•Check of scale independence

rlogs = Simplify[logsFull0 /. Log[ParticleMass[Vector[1], ___]^2/ScaleMu^2] -> 0 /. ParticleMass[Vector[1], ___]^2 -> 0 /. logRule1 /. logRule // ChargeEliminate // manred[MandelstamU] // Expand]

1/(48 π^2 C^(r ) (f _ π^(ó  ))^4) (log(1/μ^2) (12 (m _ π^+^(ó  r ))^2 ((m _ π^+^(ó  r ))^2 - (m _ π^0^(ó  r ))^2) (f _ π^(ó  ))^4 + C^(r ) (16 (m _ π^+^(ó  r ))^4 - 10 (m _ π^0^(ó  r ))^2 (m _ π^+^(ó  r ))^2 + (m _ π^0^(ó  r ))^2 (5 (m _ π^0^(ó  r ))^2 - 6 (s + t)))))

slogs = Simplify[(cts0 /. scaleRule) - (cts0 /. scaleRule /. _Log -> 0) /. logRule1 /. logRule // ChargeEliminate // manred[MandelstamU] // Expand]

1/(48 π^2 C^(r ) (f _ π^(ó  ))^4) (log(1/μ^2) (12 (m _ π^+^(ó  r ))^2 ((m _ π^0^(ó  r ))^2 - (m _ π^+^(ó  r ))^2) (f _ π^(ó  ))^4 + C^(r ) (-16 (m _ π^+^(ó  r ))^4 + 10 (m _ π^0^(ó  r ))^2 (m _ π^+^(ó  r ))^2 + (m _ π^0^(ó  r ))^2 (6 (s + t) - 5 (m _ π^0^(ó  r ))^2))))

slogs + rlogs // ChargeEliminate // Simplify

0

rlogs = Simplify[logsFull1 /. Log[ParticleMass[Vector[1], ___]^2/ScaleMu^2] -> 0 /. ParticleMass[Vector[1], ___]^2 -> 0 /. logRule1 /. logRule // ChargeEliminate // manred[MandelstamU] // Expand]

-1/(96 π^2 (C^(r ))^2 (f _ π^(ó  ))^4) (log(1/μ^2) (6 ((m _ π^+^(ó  r ))^2 - (m _ π^0^(ó  r ))^2)^2 (f _ π^(ó  ))^8 + 3 C^(r ) ((m _ π^+^(ó  r ))^2 - (m _ π^0^(ó  r ))^2) (32 (m _ π^+^(ó  r ))^2 - 3 (4 (m _ π^0^(ó  r ))^2 + s + t)) (f _ π^(ó  ))^4 + 4 (C^(r ))^2 (20 (m _ π^+^(ó  r ))^4 + (-29 (m _ π^0^(ó  r ))^2 + s + t) (m _ π^+^(ó  r ))^2 + 19 (m _ π^0^(ó  r ))^4 - 9 (s + t) (m _ π^0^(ó  r ))^2 + 2 (s^2 + t s + t^2))))

slogs = Simplify[(cts1 /. scaleRule) - (cts1 /. scaleRule /. _Log -> 0) /. logRule1 /. logRule // ChargeEliminate // manred[MandelstamU] // Expand]

1/(96 π^2 (C^(r ))^2 (f _ π^(ó  ))^4) (log(1/μ^2) (18 ((m _ π^+^(ó  r ))^2 - (m _ π^0^(ó  r ))^2)^2 (f _ π^(ó  ))^8 + 3 C^(r ) ((m _ π^+^(ó  r ))^2 - (m _ π^0^(ó  r ))^2) (32 (m _ π^+^(ó  r ))^2 - 3 (4 (m _ π^0^(ó  r ))^2 + s + t)) (f _ π^(ó  ))^4 + 4 (C^(r ))^2 (20 (m _ π^+^(ó  r ))^4 + (-29 (m _ π^0^(ó  r ))^2 + s + t) (m _ π^+^(ó  r ))^2 + 19 (m _ π^0^(ó  r ))^4 - 9 (s + t) (m _ π^0^(ó  r ))^2 + 2 (s^2 + t s + t^2))))

slogs + rlogs // ChargeEliminate // Simplify

((f _ π^(ó  ))^4 log(1/μ^2) ((m _ π^+^(ó  r ))^2 - (m _ π^0^(ó  r ))^2)^2)/(8 π^2 (C^(r ))^2)

Converted by Mathematica  (July 10, 2003)