•Calculation of the amplitude

Calculation of the amplitude + wave-function renormalization:

amplFC = CreateFCAmp[mesontreeinsert, WFRenormalize -> True][[1]] // MandelstamReduce[#, Cancel -> None] & ;

Renormalization of masses and decay constants:

ampl2mult = (DiscardOrders[amplFC // DCRenormalize // PMRenormalize, PerturbationOrder -> 4] /. manrules /. Log[a_] + Log[b_] :> Log[a b] // SUNReduce // Renormalize // Simplify) /. fren // Simplify

1/(288 π^2 (f _ π^(ó  r ))^4) (3 (512 π^2 L _ 4^(r ) + 256 π^2 L _ 5^(r ) - 1024 π^2 L _ 6^(r ) - 512 π^2 L _ 8^(r ) - log((m _ π^(ó  r ))^2/μ^2)) (m _ π^(ó  r ))^4 (δ _ (i _ 1 i _ 4)^(2) δ _ (i _ 2 i _ 3)^(2) + δ _ (i _ 1 i _ 3)^(2) δ _ (i _ 2 i _ 4)^(2) + δ _ (i _ 1 i _ 2)^(2) δ _ (i _ 3 i _ 4)^(2)) - 4 (24 π^2 (f _ π^(ó  r ))^2 ((-(m _ π^(ó  r ))^2 + s - 2 t + u) δ _ (i _ 1 i _ 4)^(2) δ _ (i _ 2 i _ 3)^(2) + 3 ((m _ π^(ó  r ))^2 - u) δ _ (i _ 1 i _ 3)^(2) δ _ (i _ 2 i _ 4)^(2) + (-(m _ π^(ó  r ))^2 - 2 s + t + u) δ _ (i _ 1 i _ 2)^(2) δ _ (i _ 3 i _ 4)^(2)) - (384 π^2 L _ 4^(r ) + 192 π^2 L _ 5^(r ) + 128 π^2 λ + log((m _ π^(ó  r ))^2/μ^2)) (m _ π^(ó  r ))^2 ((-(m _ π^(ó  r ))^2 + s - 2 t + u) δ _ (i _ 1 i _ 4)^(2) δ _ (i _ 2 i _ 3)^(2) + (-(m _ π^(ó  r ))^2 + s + t - 2 u) δ _ (i _ 1 i _ 3)^(2) δ _ (i _ 2 i _ 4)^(2) + (-(m _ π^(ó  r ))^2 - 2 s + t + u) δ _ (i _ 1 i _ 2)^(2) δ _ (i _ 3 i _ 4)^(2))))

Converted by Mathematica  (July 10, 2003)