•Calculation of the amplitude

$ConstantIsoIndices = {i1, i3, I1} ;

ampFC = CreateFCAmp[mesontreeinsert] /. i3 -> i1 // SUNReduce // IndicesCleanup // CommutatorReduce // Simplify

{(p _ 1^ρ1 µ _ ρ1^*(p _ 3) (15 (d _ (i _ 1 I _ 1 k1)^(3))^2 - 9 (f _ (i _ 1 I _ 1 k1)^(3))^2 - 15 d _ (i _ 1 i _ 1 k1)^(3) d _ (I _ 1 I _ 1 k1)^(3) + 10 δ _ (i _ 1 I _ 1)^(3) - 10) SumOver(I _ 1, {0, 1, 2, 3, 4, 5, 6, 7, 8}))/(576 π^4 f _ ϕ^(ó  ) (q _ 1^2 - (m _ ϕ^(I _ 1 ))^2))}

amplFC = (ampFC[[1]] // DoSumOver // SUNReduce // SUNReduce) /. subpar /. udrules // Simplify

1/(576 π^4 f _ ϕ^(ó  )) (p _ 1^ρ1 µ _ ρ1^*(p _ 3) (1/(q _ 1^2 - (m _ π^(ó  ))^2) (15 (d _ (1 i _ 1 k1)^(3))^2 + 15 (d _ (2 i _ 1 k1)^(3))^2 + 15 (d _ (3 i _ 1 k1)^(3))^2 - 9 (f _ (1 i _ 1 k1)^(3))^2 - 9 (f _ (2 i _ 1 k1)^(3))^2 - 9 (f _ (3 i _ 1 k1)^(3))^2 - 15 3^(1/2) d _ (8 i _ 1 i _ 1)^(3) + 10 δ _ (1 i _ 1)^(3) + 10 δ _ (2 i _ 1)^(3) + 10 δ _ (3 i _ 1)^(3) - 30) + 1/(q _ 1^2 - (m _ K^(ó  ))^2) (15 (d _ (4 i _ 1 k1)^(3))^2 + 15 (d _ (5 i _ 1 k1)^(3))^2 + 15 (d _ (6 i _ 1 k1)^(3))^2 + 15 (d _ (7 i _ 1 k1)^(3))^2 - 9 (f _ (4 i _ 1 k1)^(3))^2 - 9 (f _ (5 i _ 1 k1)^(3))^2 - 9 (f _ (6 i _ 1 k1)^(3))^2 - 9 (f _ (7 i _ 1 k1)^(3))^2 + 10 3^(1/2) d _ (8 i _ 1 i _ 1)^(3) + 10 δ _ (4 i _ 1)^(3) + 10 δ _ (5 i _ 1)^(3) + 10 δ _ (6 i _ 1)^(3) + 10 δ _ (7 i _ 1)^(3) - 40) + (15 (d _ (8 i _ 1 k1)^(3))^2 - 9 (f _ (8 i _ 1 k1)^(3))^2 + 5 3^(1/2) d _ (8 i _ 1 i _ 1)^(3) + 10 δ _ (8 i _ 1)^(3) - 10)/(q _ 1^2 - (m _ η^(ó  ))^2)))

Converted by Mathematica  (July 10, 2003)