•Calculation of the amplitude

Calculation of the amplitude:

$ConstantIsoIndices = {i1, i3, I1, I2} ;

ampFC = CreateFCAmp[mesontreeinsert, AmplitudeLevel -> Classes] ;

amplFC = ampFC /. subpar /. udrules // SUNReduce[#, FullReduce -> True] & // Simplify

{(i (!, _ 0^( ))^2 δ _ (i _ 1 I _ 1)^(3) (3 d _ (I _ 1 i _ 3 k1)^(3) d _ (I _ 2 I _ 2 k1)^(3) + 6 d _ (I _ 1 I _ 2 k1)^(3) d _ (I _ 2 i _ 3 k1)^(3) + 9 d _ (I _ 1 I _ 2 I _ 2)^(3) δ _ (0 i _ 3)^(3) + 2 δ _ (I _ 1 i _ 3)^(3) + 4 δ _ (I _ 1 I _ 2)^(3) δ _ (I _ 2 i _ 3)^(3)) SumOver(I _ 1, {0, 1, 2, 3, 4, 5, 6, 7, 8}) SumOver(I _ 2, {0, 1, 2, 3, 4, 5, 6, 7, 8}))/(72 π^4 (p _ 3^2 - (m _ ϕ^(I _ 1 ))^2) (q _ 1^2 - (m _ ϕ^(I _ 2 ))^2)), (i (!, _ 0^( ))^2 (6 d _ (i _ 1 I _ 2 k1)^(3) d _ (I _ 1 I _ 2 k1)^(3) + 3 d _ (i _ 1 I _ 1 k1)^(3) d _ (I _ 2 I _ 2 k1)^(3) + 9 d _ (I _ 1 I _ 2 I _ 2)^(3) δ _ (0 i _ 1)^(3) + 2 δ _ (i _ 1 I _ 1)^(3) + 4 δ _ (i _ 1 I _ 2)^(3) δ _ (I _ 1 I _ 2)^(3)) δ _ (I _ 1 i _ 3)^(3) SumOver(I _ 1, {0, 1, 2, 3, 4, 5, 6, 7, 8}) SumOver(I _ 2, {0, 1, 2, 3, 4, 5, 6, 7, 8}))/(72 π^4 (p _ 3^2 - (m _ ϕ^(I _ 1 ))^2) (q _ 1^2 - (m _ ϕ^(I _ 2 ))^2))}

Converted by Mathematica  (July 10, 2003)