•ππγγ

lll = CheckF[(WriteString["stdout", "."] ; DiscardTerms[#, Retain -> {Particle[Pion , RenormalizationState[0]] -> 2, Particle[Photon , RenormalizationState[0]] -> 2}, Method -> Expand]) & /@ lltt, "lll3mesonPhoton", NoSave -> False] ;

...........

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

$IsoIndicesCounter = 0 ;

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

1/(2 (f _ π^(ó  ))^2) ((e^( ))^2 (16 L _ 4^( ) (m _ π^(ó  ))^2 δ _ (3 k3) δ _ (3 k4) f _ (k1 k3 k5) f _ (k2 k4 k5) π^( )^k1 π^( )^k2 γ^( ) _ ρ1^2 + 8 L _ 5^( ) (m _ π^(ó  ))^2 δ _ (3 k3) δ _ (3 k4) f _ (k1 k3 k5) f _ (k2 k4 k5) π^( )^k1 π^( )^k2 γ^( ) _ ρ1^2 - (L _ 10^( ) π^( )^k1 (π^( )^k1 + (3 δ _ (3 k3) δ _ (3 k4) f _ (k1 k3 k5) f _ (k2 k4 k5) - δ _ (3 k1) δ _ (3 k2)) π^( )^k2) ∂ _ μ γ^( ) _ ν^ó  + L _ 9^( ) γ^( ) _ μ (π^( )^k1 (2 ∂ _ ν π^( ) _ ó ^k1 + (δ _ (3 k3) (2 δ _ (3 k4) (f _ (k1 k4 k5) f _ (k2 k3 k5) + 2 f _ (k1 k3 k5) f _ (k2 k4 k5)) - i f _ (k1 k2 k3)) - 2 δ _ (3 k1) δ _ (3 k2)) ∂ _ ν π^( ) _ ó ^k2) - i δ _ (3 k3) f _ (k1 k2 k3) π^( )^k2 ∂ _ ν π^( ) _ ó ^k1)) (∂ _ μ γ^( ) _ ν^ó  - ∂ _ ν γ^( ) _ μ^ó )))

fields = {QuantumField[Particle[Pion, RenormalizationState[0]], SUNIndex[I1]][p1], QuantumField[Particle[Pion, RenormalizationState[0]], SUNIndex[I2]][p2], QuantumField[Particle[Photon, RenormalizationState[0]], LorentzIndex[μ3]][p3], QuantumField[Particle[Photon, RenormalizationState[0]], LorentzIndex[μ4]][p4]}

{π^( )^I _ 1, π^( )^I _ 2, γ^( ) _ μ _ 3, γ^( ) _ μ _ 4}

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

-1/(f _ π^(ó  ))^2 (4 i (e^( ))^2 (4 (2 L _ 4^( ) + L _ 5^( )) g^(μ _ 3 μ _ 4) (m _ π^(ó  ))^2 + L _ 9^( ) (p _ 4^μ _ 3 (p _ 1^μ _ 4 + p _ 2^μ _ 4) + p _ 1^μ _ 3 p _ 3^μ _ 4 + p _ 2^μ _ 3 p _ 3^μ _ 4 - g^(μ _ 3 μ _ 4) p _ 1 · p _ 3 - g^(μ _ 3 μ _ 4) p _ 1 · p _ 4 - g^(μ _ 3 μ _ 4) p _ 2 · p _ 3 - g^(μ _ 3 μ _ 4) p _ 2 · p _ 4) + L _ 10^( ) (2 g^(μ _ 3 μ _ 4) p _ 3 · p _ 4 - 2 p _ 4^μ _ 3 p _ 3^μ _ 4)) (δ _ (3 I _ 1)^(2) δ _ (3 I _ 2)^(2) - δ _ (I _ 1 I _ 2)^(2)))

Converted by Mathematica  (July 10, 2003)