•Calculation of the amplitude

Calculation of the amplitude:

amplFC = CreateFCAmp[mesontreeinsert] ;

$VeryVerbose = 1 ;

amplFC2 = CheckF[(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 = (++ tmpi ; WriteString["stdout", tmpi, " "] ; SUNReduce[SUNReduce[Sum[#, Evaluate[sums]], Explicit -> True, HoldSums -> False]]) & /@ summ) & /@ Take[amplFC, {1, -1}], "KPiPiamplFC2leading"] ;

Using file name /home/fjob/.Mathematica/Applications/HighEnergyPhysics/Phi/Storage/KPiPiamplFC2leading

File exists, loading

$VeryVerbose = 0 ;

amp[K1_, K2_, K3_] := amplFC2 /. {i1 -> K1, i2 -> K2, i3 -> K3} ;

restree = ((Simplify[(((SUNReduce[SUNReduce[#]] & /@ #[7, 3, 3]) & @ amp) /. p1 -> -p3 - p4 /. subpar /. udrules // MomentumExpand // ExpandScalarProduct // PropagatorDenominatorExplicit)]) /. Pair[Momentum[p3, ___], Momentum[p4, ___]] -> (MandelstamS - Pair[Momentum[p3], Momentum[p3]] - Pair[Momentum[p4], Momentum[p4]])/2 /. {Pair[Momentum[p3, ___], Momentum[p3, ___]] -> ParticleMass[Pion, RenormalizationState[1]]^2, Pair[Momentum[p4, ___], Momentum[p4, ___]] -> ParticleMass[Pion, RenormalizationState[1]]^2, Pair[Momentum[p1, ___], Momentum[p1, ___]] -> MandelstamS} // MomentumCombine) /. {p3 + p4 -> -p1, -p3 - p4 -> p1} // Simplify

{(i c _ 2^( ) p _ 1^μ _ 1 µ _ μ _ 1(p _ 1))/(f _ ϕ^(ó  ))^2, -(2 i p _ 1^μ _ 1 µ _ μ _ 1(p _ 1) (3 c _ 2^( ) (s - (m _ π^(ó  r ))^2) + 2 c _ 5^( ) ((m _ π^(ó  ))^2 - (m _ K^(ó  ))^2)))/(3 (f _ ϕ^(ó  ))^2 (s - (m _ K^(ó  ))^2)), (2 i c _ 5^( ) p _ 1^μ _ 1 µ _ μ _ 1(p _ 1) ((m _ K^(ó  ))^2 - (m _ π^(ó  ))^2))/(3 (f _ ϕ^(ó  ))^2 (m _ K^(ó  ))^2), (2 i c _ 5^( ) p _ 1^μ _ 1 µ _ μ _ 1(p _ 1) ((m _ K^(ó  ))^2 - (m _ π^(ó  ))^2) ((m _ π^(ó  ))^2 - (m _ π^(ó  r ))^2 + (m _ K^(ó  ))^2 + s))/(3 (f _ ϕ^(ó  ))^2 (m _ K^(ó  ))^2 ((m _ K^(ó  ))^2 - s))}

restree1 = restree /. ParticleMass[Pion, RenormalizationState[1]] -> ParticleMass[Pion, RenormalizationState[0]] // Simplify

{(i c _ 2^( ) p _ 1^μ _ 1 µ _ μ _ 1(p _ 1))/(f _ ϕ^(ó  ))^2, -(2 i p _ 1^μ _ 1 µ _ μ _ 1(p _ 1) (3 c _ 2^( ) (s - (m _ π^(ó  ))^2) + 2 c _ 5^( ) ((m _ π^(ó  ))^2 - (m _ K^(ó  ))^2)))/(3 (f _ ϕ^(ó  ))^2 (s - (m _ K^(ó  ))^2)), (2 i c _ 5^( ) p _ 1^μ _ 1 µ _ μ _ 1(p _ 1) ((m _ K^(ó  ))^2 - (m _ π^(ó  ))^2))/(3 (f _ ϕ^(ó  ))^2 (m _ K^(ó  ))^2), (2 i c _ 5^( ) p _ 1^μ _ 1 µ _ μ _ 1(p _ 1) ((m _ K^(ó  ))^2 + s) ((m _ K^(ó  ))^2 - (m _ π^(ó  ))^2))/(3 (f _ ϕ^(ó  ))^2 (m _ K^(ó  ))^2 ((m _ K^(ó  ))^2 - s))}

Plus @@ restree1 // Simplify

-(i c _ 2^( ) p _ 1^μ _ 1 µ _ μ _ 1(p _ 1) (-2 (m _ π^(ó  ))^2 + (m _ K^(ó  ))^2 + s))/((f _ ϕ^(ó  ))^2 (s - (m _ K^(ó  ))^2))

restree1[[2]] + restree1[[4]] /. C5 -> 0 // Simplify

-(2 i c _ 2^( ) p _ 1^μ _ 1 µ _ μ _ 1(p _ 1) (s - (m _ π^(ó  ))^2))/((f _ ϕ^(ó  ))^2 (s - (m _ K^(ó  ))^2))

Converted by Mathematica  (July 10, 2003)