•S2

Lagrangian[ChPTW3[2]]

c _ 5^( ) (< σ^6 '6 ÷„^† '6 χ > + < σ^6 '6 χ^† '6 ÷„ >) + c _ 2^( ) < σ^6 '6 ÷s _ μ(÷„)^† '6 ÷s _ μ(÷„) >

Sources are set to 0:

IsoVector[QuantumField[Particle[(Vector | AxialVector | PseudoScalar)[0], ___], ___], ___][_] := 0 ;

The evaluated leading order Lagrangian:

ll = ArgumentsSupply[Lagrangian[ChPTW3[2]], x, RenormalizationState[0], ExpansionOrder -> 1, DropOrder -> 1, DiagonalToU -> True] ;

Redundant terms are discarded:

lll = DiscardTerms[ll, Retain -> {Particle[PhiMeson , RenormalizationState[0]] -> 1, Particle[Scalar[2], RenormalizationState[0]] -> 1}, CommutatorReduce -> True, Method -> Expand] // Simplify

-(2 i c _ 5^( ) !, _ 0^( ) (< σ^6 '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] '6 Overscript[s^( ), ->] · Overscript[σ, ->] > - < σ^6 '6 Overscript[s^( ), ->] · Overscript[σ, ->] '6 Overscript[ϕ^( ), ->] · Overscript[σ, ->] >))/f _ ϕ^(ó  )

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[2], RenormalizationState[0]], SUNIndex[I2]][p2]}

{ϕ^( )^I _ 1, s^( )^I _ 2}

lal = Expand[llll] ;

melsimplified = IndicesCleanup[SUNReduce[FeynRule[lal, fields], FullReduce -> True]] ;

melsimplified // Simplify

(8 i c _ 5^( ) !, _ 0^( ) f _ (6 I _ 1 I _ 2)^(3))/f _ ϕ^(ó  )

Converted by Mathematica  (July 10, 2003)