A7PiPiAmplitude.nb

•Calculation of the amplitude

Calculation of the amplitude:

$amplFC2 = CheckF[(summ = SUNReduce[SUNReduce[#]] & /@ (Print["Expanding..."] ; tmp = Expand[#] ; Print["Reducing..."] ; tmp) ; suminds = (#[[1]]) & /@ Union[Cases[#, _SumOver, Infinity]] ; sums = If[suminds === {}, {I1, 1}, Sequence @@ ((({#, If[FreeQ[summ, #], 1, 8]} & /@ suminds)))] ; Print["Length of expression: ", Length[summ]] ; tmpii = 0 ; res = (If[IntegerQ[tmpii/100], WriteString["stdout", tmpii, " "]] ; ++ tmpii ; SUNReduce[SUNReduce[Sum[WriteOutUMatrices[#], Evaluate[sums]], Explicit -> True, HoldSums -> False]]) & /@ summ) & /@ Take[amplFC /. {i1 -> 7, i2 -> 3, i3 -> 3}, {1, -1}], "KPiPiCTs"] ;$
$rest1 = Simplify[(Simplify[(# /. p1 -> -p3 - p4 /. subpar /. udrules // MomentumExpand // ExpandScalarProduct // PropagatorDenominatorExplicit)] /. Pair[Momentum[p3, s_], Momentum[p4, s_]] -> (MandelstamS - Pair[Momentum[p3, s], Momentum[p3, s]] - Pair[Momentum[p4, s], Momentum[p4, s]])/2 /. {Pair[Momentum[p3, _], Momentum[p3, _]] -> ParticleMass[Pion, RenormalizationState[0]]^2, Pair[Momentum[p4, _], Momentum[p4, _]] -> ParticleMass[Pion, RenormalizationState[0]]^2, Pair[Momentum[p1, s_], Momentum[p1, s_]] -> MandelstamS} // Simplify // MomentumCombine) /. {p3 + p4 -> -p1, -p3 - p4 -> p1}] & /@ amplFC2$

${-(2 i c _ 2^( ) p _ 1^μ _ 1 µ _ μ _ 1(p _ 1) (-2 N _ 9^( ) (m _ π^(ó ))^2 + N _ 22^( ) (m _ π^(ó ))^2 + 2 N _ 23^( ) (m _ π^(ó ))^2 - 2 N _ 5^( ) (m _ K^(ó ))^2 + N _ 20^( ) (s - 2 (m _ π^(ó ))^2) - N _ 8^( ) ((m _ π^(ó ))^2 + 2 (m _ K^(ó ))^2)))/(f _ ϕ^(ó ))^4, -1/(3 (f _ ϕ^(ó ))^4 (s - (m _ K^(ó ))^2)) (4 i c _ 2^( ) p _ 1^μ _ 1 µ _ μ _ 1(p _ 1) (3 N _ 8^( ) (s - (m _ π^(ó ))^2) ((m _ π^(ó ))^2 + 2 (m _ K^(ó ))^2) + 3 N _ 5^( ) (-2 (m _ π^(ó ))^4 + s (m _ π^(ó ))^2 + s (m _ K^(ó ))^2) + 3 N _ 9^( ) ((s - 2 (m _ K^(ó ))^2) (m _ π^(ó ))^2 + s (m _ K^(ó ))^2) + 2 ((m _ π^(ó ))^2 - (m _ K^(ó ))^2) (7 N _ 11^( ) (m _ π^(ó ))^2 + 3 N _ 12^( ) (m _ π^(ó ))^2 + 2 N _ 11^( ) (m _ K^(ó ))^2 + 3 N _ 7^( ) (s - 2 (m _ π^(ó ))^2) + N _ 10^( ) (3 (m _ π^(ó ))^2 + 2 (m _ K^(ó ))^2)))), (4 i c _ 2^( ) p _ 1^μ _ 1 µ _ μ _ 1(p _ 1) ((m _ K^(ó ))^2 - (m _ π^(ó ))^2) (2 N _ 10^( ) (m _ K^(ó ))^2 + N _ 11^( ) ((m _ π^(ó ))^2 + 2 (m _ K^(ó ))^2)))/(3 (f _ ϕ^(ó ))^4 (m _ K^(ó ))^2), -(8 i c _ 5^( ) p _ 1^μ _ 1 µ _ μ _ 1(p _ 1) ((m _ π^(ó ))^2 - (m _ K^(ó ))^2) (2 L _ 4^( ) ((m _ π^(ó ))^2 + 2 (m _ K^(ó ))^2) - L _ 5^( ) (m _ K^(ó ))^2))/(3 (f _ ϕ^(ó ))^4 (m _ K^(ó ))^2), (4 i c _ 2^( ) p _ 1^μ _ 1 µ _ μ _ 1(p _ 1) ((m _ K^(ó ))^2 + s) ((m _ K^(ó ))^2 - (m _ π^(ó ))^2) (2 N _ 10^( ) (m _ K^(ó ))^2 + N _ 11^( ) ((m _ π^(ó ))^2 + 2 (m _ K^(ó ))^2)))/(3 (f _ ϕ^(ó ))^4 (m _ K^(ó ))^2 ((m _ K^(ó ))^2 - s)), 1/(3 (f _ ϕ^(ó ))^4 (m _ K^(ó ))^2 ((m _ K^(ó ))^2 - s)) (16 i c _ 5^( ) p _ 1^μ _ 1 µ _ μ _ 1(p _ 1) ((m _ K^(ó ))^2 - (m _ π^(ó ))^2) (-L _ 5^( ) ((m _ π^(ó ))^4 + 3 (m _ K^(ó ))^2 (m _ π^(ó ))^2 - s (m _ K^(ó ))^2) + L _ 4^( ) (-(m _ π^(ó ))^4 + (s - 14 (m _ K^(ó ))^2) (m _ π^(ó ))^2 + 8 s (m _ K^(ó ))^2) + 2 (L _ 8^( ) ((m _ π^(ó ))^4 + 6 (m _ K^(ó ))^2 (m _ π^(ó ))^2 + (m _ K^(ó ))^4) + L _ 6^( ) ((m _ π^(ó ))^4 + 15 (m _ K^(ó ))^2 (m _ π^(ó ))^2 + 2 (m _ K^(ó ))^4))))}$

Converted by Mathematica (July 10, 2003)