•5ϕS

The evaluated leading order Lagrangian:

ll = ArgumentsSupply[Lagrangian[ChPTWS3[2]], x, RenormalizationState[0], ExpansionOrder -> 5, DropOrder -> 5, DiagonalToU -> True] ;

Redundant terms are discarded:

lll = DiscardTerms[ll, Retain -> {Particle[PhiMeson , RenormalizationState[0]] -> 5, Particle[Scalar[1], RenormalizationState[0]] -> 1}, CommutatorReduce -> True, Method -> Expand] // Simplify ;

Generator matrices are traced:

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

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[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], QuantumField[Particle[Scalar[1], RenormalizationState[0]]][p6]}

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

lal = Expand[llll // PhiToFC] ;

lal // Length

508

melsimplified = CheckF[((WriteString["stdout", "."] ; Simplify[I * SUNReduce[SUNReduce[SUNReduce[FunctionalD[#, fields] // Contract]]]]) & /@ lal), "ChPTW3-5meson-melsimplified"] ;

Another check that two different evaluations with specific components give the same result:

(SUNReduce[#, Explicit -> True, HoldSums -> False] & /@ (melsimplified /. {I1 -> 7, I2 -> 3, I3 -> 3, I4 -> 3, I5 -> 3} // Expand)) // Simplify

-1/(30 (f _ ϕ^(ó  ))^5) (i (5 c _ 2^( ) (3 p _ 1 · p _ 2 + 3 p _ 1 · p _ 3 + 3 p _ 1 · p _ 4 + 3 p _ 1 · p _ 5 - 2 p _ 2 · p _ 3 - 2 p _ 2 · p _ 4 - 2 p _ 2 · p _ 5 - 2 p _ 3 · p _ 4 - 2 p _ 3 · p _ 5 - 2 p _ 4 · p _ 5) + 24 c _ 5^( ) ((m _ K^+^(ó  ))^2 - (m _ π^(ó  ))^2)))

(SUNReduce /@ SUNReduce /@ SUNReduce /@ SUNReduce /@ SUNReduce /@ SUNReduce /@ SUNReduce /@ SUNReduce /@ SUNReduce /@ SUNReduce /@ SUNReduce /@ (melsimplified /. {I1 -> 7, I2 -> 3, I3 -> 3, I4 -> 3, I5 -> 3} // Expand)) // Simplify

-1/(30 (f _ ϕ^(ó  ))^5) (i (5 c _ 2^( ) (3 p _ 1 · p _ 2 + 3 p _ 1 · p _ 3 + 3 p _ 1 · p _ 4 + 3 p _ 1 · p _ 5 - 2 p _ 2 · p _ 3 - 2 p _ 2 · p _ 4 - 2 p _ 2 · p _ 5 - 2 p _ 3 · p _ 4 - 2 p _ 3 · p _ 5 - 2 p _ 4 · p _ 5) + 24 c _ 5^( ) ((m _ K^+^(ó  ))^2 - (m _ π^(ó  ))^2)))

Converted by Mathematica  (July 10, 2003)