KSS2Amplitude.nb

•Calculation of the amplitude

Calculation of the amplitude:

Specialization to the (6,3) isospin channel and isospin reduction:

$amplFC2 = (summ = SUNReduce[SUNReduce[#]] & /@ (Print["Expanding..."] ; tmp = Expand[#] ; Print["Reducing..."] ; tmp) ; suminds = (#[[1]]) & /@ Union[Cases[#, _SumOver, Infinity]] ; sums = If[suminds === {}, {I1, 1}, Sequence @@ ((({#, If[FreeQ[summ, #], 1, 8]} & /@ suminds)))] ; Print["Length of expression: ", Length[summ]] ; tmpii = 0 ; res = (If[IntegerQ[tmpii/100], Print[tmpii]] ; ++ tmpii ; SUNReduce[SUNReduce[Sum[WriteOutUMatrices[#], Evaluate[sums]], Explicit -> True, HoldSums -> False]]) & /@ summ) & /@ amplFC ;$

Further reduction and change to Mandelstam variables:

${1/(f _ ϕ^(ó ))^3 (8 c _ 2^( ) !, _ 0^( ) (N _ 11^( ) ((m _ π^(ó ))^2 (6 δ _ (0 i)^(3) + σ _ (2 2)^i - σ _ (3 3)^i) - 2 (m _ K^(ó ))^2 (3 δ _ (0 i)^(3) - σ _ (2 2)^i + σ _ (3 3)^i)) + 2 N _ 10^( ) ((m _ π^(ó ))^2 (2 δ _ (0 i)^(3) + σ _ (2 2)^i + σ _ (3 3)^i) - 2 (m _ K^(ó ))^2 (δ _ (0 i)^(3) + σ _ (3 3)^i)))), 1/(3 (f _ ϕ^(ó ))^3 (p _ 2^2 - (m _ K^(ó ))^2)) (16 c _ 5^( ) ((m _ K^(ó ))^2 - (m _ π^(ó ))^2) !, _ 0^( ) (18 L _ 4^( ) (p _ 1^2 + p _ 2^2 - p _ 3^2) δ _ (0 i)^(3) + L _ 5^( ) (p _ 1^2 + p _ 2^2 - p _ 3^2) (6 δ _ (0 i)^(3) - 3 δ _ (3 i)^(3) - 3^(1/2) δ _ (8 i)^(3)) + 4 (2 L _ 8^( ) (-6 δ _ (0 i)^(3) + 3 δ _ (3 i)^(3) + 3^(1/2) δ _ (8 i)^(3)) (m _ K^(ó ))^2 + L _ 6^( ) ((-6 δ _ (0 i)^(3) + 3 δ _ (3 i)^(3) + 3^(1/2) δ _ (8 i)^(3)) (m _ π^(ó ))^2 + 2 (m _ K^(ó ))^2 (-15 δ _ (0 i)^(3) + 3 δ _ (3 i)^(3) + 3^(1/2) δ _ (8 i)^(3))))))}$

Converted by Mathematica (July 10, 2003)