•4πS

ll = ArgumentsSupply[Lagrangian[ChPT2[2]], x, RenormalizationState[0], ExpansionOrder -> 4, DropOrder -> 4] ;

lll = DiscardTerms[ll, Retain -> {Particle[Pion , RenormalizationState[0]] -> 4, Particle[Scalar[2] , RenormalizationState[0]] -> 1}, CommutatorReduce -> True] ;

llle = ExpandU[lll]

((Overscript[π^( ), ->] · Overscript[π^( ), ->])^2 !, _ 0^( ) s^( )^0)/(12 (f _ π^(ó  ))^2)

$IsoIndicesCounter = 0 ;

llll = IsoIndicesSupply[llle] // SUNReduce[#, FullReduce -> True] & // CommutatorReduce[#, FullReduce -> True] & // IndicesCleanup // Simplify

(!, _ 0^( ) (π^( )^k1)^2 (π^( )^k2)^2 s^( )^0)/(12 (f _ π^(ó  ))^2)

fields = {QuantumField[Particle[Pion, RenormalizationState[0]], SUNIndex[I1]][p1], QuantumField[Particle[Pion, RenormalizationState[0]], SUNIndex[I2]][p2], QuantumField[Particle[Pion, RenormalizationState[0]], SUNIndex[I3]][p3], QuantumField[Particle[Pion, RenormalizationState[0]], SUNIndex[I4]][p4], QuantumField[Particle[Scalar[2], RenormalizationState[0]], SUNIndex[I5]][p5]}

{π^( )^I _ 1, π^( )^I _ 2, π^( )^I _ 3, π^( )^I _ 4, s^( )^I _ 5}

melsimplified = FeynRule[llll, fields] // SUNReduce[#, FullReduce -> True] & // Simplify

(2 i !, _ 0^( ) δ _ (0 I _ 5)^(2) (δ _ (I _ 1 I _ 4)^(2) δ _ (I _ 2 I _ 3)^(2) + δ _ (I _ 1 I _ 3)^(2) δ _ (I _ 2 I _ 4)^(2) + δ _ (I _ 1 I _ 2)^(2) δ _ (I _ 3 I _ 4)^(2)))/(3 (f _ π^(ó  ))^2)

Converted by Mathematica  (July 10, 2003)