•Calculation of the amplitude

amp4 = CreateFCAmp[mesontreeinsert, AmplitudeLevel -> Classes] /. D -> Sequence[] // SUNReduce // Contract // Simplify

{(4 i e^( ) (2 (2 L _ 4^( ) + L _ 5^( )) (p _ 3 · µ ( p _ 1 ) - p _ 4 · µ ( p _ 1 )) (m _ π^(ó  ))^2 + L _ 9^( ) (p _ 1 · p _ 3 p _ 4 · µ ( p _ 1 ) - p _ 1 · p _ 4 p _ 3 · µ ( p _ 1 ))) f _ (3 i _ 1 i _ 2)^(2))/(f _ π^(ó  ))^2}

symmrules2 = {Pair[Momentum[p1], Momentum[p4]] -> 1/2 (Pair[Momentum[p1], Momentum[p4]] - Pair[Momentum[p1], Momentum[p3]] - Pair[Momentum[p1], Momentum[p1]]), Pair[Momentum[p1], Momentum[p3]] -> 1/2 (Pair[Momentum[p1], Momentum[p3]] - Pair[Momentum[p1], Momentum[p4]] - Pair[Momentum[p1], Momentum[p1]])}

{p _ 1 · p _ 4 -> 1/2 (-p _ 1^2 - p _ 1 · p _ 3 + p _ 1 · p _ 4), p _ 1 · p _ 3 -> 1/2 (-p _ 1^2 + p _ 1 · p _ 3 - p _ 1 · p _ 4)}

ampl4 = amp4[[1]] /. symmrules1 /. symmrules2 // Simplify

-(2 i e^( ) ( p _ 4 - p _ 3 ) · µ ( p _ 1 ) (4 (2 L _ 4^( ) + L _ 5^( )) (m _ π^(ó  ))^2 + L _ 9^( ) p _ 1^2) f _ (3 i _ 1 i _ 2)^(2))/(f _ π^(ó  ))^2

Converted by Mathematica  (July 10, 2003)