•The eta

zeta = CheckF[dum, "ChPT3P110o2.Fac"]

((32 π^2 (24 L _ 4^( ) + 16 L _ 5^( ) - 3 λ) - 3 log((m _ K^(ó  ))^2/μ^2)) (m _ K^(ó  ))^2 + 16 π^2 (3 (f _ ϕ^(ó  ))^2 + 8 (3 L _ 4^( ) - L _ 5^( )) (m _ π^(ó  ))^2))/(48 π^2 (f _ ϕ^(ó  ))^2)

ff2 = amplFC2 /. D -> Sequence[] /. i1 -> 8

(4 (f _ ϕ^(ó  ))^2 (!, _ 0^( ))^2)/((m _ η^(ó  ))^2 - p _ 3^2)

$ConstantIsoIndices = {i1, i3, I1, I2} ;

amploop = Plus @@ ampinfinities /. i1 -> 8 // SUNReduce // SUNReduce // Simplify

((3 (32 π^2 λ + log((m _ π^(ó  ))^2/μ^2)) (m _ π^(ó  ))^2 + 4 (32 π^2 λ + log((m _ K^(ó  ))^2/μ^2)) (m _ K^(ó  ))^2 + 3 (32 π^2 λ + log((m _ η^(ó  ))^2/μ^2)) (m _ η^(ó  ))^2) (!, _ 0^( ))^2)/(12 π^2 (p _ 3^2 - (m _ η^(ó  ))^2))

Take[amplFC4, {1, 1}] /. i1 -> 8 // Simplify

{16 (H _ 2^( ) - 2 L _ 8^( )) (!, _ 0^( ))^2}

ampct = Plus @@ Take[amplFC4, {1, 3}] /. i1 -> 8 // Simplify

-(16 (L _ 8^( ) (-8 (m _ π^(ó  ))^2 + 32 (m _ K^(ó  ))^2 - 6 (m _ η^(ó  ))^2 + 6 p _ 3^2) + 3 (8 L _ 6^( ) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2) + H _ 2^( ) ((m _ η^(ó  ))^2 - p _ 3^2))) (!, _ 0^( ))^2)/(3 (p _ 3^2 - (m _ η^(ó  ))^2))

Z^(-1) ~~ 1 + ϵ. The first order tree amplitude is multiplied with Z ~~ 1 - ϵ = 1 - (Z^(-1) - 1) = 2 - Z^(-1):

ampwf = ff2 * (2 - zeta) // Simplify

(4 (f _ ϕ^(ó  ))^2 (2 - ((32 π^2 (24 L _ 4^( ) + 16 L _ 5^( ) - 3 λ) - 3 log((m _ K^(ó  ))^2/μ^2)) (m _ K^(ó  ))^2 + 16 π^2 (3 (f _ ϕ^(ó  ))^2 + 8 (3 L _ 4^( ) - L _ 5^( )) (m _ π^(ó  ))^2))/(48 π^2 (f _ ϕ^(ó  ))^2)) (!, _ 0^( ))^2)/((m _ η^(ó  ))^2 - p _ 3^2)

ff4 = amploop + ampct + ampwf /. D -> Sequence[] // FullSimplify

1/(12 π^2 (p _ 3^2 - (m _ η^(ó  ))^2)) ((-48 π^2 (f _ ϕ^(ó  ))^2 + 384 π^2 L _ 4^( ) (m _ π^(ó  ))^2 - 128 π^2 L _ 5^( ) (m _ π^(ó  ))^2 - 1536 π^2 L _ 6^( ) (m _ π^(ó  ))^2 + 96 π^2 λ (m _ π^(ó  ))^2 + 3 log((m _ π^(ó  ))^2/μ^2) (m _ π^(ó  ))^2 + 768 π^2 L _ 4^( ) (m _ K^(ó  ))^2 + 512 π^2 L _ 5^( ) (m _ K^(ó  ))^2 - 3072 π^2 L _ 6^( ) (m _ K^(ó  ))^2 + 32 π^2 λ (m _ K^(ó  ))^2 + log((m _ K^(ó  ))^2/μ^2) (m _ K^(ó  ))^2 + 3 (32 π^2 (λ - 2 H _ 2^( )) + log((m _ η^(ó  ))^2/μ^2)) (m _ η^(ó  ))^2 + 192 π^2 H _ 2^( ) p _ 3^2 - 128 π^2 L _ 8^( ) (-4 (m _ π^(ó  ))^2 + 16 (m _ K^(ó  ))^2 - 3 (m _ η^(ó  ))^2 + 3 p _ 3^2)) (!, _ 0^( ))^2)

z = (ff4/ff2 // Renormalize // Simplify) /. Pair[Momentum[p3], Momentum[p3]] -> ParticleMass[EtaMeson, RenormalizationState[0]]^2 /. gellmannOkubo /. a_Log :> (a /. toEtaRules) // FullSimplify

1/(48 π^2 (f _ ϕ^(ó  ))^2) (48 π^2 (f _ ϕ^(ó  ))^2 + (128 π^2 (-3 L _ 4^(r ) + L _ 5^(r ) + 12 L _ 6^(r ) - 4 L _ 8^(r )) - 3 log((m _ π^(ó  ))^2/μ^2) + log((m _ η^(ó  ))^2/μ^2)) (m _ π^(ó  ))^2 - (256 π^2 (3 L _ 4^(r ) + 2 (L _ 5^(r ) - 6 L _ 6^(r ) - 4 L _ 8^(r ))) + log((m _ K^(ó  ))^2/μ^2) + 4 log((m _ η^(ó  ))^2/μ^2)) (m _ K^(ó  ))^2)

$VeryVerbose = 2 ;

CheckF[z, "ChPT3P011o2.Fac"] ;

Using file name D:\\Program Files\\Wolfram Research\\Mathematica\\4.1\\AddOns\\Applications\\HighEnergyPhysics\\Phi\\Factors\\ChPT3P011o2.Fac

File does not exist, evaluating

Saving

$VeryVerbose = 0 ;

Converted by Mathematica  (July 10, 2003)