5^( ) p _ 1 · p _ 2 (m _ π^(ó  ))^2 + 36 L _ 4^( ) p _ 1 · p _ 3 (m _ π^(ó  ))^2 + 18 L _ 5^( ) p _ 1 · p _ 3 (m _ π^(ó  ))^2 + 36 L _ 4^( ) p _ 1 · p _ 4 (m _ π^(ó  ))^2 + 18 L _ 5^( ) p _ 1 · p _ 4 (m _ π^(ó  ))^2 + 36 L _ 4^( ) p _ 2 · p _ 3 (m _ π^(ó  ))^2 + 18 L _ 5^( ) p _ 2 · p _ 3 (m _ π^(ó  ))^2 + 36 L _ 4^( ) p _ 2 · p _ 4 (m _ π^(ó  ))^2 + 18 L _ 5^( ) p _ 2 · p _ 4 (m _ π^(ó  ))^2 + 36 L _ 4^( ) p _ 3 · p _ 4 (m _ π^(ó  ))^2 + 18 L _ 5^( ) p _ 3 · p _ 4 (m _ π^(ó  ))^2 + 36 L _ 3^( ) p _ 1 · p _ 4 p _ 2 · p _ 3 + 36 L _ 3^( ) p _ 1 · p _ 3 p _ 2 · p _ 4 + 36 L _ 3^( ) p _ 1 · p _ 2 p _ 3 · p _ 4 + 72 L _ 1^( ) (p _ 1 · p _ 4 p _ 2 · p _ 3 + p _ 1 · p _ 3 p _ 2 · p _ 4 + p _ 1 · p _ 2 p _ 3 · p _ 4) + 72 L _ 2^( ) (p _ 1 · p _ 4 p _ 2 · p _ 3 + p _ 1 · p _ 3 p _ 2 · p _ 4 + p _ 1 · p _ 2 p _ 3 · p _ 4))), 0, 0, 0, 0, 0, 0}

ampl4 = (Simplify /@ Collect[Contract[PropagatorDenominatorExplicit[Plus @@ ampp4]] /. pirule // MandelstamReduce[#, Cancel -> None] & // Expand, _DecayConstant]) // FullSimplify

1/(9 (f _ π^(ó  ))^4) (-144 (6 L _ 1^( ) + 6 L _ 2^( ) + 3 L _ 3^( ) - 8 L _ 6^( ) - 4 L _ 8^( )) (m _ π^0^(ó  ))^4 + 4 (5 (e^( ))^2 (k _ 7^( ) + k _ 11^( )) (f _ π^(ó  ))^2 + 9 (s + t + u) (12 L _ 1^( ) + 12 L _ 2^( ) + 6 L _ 3^( ) - 2 L _ 4^( ) - L _ 5^( ))) (m _ π^0^(ó  ))^2 - 72 (t u + s (t + u)) (2 (L _ 1^( ) + L _ 2^( )) + L _ 3^( )))

Converted by Mathematica  (July 10, 2003)