•PP

lag = Lagrangian[ChPTW3[4]] /. CouplingConstant[ChPTW3[4], _ ? (((# > 13 && # =!= 36)) &), ___] :> 0 ;

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

llu = (WriteString["stdout", "."] ; UNMSplit[#, x, DropOrder -> 0]) & /@ Expand[lag] ;

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

lluu = NMExpand[llu] ;

Remaining 'raw' quantites are given arguments:

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

Redundant terms are discarded:

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

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

lld = (WriteString["stdout", "."] ; DiscardTerms[#, Retain -> {Particle[PseudoScalar[0], RenormalizationState[0]] -> 2}, CommutatorReduce -> True, Method -> Coefficient]) & /@ lldd

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

-(16 c _ 2^( ) N _ 12^( ) < σ^6 '6 Overscript[p^( ), ->] · Overscript[σ, ->] '6 Overscript[p^( ), ->] · Overscript[σ, ->] > (!, _ 0^( ))^2)/(f _ ϕ^(ó  ))^2 + (16 c _ 2^( ) N _ 36^( ) < σ^6 '6 Overscript[p^( ), ->] · Overscript[σ, ->] '6 Overscript[p^( ), ->] · Overscript[σ, ->] > (!, _ 0^( ))^2)/(f _ ϕ^(ó  ))^2 - (32 c _ 2^( ) N _ 12^( ) < σ^6 '6 Overscript[p^( ), ->] · Overscript[σ, ->] > p^( )^0 (!, _ 0^( ))^2)/(f _ ϕ^(ó  ))^2 - (48 c _ 2^( ) N _ 13^( ) < σ^6 '6 Overscript[p^( ), ->] · Overscript[σ, ->] > p^( )^0 (!, _ 0^( ))^2)/(f _ ϕ^(ó  ))^2 + (32 c _ 2^( ) N _ 36^( ) < σ^6 '6 Overscript[p^( ), ->] · Overscript[σ, ->] > p^( )^0 (!, _ 0^( ))^2)/(f _ ϕ^(ó  ))^2

lldd = lld // ExpandU

-(32 c _ 2^( ) N _ 12^( ) Overscript[öõ(6), ->] ⊗ Overscript[p^( ), ->] · Overscript[p^( ), ->] (!, _ 0^( ))^2)/(f _ ϕ^(ó  ))^2 + (32 c _ 2^( ) N _ 36^( ) Overscript[öõ(6), ->] ⊗ Overscript[p^( ), ->] · Overscript[p^( ), ->] (!, _ 0^( ))^2)/(f _ ϕ^(ó  ))^2 - (64 c _ 2^( ) N _ 12^( ) Overscript[öõ(6), ->] · Overscript[p^( ), ->] p^( )^0 (!, _ 0^( ))^2)/(f _ ϕ^(ó  ))^2 - (96 c _ 2^( ) N _ 13^( ) Overscript[öõ(6), ->] · Overscript[p^( ), ->] p^( )^0 (!, _ 0^( ))^2)/(f _ ϕ^(ó  ))^2 + (64 c _ 2^( ) N _ 36^( ) Overscript[öõ(6), ->] · Overscript[p^( ), ->] p^( )^0 (!, _ 0^( ))^2)/(f _ ϕ^(ó  ))^2

lal = IsoIndicesSupply[lldd] // IndicesCleanup

-(64 c _ 2^( ) N _ 12^( ) δ _ (6 k1) p^( )^0 p^( )^k1 (!, _ 0^( ))^2)/(f _ ϕ^(ó  ))^2 - (96 c _ 2^( ) N _ 13^( ) δ _ (6 k1) p^( )^0 p^( )^k1 (!, _ 0^( ))^2)/(f _ ϕ^(ó  ))^2 + (64 c _ 2^( ) N _ 36^( ) δ _ (6 k1) p^( )^0 p^( )^k1 (!, _ 0^( ))^2)/(f _ ϕ^(ó  ))^2 - (32 c _ 2^( ) N _ 12^( ) d _ (k1 k2 k3) δ _ (6 k3) p^( )^k1 p^( )^k2 (!, _ 0^( ))^2)/(f _ ϕ^(ó  ))^2 + (32 c _ 2^( ) N _ 36^( ) d _ (k1 k2 k3) δ _ (6 k3) p^( )^k1 p^( )^k2 (!, _ 0^( ))^2)/(f _ ϕ^(ó  ))^2

Calculation of the Feynman rule:

fields = {QuantumField[Particle[PseudoScalar[0], RenormalizationState[0]], SUNIndex[I1]][p1], QuantumField[Particle[PseudoScalar[0], RenormalizationState[0]], SUNIndex[I2]][p2]}

{p^( )^I _ 1, p^( )^I _ 2}

res = Simplify[FeynRule[lal, fields]] // SUNReduce // Simplify

-1/(f _ ϕ^(ó  ))^2 (32 i c _ 2^( ) (!, _ 0^( ))^2 (3 N _ 13^( ) (δ _ (0 I _ 2)^(3) δ _ (6 I _ 1)^(3) + δ _ (0 I _ 1)^(3) δ _ (6 I _ 2)^(3)) + 2 N _ 12^( ) (d _ (6 I _ 1 I _ 2)^(3) + δ _ (0 I _ 2)^(3) δ _ (6 I _ 1)^(3) + δ _ (0 I _ 1)^(3) δ _ (6 I _ 2)^(3)) - 2 N _ 36^( ) (d _ (6 I _ 1 I _ 2)^(3) + δ _ (0 I _ 2)^(3) δ _ (6 I _ 1)^(3) + δ _ (0 I _ 1)^(3) δ _ (6 I _ 2)^(3))))

UndeclareUScalar[QuantumField[aa___, Particle[bb__], cc___][x_]] ; <br /> UndeclareUScalar[UTrace1] ; <br /> UnDeclareNonCommutative[UMatrix[a__]] ;

Converted by Mathematica  (July 10, 2003)