•Preliminaries

IsoVector[QuantumField[Particle[AxialVector[0], ___], ___], ___][_] := 0 ; IsoVector[QuantumField[Particle[Vector[0], ___], ___], ___][_] := 0 ; IsoVector[QuantumField[Particle[Scalar[1 | 2], ___], ___], ___][_] := 0 ; QuantumField[Particle[Scalar[1 | 2], ___], ___][_] := 0 ; QuantumField[___, Particle[PseudoScalar[0], ___], ___, SUNIndex[0], ___][_] := 0

subpar = Table[(ParticleMass[PseudoScalar[1], SUNIndex[i], r___] -> ParticleMass[Select[$IsoSpinProjectionRules, (! FreeQ[#, {i}] &)][[1]][[1]], r]), {i, 8}]

{ParticleMass(ϕ, 1, r___) -> ParticleMass(π^+, r), ParticleMass(ϕ, 2, r___) -> ParticleMass(π^+, r), ParticleMass(ϕ, 3, r___) -> ParticleMass(π^0, r), ParticleMass(ϕ, 4, r___) -> ParticleMass(K^+, r), ParticleMass(ϕ, 5, r___) -> ParticleMass(K^+, r), ParticleMass(ϕ, 6, r___) -> ParticleMass(K^0, r), ParticleMass(ϕ, 7, r___) -> ParticleMass(K^0, r), ParticleMass(ϕ, 8, r___) -> ParticleMass(η, r)}

udrules = {PionPlus -> Pion, PionZero -> Pion, KaonPlus -> Kaon, KaonZero -> Kaon}

{π^+ -> π, π^0 -> π, K^+ -> K, K^0 -> K}

toEtaRules = {ParticleMass[PseudoScalar[2], r___]^2 - 4 ParticleMass[PseudoScalar[6], r___]^2 :> -3 * ParticleMass[PseudoScalar[11], r]^2, -ParticleMass[PseudoScalar[2], r___]^2 + 4 ParticleMass[PseudoScalar[6], r___]^2 :> 3 * ParticleMass[PseudoScalar[11], r]^2} ;

gellmannOkubo = {ParticleMass[EtaMeson, r___]^2 -> (4 ParticleMass[Kaon, r]^2 - ParticleMass[Pion, r]^2)/3, ParticleMass[EtaMeson, r___]^n_ -> ((4 ParticleMass[Kaon, r]^2 - ParticleMass[Pion, r]^2)/3)^(n/2)} ;

Converted by Mathematica  (July 10, 2003)