•ϕϕϕϕA

The evaluated leading order Lagrangian:

ll = ArgumentsSupply[Lagrangian[ChPTW3[2]], x, RenormalizationState[0], ExpansionOrder -> 4, DropOrder -> 4, DiagonalToU -> True] ;

Redundant terms are discarded:

lll = DiscardTerms[ll, Retain -> {Particle[PhiMeson , RenormalizationState[0]] -> 4, Particle[AxialVector[0] , RenormalizationState[0]] -> 1}, CommutatorReduce -> True, Method -> Coefficient] // Simplify ;

Generator matrices are traced:

llle = ExpandU[lll, CommutatorReduce -> True] // Simplify ;

Indices are supplied:

$IsoIndicesCounter = 0 ;

llll = CheckF[llle // IsoIndicesSupply // IndicesCleanup, "4MesonAllll.m"] ;

Calculation of the Feynman rule:

fields = {QuantumField[Particle[AxialVector[0], RenormalizationState[0]], LorentzIndex[μ1], SUNIndex[I1]][p1], QuantumField[Particle[PhiMeson, RenormalizationState[0]], SUNIndex[I2]][p2], QuantumField[Particle[PhiMeson, RenormalizationState[0]], SUNIndex[I3]][p3], QuantumField[Particle[PhiMeson, RenormalizationState[0]], SUNIndex[I4]][p4], QuantumField[Particle[PhiMeson, RenormalizationState[0]], SUNIndex[I5]][p5]}

{A^( ) _ μ _ 1^I _ 1, ϕ^( )^I _ 2, ϕ^( )^I _ 3, ϕ^( )^I _ 4, ϕ^( )^I _ 5}

lal = llll // Expand ;

lal // Length

343

lal // LeafCount

32055

lal[[1]]

(i c _ 2^( ) d _ (k2 k5 k6) d _ (k3 k4 k6) δ _ (6 k5) ϕ^( )^k1 ϕ^( )^k3 ϕ^( )^k4 ∂ _ τ1 ϕ^( ) _ ó ^k2 A^( ) _ τ1^k1)/(9 (f _ ϕ^(ó  ))^4)

$ConstantIsoIndices = {I1, I2, I3, I4, I5} ;

Cases[lal, UTrace1[__ ? ((! FreeQ[{#}, QuantumField, Infinity, Heads -> True]) &)], Infinity, Heads -> True] // Length

0

melsimplified = CheckF[I * (If[Head[lal] == Plus, Plus @@ ((WriteString["stdout", "."] ; IndicesCleanup[Contract[FunctionalD[PhiToFC[#], fields]] // SUNReduce // SUNReduce // SUNReduce // SUNReduce // SUNReduce // SUNReduce]) & /@ (List @@ lal))]), "A4MesonWeakMel"] ;

.......................................................................................................................................................................................................................................................................................................................................................

melsimplified // LeafCount

154105

Converted by Mathematica  (July 10, 2003)