•2π S2

IsoVector[QuantumField[___, Particle[AxialVector[0], ___], ___], ___][_] := 0 ; <br /> QuantumField[___, Particle[AxialVector[0], ___], ___][_] := 0 ; <br /> QuantumField[Particle[PseudoScalar[0], ___], SUNIndex[0]][_] := 0 ;

Lagrangian[ChPT3[4]]

L _ 7^( ) ((< χ '6 ÷„^† > - < ÷„ '6 χ^† >) '6 (< χ '6 ÷„^† > - < ÷„ '6 χ^† >)) + L _ 6^( ) ((< ÷„ '6 χ^† > + < χ '6 ÷„^† >) '6 (< ÷„ '6 χ^† > + < χ '6 ÷„^† >)) + L _ 4^( ) (< ÷s _ μ(÷„) '6 ÷s _ μ(÷„)^† > '6 (< ÷„ '6 χ^† > + < χ '6 ÷„^† >)) + L _ 1^( ) (< ÷s _ μ(÷„) '6 ÷s _ μ(÷„)^† > '6 < ÷s _ ν(÷„) '6 ÷s _ ν(÷„)^† >) + L _ 2^( ) (< ÷s _ μ(÷„) '6 ÷s _ ν(÷„)^† > '6 < ÷s _ μ(÷„) '6 ÷s _ ν(÷„)^† >) + H _ 2^( ) < χ^† '6 χ > + H _ 1^( ) (< L _ (μ ν) '6 L _ (μ ν) > + < R _ (μ ν) '6 R _ (μ ν) >) + L _ 5^( ) < ÷s _ μ(÷„) '6 ÷s _ μ(÷„)^† '6 (÷„ '6 χ^† + χ '6 ÷„^†) > + i L _ 9^( ) (< L _ (μ ν) '6 ÷s _ μ(÷„) '6 ÷s _ ν(÷„)^† > + < R _ (μ ν) '6 ÷s _ μ(÷„)^† '6 ÷s _ ν(÷„) >) + L _ 8^( ) (< ÷„ '6 χ^† '6 ÷„ '6 χ^† > + < χ '6 ÷„^† '6 χ '6 ÷„^† >) + L _ 3^( ) < ÷s _ μ(÷„) '6 ÷s _ μ(÷„)^† '6 ÷s _ ν(÷„) '6 ÷s _ ν(÷„)^† > + L _ 10^( ) < L _ (μ ν) '6 ÷„ '6 R _ (μ ν) '6 ÷„^† >

llt = UNMSplit[Lagrangian[ChPT3[4]], x, DropOrder -> 2, DiagonalToU -> True] ;

lllt = Select[llt // NMExpand // Expand, (! FreeQ[#, UChiMatrix] &)] ;

lllt // Length

67

lltt = ArgumentsSupply[lllt, x, RenormalizationState[0], ExpansionOrder -> 2, DropOrder -> 2, DiagonalToU -> True] ;

ArgumentsSupply :: argxpr : Warning : The argument x is already in the expression.

lltt // Length

46

llltt = (WriteString["stdout", "."] ; (# /. UTrace1 -> tr // NMExpand) /. tr -> UTrace // ExpandAll // NMExpand // Expand) & /@ lltt ;

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

llltt // Length

913

lll = (WriteString["stdout", "."] ; DiscardTerms[#, Retain -> {Particle[PhiMeson , RenormalizationState[0]] -> 2, Particle[Scalar[2], RenormalizationState[0]] -> 1}, Method -> Expand]) & /@ llltt ;

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

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

$IsoIndicesCounter = 0 ;

llll = llle // IsoIndicesSupply // SUNReduce // IndicesCleanup // Simplify ;

fields = {QuantumField[Particle[PhiMeson, RenormalizationState[0]], SUNIndex[I1]][p1], QuantumField[Particle[PhiMeson, RenormalizationState[0]], SUNIndex[I2]][p2], QuantumField[Particle[Scalar[2], RenormalizationState[0]], SUNIndex[I3]][p3]}

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

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

melsimplified /. {I1 -> 7, I2 -> 7, I3 -> 8} // SUNReduce[#, FullReduce -> True] & // Simplify

(8 i (L _ 5^( ) p _ 1 · p _ 2 + 2 (2 L _ 8^( ) (m _ K^0^(ó  ))^2 + L _ 6^( ) ((m _ π^(ó  ))^2 + (m _ K^+^(ó  ))^2 + (m _ K^0^(ó  ))^2))) !, _ 0^( ))/(3^(1/2) (f _ ϕ^(ó  ))^2)

Converted by Mathematica  (July 10, 2003)