KSPiAmplitude.nb

•Calculation of the amplitude

Calculation of the amplitude:

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

$amplFC2 = CheckF[(summ = SUNReduce[SUNReduce[#]] & /@ (Print["Expanding..."] ; tmp = Expand[#] ; Print["Reducing..."] ; tmp) ; suminds = (#[[1]]) & /@ Union[Cases[#, _SumOver, Infinity]] ; sums = If[suminds === {}, {I1, 1}, Sequence @@ ((({#, If[FreeQ[summ, #], 1, 8]} & /@ suminds)))] ; Print["Length of expression: ", Length[summ]] ; tmpii = 0 ; res = (If[IntegerQ[tmpii/100], Print[tmpii]] ; ++ tmpii ; SUNReduce[SUNReduce[Sum[WriteOutUMatrices[#], Evaluate[sums]], Explicit -> True, HoldSums -> False]]) & /@ summ) & /@ Take[amplFC /. {i1 -> 6, i3 -> 3}, {1, -1}], "KSPiCTolds.1.m"] ;$

Further reduction and change to Mandelstam variables:

${(32 c _ 2^( ) (N _ 12^( ) - N _ 36^( )) (!, _ 0^( ))^2)/(f _ ϕ^(ó ))^2, (128 c _ 5^( ) (L _ 8^( ) (m _ π^(ó ))^2 + L _ 6^( ) ((m _ π^(ó ))^2 + 2 (m _ K^(ó ))^2)) (!, _ 0^( ))^2)/((f _ ϕ^(ó ))^2 (p _ 3^2 - (m _ π^(ó ))^2)), (128 c _ 5^( ) (L _ 8^( ) (m _ K^(ó ))^2 + L _ 6^( ) ((m _ π^(ó ))^2 + 2 (m _ K^(ó ))^2)) (!, _ 0^( ))^2)/((f _ ϕ^(ó ))^2 (p _ 1^2 - (m _ K^(ó ))^2)), (16 c _ 2^( ) (2 (N _ 10^( ) + N _ 12^( )) (m _ K^(ó ))^2 + N _ 11^( ) ((m _ π^(ó ))^2 + 2 (m _ K^(ó ))^2)) (!, _ 0^( ))^2)/((f _ ϕ^(ó ))^2 (p _ 1^2 - (m _ K^(ó ))^2)), (16 c _ 2^( ) (N _ 11^( ) ((m _ π^(ó ))^2 + 2 (m _ K^(ó ))^2) + 2 (N _ 12^( ) (m _ π^(ó ))^2 + N _ 10^( ) (m _ K^(ó ))^2)) (!, _ 0^( ))^2)/((f _ ϕ^(ó ))^2 (p _ 3^2 - (m _ π^(ó ))^2)), -(64 (c _ 2^( ) (p _ 1^2 - p _ 2^2 + p _ 3^2) - 2 c _ 5^( ) (m _ K^(ó ))^2) (L _ 8^( ) (m _ π^(ó ))^2 + L _ 6^( ) ((m _ π^(ó ))^2 + 2 (m _ K^(ó ))^2)) (!, _ 0^( ))^2)/((f _ ϕ^(ó ))^2 (p _ 3^2 - (m _ π^(ó ))^2) (p _ 1^2 - (m _ K^(ó ))^2)), -(8 c _ 2^( ) (N _ 8^( ) (p _ 1^2 - p _ 2^2 + p _ 3^2) ((m _ π^(ó ))^2 + 2 (m _ K^(ó ))^2) - 2 (m _ K^(ó ))^2 (-N _ 5^( ) (p _ 1^2 - p _ 2^2 + p _ 3^2) + N _ 11^( ) ((m _ π^(ó ))^2 + 2 (m _ K^(ó ))^2) + 2 (N _ 12^( ) (m _ π^(ó ))^2 + N _ 10^( ) (m _ K^(ó ))^2))) (!, _ 0^( ))^2)/((f _ ϕ^(ó ))^2 (p _ 3^2 - (m _ π^(ó ))^2) (p _ 1^2 - (m _ K^(ó ))^2)), -(64 (c _ 2^( ) (p _ 1^2 - p _ 2^2 + p _ 3^2) - 2 c _ 5^( ) (m _ K^(ó ))^2) (L _ 8^( ) (m _ K^(ó ))^2 + L _ 6^( ) ((m _ π^(ó ))^2 + 2 (m _ K^(ó ))^2)) (!, _ 0^( ))^2)/((f _ ϕ^(ó ))^2 (p _ 3^2 - (m _ π^(ó ))^2) (p _ 1^2 - (m _ K^(ó ))^2))}$

Converted by Mathematica (July 10, 2003)