•ϕS

IsoVector[QuantumField[___, Particle[AxialVector[0], ___], ___], ___][_] := 0 ; QuantumField[___, Particle[AxialVector[0], ___], ___][_] := 0 ;

The evaluated leading order Lagrangian:

ll = ArgumentsSupply[Lagrangian[ChPTWS3[2]], x, RenormalizationState[0], ExpansionOrder -> 1, DropOrder -> 1, DiagonalToU -> True] ;

Redundant terms are discarded:

lll = DiscardTerms[ll, Retain -> {Particle[PhiMeson , RenormalizationState[0]] -> 1}, CommutatorReduce -> True, Method -> Coefficient] // Simplify

1/(3 f _ ϕ^(ó  )) (c _ 5^( ) s^( ) (6 !, _ 0^( ) (< σ^6 '6 Overscript[p^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] > + < σ^6 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[p^( ), ->] · Overscript[σ, ->] > - i < σ^6 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[s^( ), ->] · Overscript[σ, ->] > + i < σ^6 '6 Overscript[s^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] > + 2 < σ^6 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] > p^( )^0) - i (2 3^(1/2) (< σ^6 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 σ^8 > - < σ^6 '6 σ^8 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] >) (m _ π^(ó  ))^2 + (m _ K^+^(ó  ))^2 (3 < σ^6 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 σ^3 > - 3^(1/2) < σ^6 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 σ^8 > - 3 < σ^6 '6 σ^3 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] > + 3^(1/2) < σ^6 '6 σ^8 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] >) + (m _ K^0^(ó  ))^2 (-3 < σ^6 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 σ^3 > - 3^(1/2) < σ^6 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 σ^8 > + 3 < σ^6 '6 σ^3 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] > + 3^(1/2) < σ^6 '6 σ^8 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] >))))

Generator matrices are traced:

llle = ExpandU[lll] ;

Indices are supplied:

$IsoIndicesCounter = 0 ;

llll = llle // IsoIndicesSupply // IndicesCleanup ;

Calculation of the Feynman rule:

fields = {QuantumField[Particle[PhiMeson, RenormalizationState[0]], SUNIndex[I1]][p1], QuantumField[Particle[Scalar[1], RenormalizationState[0]]][p2]}

{ϕ^( )^I _ 1, s^( )}

lal = Expand[llll] ;

$ConstantIsoIndices = {} ;

melsimplified = If[Head[lal] == Plus, Plus @@ (IndicesCleanup[SUNReduce[FeynRule[#, fields], FullReduce -> True]] & /@ (List @@ lal))] ;

melsimplified // Simplify

(4 i c _ 5^( ) ((m _ π^(ó  ))^2 - (m _ K^+^(ó  ))^2) δ _ (7 I _ 1)^(3))/f _ ϕ^(ó  )

Converted by Mathematica  (July 10, 2003)