KSS2Amplitude.nb

•Calculation of the amplitude

Calculation of the amplitude:

${(8 c _ 5^( ) !, _ 0^( ) f _ (6 7 i)^(3))/f _ ϕ^(ó ), -(2 i !, _ 0^( ) SumOver(I _ 1, 8) ((4 i c _ 5^( ) (m _ π^(ó ))^2 δ _ (7 I1))/f _ ϕ^(ó ) - (4 i c _ 5^( ) (m _ K^+^(ó ))^2 δ _ (7 I1))/f _ ϕ^(ó )) (d _ (7 i I _ 1)^(3) + δ _ (0 i) δ _ (7 I1)))/(p _ 2^2 - (m _ ϕ^(I _ 1 ))^2)}$

Isospin reduction:

$amplFC2 = (Print["Reducing..."] ; summ = SUNReduce[SUNReduce[#]] & /@ (Print["Expanding..."] ; Expand[#]) ; suminds = (#[[1]]) & /@ Union[Cases[#, _SumOver, Infinity]] ; sums = If[suminds === {}, {I1, 1}, Sequence @@ ((({#, If[FreeQ[summ, #], 1, 8]} & /@ suminds)))] ; Print["Length of expression: ", Length[summ]] ; tmpi = 0 ; res = If[Head[summ] === Plus, (++ tmpi ; WriteString["stdout", tmpi] ; SUNReduce[SUNReduce[Sum[#, Evaluate[sums]], Explicit -> True, HoldSums -> False]]) & /@ summ, SUNReduce[SUNReduce[Sum[summ, Evaluate[sums]], Explicit -> True, HoldSums -> False]]]) & /@ Take[amplFC, {1, -1}] ;$

1234

The leading order amplitude:

${-(4 c _ 5^( ) !, _ 0^( ) (δ _ (3 i)^(3) - 3^(1/2) δ _ (8 i)^(3)))/f _ ϕ^(ó ), (4 c _ 5^( ) ((m _ π^(ó ))^2 - (m _ K^(ó ))^2) !, _ 0^( ) (6 δ _ (0 i)^(3) - 3 δ _ (3 i)^(3) - 3^(1/2) δ _ (8 i)^(3)))/(3 f _ ϕ^(ó ) (p _ 2^2 - (m _ K^(ó ))^2))}$

(4 c _ 5^( ) !, _ 0^( ) (-3 δ _ (3 i)^(3) + 3 3^(1/2) δ _ (8 i)^(3) + (((m _ π^(ó ))^2 - (m _ K^(ó ))^2) (6 δ _ (0 i)^(3) - 3 δ _ (3 i)^(3) - 3^(1/2) δ _ (8 i)^(3)))/(p _ 2^2 - (m _ K^(ó ))^2)))/(3 f _ ϕ^(ó ))

Converted by Mathematica (July 10, 2003)