•ϕ

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

The next to leading order Lagrangian in raw form:

lag = Lagrangian[ChPTW3[4]] /. CouplingConstant[ChPTW3[4], _ ? ((# > 13) &)] :> 0 ;

First, UNMSplit is used to expand NM products of U matrices into meson fields:

llu = (WriteString["stdout", "."] ; UNMSplit[#, x, DropOrder -> 1]) & /@ lag ;

...

lluu = NMExpand[llu] // Simplify ;

lld = DiscardTerms[#, Retain -> {Particle[PhiMeson ] -> 1}, CommutatorReduce -> True, Method -> Coefficient] & /@ Expand[lluu] ;

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

ArgumentsSupply :: argxpr : Warning : The argument x is already in the expression.

Generator matrices are traced:

lll = (WriteString["stdout", "."] ; Simplify[NMExpand[#]]) & /@ ll ;

....

llll = ((WriteString["stdout", "."] ; Simplify[NMExpand[WriteOutUMatrices[WriteOutIsoVectors[#]]] /. NM -> Times]) & /@ lll) // Simplify ;

....

llll

(8 c _ 2^( ) ((m _ π^(ó  ))^2 - (m _ K^+^(ó  ))^2) (2 N _ 10^( ) (m _ K^0^(ó  ))^2 + N _ 11^( ) ((m _ π^(ó  ))^2 + (m _ K^+^(ó  ))^2 + (m _ K^0^(ó  ))^2)) ϕ^( )^7)/(f _ ϕ^(ó  ))^3

Calculation of the Feynman rule:

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

{ϕ^( )^I _ 1}

$VeryVerbose = 0 ;

melsimplified = Simplify[SUNReduce[FeynRule[llll, fields]]] // IndicesCleanup // CommutatorReduce // Simplify

(8 i c _ 2^( ) ((m _ π^(ó  ))^2 - (m _ K^+^(ó  ))^2) (2 N _ 10^( ) (m _ K^0^(ó  ))^2 + N _ 11^( ) ((m _ π^(ó  ))^2 + (m _ K^+^(ó  ))^2 + (m _ K^0^(ó  ))^2)) δ _ (7 I _ 1)^(3))/(f _ ϕ^(ó  ))^3

Converted by Mathematica  (July 10, 2003)