•Renormalization

zpion = CheckF[dum, "ChPT2P20o2.Fac"]

((384 π^2 L _ 4^( ) + 192 π^2 L _ 5^( ) - 32 π^2 λ - log((m _ π^(ó  ))^2/μ^2)) (m _ π^(ó  ))^2)/(24 π^2 (f _ π^(ó  ))^2) + 1

ff2 = melsimplified /. _SU2Delta -> 1

2 f _ π^(ó  ) !, _ 0^( )

amploop = ampinfinities // Simplify

-(5 (32 π^2 λ + log((m _ π^(ó  ))^2/μ^2)) (m _ π^(ó  ))^2 !, _ 0^( ))/(48 π^2 f _ π^(ó  ))

ampwf4 = amp4 /. _SU2Delta -> 1 // Simplify

(32 (2 L _ 6^( ) + L _ 8^( )) (m _ π^(ó  ))^2 !, _ 0^( ))/f _ π^(ó  )

amppf4 = ff2 ((3 - zpion)/2) // Simplify

f _ π^(ó  ) (2 - ((384 π^2 L _ 4^( ) + 192 π^2 L _ 5^( ) - 32 π^2 λ - log((m _ π^(ó  ))^2/μ^2)) (m _ π^(ó  ))^2)/(24 π^2 (f _ π^(ó  ))^2)) !, _ 0^( )

ff4 = amploop + ampwf4 + amppf4 // ExpandAll // FullSimplify

((32 π^2 (f _ π^(ó  ))^2 - (32 π^2 (8 L _ 4^( ) + 4 (L _ 5^( ) - 8 L _ 6^( ) - 4 L _ 8^( )) + λ) + log((m _ π^(ó  ))^2/μ^2)) (m _ π^(ó  ))^2) !, _ 0^( ))/(16 π^2 f _ π^(ó  ))

ff4 // Renormalize // Simplify

((32 π^2 (f _ π^(ó  ))^2 - (256 π^2 L _ 4^(r ) + 128 π^2 L _ 5^(r ) - 1024 π^2 L _ 6^(r ) - 512 π^2 L _ 8^(r ) + log((m _ π^(ó  ))^2/μ^2)) (m _ π^(ó  ))^2) !, _ 0^( ))/(16 π^2 f _ π^(ó  ))

z = ff4/ff2 // Simplify

(32 π^2 (f _ π^(ó  ))^2 - (32 π^2 (8 L _ 4^( ) + 4 (L _ 5^( ) - 4 (2 L _ 6^( ) + L _ 8^( ))) + λ) + log((m _ π^(ó  ))^2/μ^2)) (m _ π^(ó  ))^2)/(32 π^2 (f _ π^(ó  ))^2)

$VeryVerbose = 2 ;

CheckF[z, "ChPT2P00P20o2.Fac"] ;

Using file name D:\\Program Files\\Wolfram Research\\Mathematica\\4.1\\AddOns\\Applications\\HighEnergyPhysics\\Phi\\Factors\\ChPT2P00P20o2.Fac

File does not exist, evaluating

Saving

$VeryVerbose = 0 ;

Converted by Mathematica  (July 10, 2003)