•The Overscript[J, _] part of the loops

The Overscript[J, _] function expanded to first order in s:

Jl[s_, m12_, m22_, ___] = Normal[(Series[LeutwylerJBar[s, m12, m22, LeutwylerJBarEvaluation -> "subthreshold"], {s, 0, 1}] /. {Sqrt[x_^2] -> x, Sqrt[x_^2 * y_^2] -> x * y} // Simplify) /. {Sqrt[x_^2] -> x, Sqrt[x_^2 * y_^2] -> x * y} // Simplify]

(s (m12^2 + 2 m22 log(m22/m12) m12 - m22^2))/(32 (m12 - m22)^3 π^2)

Despite appearances, it is finite for m2=m1:

Limit[%, m12 -> m22]

s/(96 m22 π^2)

We eliminate the Overscript[J, _]'s with equal masses and no denominator:

LoopJsExp = loopJs2 /. LeutwylerJBar[tu : (t | u), m1_, m2_ ? ((Head[#] =!= Rule) &), ___Rule] -> Jll[tu, m1, m2] /. _LeutwylerJBar -> 0 // Simplify

1/(6912 t^2 u^2 π^2 (f _ ϕ^(ó  ))^4) (i c _ 2^( ) p _ 1^μ _ 1 µ _ μ _ 1(p _ 1) (4 π^2 Jll(t, (m _ K^(ó  ))^2, (m _ η^(ó  ))^2) (-80 (m _ π^(ó  ))^8 + 10 (18 (m _ K^(ó  ))^2 + 2 s - 25 t + 2 u) (m _ π^(ó  ))^6 + (-120 (m _ K^(ó  ))^4 + (-40 s + 1193 t - 40 u) (m _ K^(ó  ))^2 + t (35 s - 213 t + 55 u)) (m _ π^(ó  ))^4 - 2 (-10 (m _ K^(ó  ))^6 - 10 (s - 23 t + u) (m _ K^(ó  ))^4 + t (131 s + 84 t + 151 u) (m _ K^(ó  ))^2 - 3 t^2 (-3 s + 28 t + 17 u)) (m _ π^(ó  ))^2 + t (57 (m _ K^(ó  ))^6 + (47 s + 67 (3 t + u)) (m _ K^(ó  ))^4 - 3 t (-150 s + 131 t + 130 u) (m _ K^(ó  ))^2 + 9 t^2 (-13 s + 15 t + 7 u)) + 4 p _ 2^4 (5 (m _ π^(ó  ))^4 + 2 (3 t - 5 (m _ K^(ó  ))^2) (m _ π^(ó  ))^2 + 5 (m _ K^(ó  ))^4 + 9 t^2 - 51 t (m _ K^(ó  ))^2) - p _ 2^2 (-60 (m _ π^(ó  ))^6 + (140 (m _ K^(ó  ))^2 + 20 s - 121 t + 20 u) (m _ π^(ó  ))^4 + 2 (-50 (m _ K^(ó  ))^4 + (-20 s + 289 t - 20 u) (m _ K^(ó  ))^2 + 3 t (4 s - 7 t + 4 u)) (m _ π^(ó  ))^2 + 20 (m _ K^(ó  ))^6 + (20 s - 97 t + 20 u) (m _ K^(ó  ))^4 - 6 t (34 s + 41 t + 34 u) (m _ K^(ó  ))^2 + 9 t^2 (4 s + 7 t + 4 u))) u^2 - 36 π^2 Jll(t, (m _ π^(ó  ))^2, (m _ K^(ó  ))^2) (16 (m _ π^(ó  ))^8 - 2 (18 (m _ K^(ó  ))^2 + 2 s + 39 t + 2 u) (m _ π^(ó  ))^6 + (24 (m _ K^(ó  ))^4 + (8 s - 61 t + 8 u) (m _ K^(ó  ))^2 + t (s + 121 t - 3 u)) (m _ π^(ó  ))^4 - 2 (2 (m _ K^(ó  ))^6 + 2 (s - 37 t + u) (m _ K^(ó  ))^4 + t (-11 s + 92 t - 15 u) (m _ K^(ó  ))^2 + t^2 (23 s - 24 t + 19 u)) (m _ π^(ó  ))^2 + t (-21 (m _ K^(ó  ))^6 + (-19 s + 43 t - 23 u) (m _ K^(ó  ))^4 + t (22 s + 53 t + 30 u) (m _ K^(ó  ))^2 + t^2 (17 s - 75 t + 13 u)) + 4 p _ 2^4 (-(m _ π^(ó  ))^4 + (2 (m _ K^(ó  ))^2 - 4 t) (m _ π^(ó  ))^2 - (m _ K^(ó  ))^4 + t^2 + 5 t (m _ K^(ó  ))^2) + p _ 2^2 (-12 (m _ π^(ó  ))^6 + (28 (m _ K^(ó  ))^2 + 4 s + 19 t + 4 u) (m _ π^(ó  ))^4 + 2 (-10 (m _ K^(ó  ))^4 + (-4 s + 13 t - 4 u) (m _ K^(ó  ))^2 + t (8 s - t + 8 u)) (m _ π^(ó  ))^2 + 4 (m _ K^(ó  ))^6 + (4 s - 37 t + 4 u) (m _ K^(ó  ))^4 + 2 t (-10 s + t - 10 u) (m _ K^(ó  ))^2 + t^2 (-4 s + 11 t - 4 u))) u^2 + t (3 u (-4 (t + u) (m _ π^(ó  ))^6 + (t^2 + 106 u t + u^2 + 77 (t + u) (m _ K^(ó  ))^2 + s (t + u)) (m _ π^(ó  ))^4 - (19 (t + u) (m _ K^(ó  ))^4 + (19 t^2 + 16 u t + 19 u^2 + 19 s (t + u)) (m _ K^(ó  ))^2 - 2 t u (4 (t + u) - 215 s)) (m _ π^(ó  ))^2 + p _ 2^4 ((t + u) (m _ π^(ó  ))^2 - 19 (t + u) (m _ K^(ó  ))^2 + 6 t u) + 2 t u (81 s^2 - 3 (t + u) s + (101 s - 19 (t + u)) (m _ K^(ó  ))^2 + 6 t u) - p _ 2^2 (-3 (t + u) (m _ π^(ó  ))^4 + (t^2 - 64 u t + u^2 + 58 (t + u) (m _ K^(ó  ))^2 + s (t + u)) (m _ π^(ó  ))^2 - 19 (t + u) (m _ K^(ó  ))^4 - (19 t^2 + 32 u t + 19 u^2 + 19 s (t + u)) (m _ K^(ó  ))^2 + 6 t u (10 s + t + u))) + 4 t π^2 Jll(u, (m _ K^(ó  ))^2, (m _ η^(ó  ))^2) (-80 (m _ π^(ó  ))^8 + 10 (18 (m _ K^(ó  ))^2 + 2 s + 2 t - 25 u) (m _ π^(ó  ))^6 + (-120 (m _ K^(ó  ))^4 + (-40 s - 40 t + 1193 u) (m _ K^(ó  ))^2 + (35 s + 55 t - 213 u) u) (m _ π^(ó  ))^4 - 2 (-10 (m _ K^(ó  ))^6 - 10 (s + t - 23 u) (m _ K^(ó  ))^4 + u (131 s + 151 t + 84 u) (m _ K^(ó  ))^2 + 3 (3 s - 17 t - 28 u) u^2) (m _ π^(ó  ))^2 + u (57 (m _ K^(ó  ))^6 + (47 s + 67 (t + 3 u)) (m _ K^(ó  ))^4 + 3 (150 s - 130 t - 131 u) u (m _ K^(ó  ))^2 + 9 u^2 (-13 s + 7 t + 15 u)) + 4 p _ 2^4 (5 (m _ π^(ó  ))^4 + 2 (3 u - 5 (m _ K^(ó  ))^2) (m _ π^(ó  ))^2 + 5 (m _ K^(ó  ))^4 + 9 u^2 - 51 u (m _ K^(ó  ))^2) - p _ 2^2 (-60 (m _ π^(ó  ))^6 + (140 (m _ K^(ó  ))^2 + 20 s + 20 t - 121 u) (m _ π^(ó  ))^4 + 2 (-50 (m _ K^(ó  ))^4 + (-20 s - 20 t + 289 u) (m _ K^(ó  ))^2 + 3 (4 s + 4 t - 7 u) u) (m _ π^(ó  ))^2 + 20 (m _ K^(ó  ))^6 + (20 s + 20 t - 97 u) (m _ K^(ó  ))^4 - 6 u (34 s + 34 t + 41 u) (m _ K^(ó  ))^2 + 9 u^2 (4 s + 4 t + 7 u))) - 36 t π^2 Jll(u, (m _ π^(ó  ))^2, (m _ K^(ó  ))^2) (16 (m _ π^(ó  ))^8 - 2 (18 (m _ K^(ó  ))^2 + 2 s + 2 t + 39 u) (m _ π^(ó  ))^6 + (24 (m _ K^(ó  ))^4 + (8 s + 8 t - 61 u) (m _ K^(ó  ))^2 + u (s - 3 t + 121 u)) (m _ π^(ó  ))^4 - 2 (2 (m _ K^(ó  ))^6 + 2 (s + t - 37 u) (m _ K^(ó  ))^4 + u (-11 s - 15 t + 92 u) (m _ K^(ó  ))^2 + (23 s + 19 t - 24 u) u^2) (m _ π^(ó  ))^2 + u (-21 (m _ K^(ó  ))^6 + (-19 s - 23 t + 43 u) (m _ K^(ó  ))^4 + u (22 s + 30 t + 53 u) (m _ K^(ó  ))^2 + (17 s + 13 t - 75 u) u^2) + 4 p _ 2^4 (-(m _ π^(ó  ))^4 + (2 (m _ K^(ó  ))^2 - 4 u) (m _ π^(ó  ))^2 - (m _ K^(ó  ))^4 + u^2 + 5 u (m _ K^(ó  ))^2) + p _ 2^2 (-12 (m _ π^(ó  ))^6 + (28 (m _ K^(ó  ))^2 + 4 s + 4 t + 19 u) (m _ π^(ó  ))^4 + 2 (-10 (m _ K^(ó  ))^4 + (-4 s - 4 t + 13 u) (m _ K^(ó  ))^2 + (8 s + 8 t - u) u) (m _ π^(ó  ))^2 + 4 (m _ K^(ó  ))^6 + (4 s + 4 t - 37 u) (m _ K^(ó  ))^4 + 2 u (-10 s - 10 t + u) (m _ K^(ó  ))^2 + u^2 (-4 s - 4 t + 11 u))))))

We arrange to have symmetric expressions in t and u:

LoopJsExp1 = LoopJsExp /. Pair[_LorentzIndex, ___] -> Sequence[] /. {Jll[t, a___] * b_ :> Jll[t, a] * (b /. MandelstamU -> -MandelstamS - MandelstamT + Pair[Momentum[p2], Momentum[p2]] + ParticleMass[Kaon]^2 + 2 ParticleMass[Pion]^2), Jll[u, a___] * b_ :> Jll[u, a] * (b /. MandelstamT -> -MandelstamS - MandelstamU + ParticleMass[Kaon]^2 + Pair[Momentum[p2], Momentum[p2]] + 2 ParticleMass[Pion]^2)} /. cancelS /. kaonOnShell /. _RenormalizationState -> Sequence[] // Simplify

1/(3456 t^2 u^2 π^2 (f _ ϕ^(ó  ))^4) (i c _ 2^( ) (8 π^2 Jll(t, (m _ K^(ó  ))^2, (m _ η^(ó  ))^2) (-10 (m _ π^(ó  ))^8 + (30 (m _ K^(ó  ))^2 - 50 t) (m _ π^(ó  ))^6 + (-30 (m _ K^(ó  ))^4 + 186 t (m _ K^(ó  ))^2 + t (5 u - 71 t)) (m _ π^(ó  ))^4 - 2 (-5 (m _ K^(ó  ))^6 + 81 t (m _ K^(ó  ))^4 + t (5 u - 122 t) (m _ K^(ó  ))^2 + 3 t^2 (2 t - 5 u)) (m _ π^(ó  ))^2 + t (26 (m _ K^(ó  ))^6 + (151 t + 5 u) (m _ K^(ó  ))^4 - 30 t (8 t + 7 u) (m _ K^(ó  ))^2 + 9 t^2 (7 t + 5 u)) - 2 p _ 2^2 (-5 (m _ π^(ó  ))^6 + (15 (m _ K^(ó  ))^2 - 16 t) (m _ π^(ó  ))^4 + (-15 (m _ K^(ó  ))^4 + 62 t (m _ K^(ó  ))^2 + 3 t^2) (m _ π^(ó  ))^2 + 5 (m _ K^(ó  ))^6 - 46 t (m _ K^(ó  ))^4 + 18 t^3 - 57 t^2 (m _ K^(ó  ))^2)) u^2 + 72 π^2 Jll(t, (m _ π^(ó  ))^2, (m _ K^(ó  ))^2) (-2 (m _ π^(ó  ))^8 + 6 ((m _ K^(ó  ))^2 + 3 t) (m _ π^(ó  ))^6 + (-6 (m _ K^(ó  ))^4 + 6 t (m _ K^(ó  ))^2 + t (u - 7 t)) (m _ π^(ó  ))^4 - 2 (-(m _ K^(ó  ))^6 + 17 t (m _ K^(ó  ))^4 + t (u - 26 t) (m _ K^(ó  ))^2 + t^2 (16 t + u)) (m _ π^(ó  ))^2 + t (t - (m _ K^(ó  ))^2) (-10 (m _ K^(ó  ))^4 + (11 t - u) (m _ K^(ó  ))^2 + t (23 t + u)) - 2 p _ 2^2 (-(m _ π^(ó  ))^6 + 3 ((m _ K^(ó  ))^2 + 2 t) (m _ π^(ó  ))^4 + (-3 (m _ K^(ó  ))^4 + 4 t (m _ K^(ó  ))^2 - 9 t^2) (m _ π^(ó  ))^2 + (m _ K^(ó  ))^6 - 10 t (m _ K^(ó  ))^4 + 4 t^3 + 5 t^2 (m _ K^(ó  ))^2)) u^2 + t (3 u (-(t + u) (m _ π^(ó  ))^6 + (20 (t + u) (m _ K^(ó  ))^2 - 54 t u) (m _ π^(ó  ))^4 - (19 (t + u) (m _ K^(ó  ))^4 - 322 t u (m _ K^(ó  ))^2 + 111 t u (t + u)) (m _ π^(ó  ))^2 + 54 t u p _ 2^4 + t u (182 (m _ K^(ó  ))^4 - 285 (t + u) (m _ K^(ó  ))^2 + 84 t^2 + 84 u^2 + 174 t u) + p _ 2^2 ((t + u) (m _ π^(ó  ))^4 + (82 t u - 20 (t + u) (m _ K^(ó  ))^2) (m _ π^(ó  ))^2 + 19 (t + u) (m _ K^(ó  ))^4 + 230 t u (m _ K^(ó  ))^2 - 138 t u (t + u))) + 8 t π^2 Jll(u, (m _ K^(ó  ))^2, (m _ η^(ó  ))^2) (-10 (m _ π^(ó  ))^8 + (30 (m _ K^(ó  ))^2 - 50 u) (m _ π^(ó  ))^6 + (-30 (m _ K^(ó  ))^4 + 186 u (m _ K^(ó  ))^2 + (5 t - 71 u) u) (m _ π^(ó  ))^4 + 2 (5 (m _ K^(ó  ))^6 - 81 u (m _ K^(ó  ))^4 + u (122 u - 5 t) (m _ K^(ó  ))^2 + 3 (5 t - 2 u) u^2) (m _ π^(ó  ))^2 + u (26 (m _ K^(ó  ))^6 + (5 t + 151 u) (m _ K^(ó  ))^4 - 30 u (7 t + 8 u) (m _ K^(ó  ))^2 + 9 u^2 (5 t + 7 u)) - 2 p _ 2^2 (-5 (m _ π^(ó  ))^6 + (15 (m _ K^(ó  ))^2 - 16 u) (m _ π^(ó  ))^4 + (-15 (m _ K^(ó  ))^4 + 62 u (m _ K^(ó  ))^2 + 3 u^2) (m _ π^(ó  ))^2 + 5 (m _ K^(ó  ))^6 - 46 u (m _ K^(ó  ))^4 + 18 u^3 - 57 u^2 (m _ K^(ó  ))^2)) + 72 t π^2 Jll(u, (m _ π^(ó  ))^2, (m _ K^(ó  ))^2) (-2 (m _ π^(ó  ))^8 + 6 ((m _ K^(ó  ))^2 + 3 u) (m _ π^(ó  ))^6 + (-6 (m _ K^(ó  ))^4 + 6 u (m _ K^(ó  ))^2 + (t - 7 u) u) (m _ π^(ó  ))^4 - 2 (-(m _ K^(ó  ))^6 + 17 u (m _ K^(ó  ))^4 + (t - 26 u) u (m _ K^(ó  ))^2 + u^2 (t + 16 u)) (m _ π^(ó  ))^2 + u (u - (m _ K^(ó  ))^2) (-10 (m _ K^(ó  ))^4 - (t - 11 u) (m _ K^(ó  ))^2 + u (t + 23 u)) - 2 p _ 2^2 (-(m _ π^(ó  ))^6 + 3 ((m _ K^(ó  ))^2 + 2 u) (m _ π^(ó  ))^4 + (-3 (m _ K^(ó  ))^4 + 4 u (m _ K^(ó  ))^2 - 9 u^2) (m _ π^(ó  ))^2 + (m _ K^(ó  ))^6 - 10 u (m _ K^(ó  ))^4 + 4 u^3 + 5 u^2 (m _ K^(ó  ))^2)))))

The above expression contains Overscript[J, _] terms and polynomial terms, both of which are symmetric in u and t:

(LoopJsExp1) - (LoopJsExp1 /. {MandelstamU -> MandelstamT, MandelstamT -> MandelstamU, u -> t, t -> u}) // Expand

0

The numerator of the above expression. It must have an overall factor of t^2 u^2 in order to not have have unwanted poles.

probJ = LoopJsExp1 * MandelstamT^2 MandelstamU^2

1/(3456 π^2 (f _ ϕ^(ó  ))^4) (i c _ 2^( ) (8 π^2 Jll(t, (m _ K^(ó  ))^2, (m _ η^(ó  ))^2) (-10 (m _ π^(ó  ))^8 + (30 (m _ K^(ó  ))^2 - 50 t) (m _ π^(ó  ))^6 + (-30 (m _ K^(ó  ))^4 + 186 t (m _ K^(ó  ))^2 + t (5 u - 71 t)) (m _ π^(ó  ))^4 - 2 (-5 (m _ K^(ó  ))^6 + 81 t (m _ K^(ó  ))^4 + t (5 u - 122 t) (m _ K^(ó  ))^2 + 3 t^2 (2 t - 5 u)) (m _ π^(ó  ))^2 + t (26 (m _ K^(ó  ))^6 + (151 t + 5 u) (m _ K^(ó  ))^4 - 30 t (8 t + 7 u) (m _ K^(ó  ))^2 + 9 t^2 (7 t + 5 u)) - 2 p _ 2^2 (-5 (m _ π^(ó  ))^6 + (15 (m _ K^(ó  ))^2 - 16 t) (m _ π^(ó  ))^4 + (-15 (m _ K^(ó  ))^4 + 62 t (m _ K^(ó  ))^2 + 3 t^2) (m _ π^(ó  ))^2 + 5 (m _ K^(ó  ))^6 - 46 t (m _ K^(ó  ))^4 + 18 t^3 - 57 t^2 (m _ K^(ó  ))^2)) u^2 + 72 π^2 Jll(t, (m _ π^(ó  ))^2, (m _ K^(ó  ))^2) (-2 (m _ π^(ó  ))^8 + 6 ((m _ K^(ó  ))^2 + 3 t) (m _ π^(ó  ))^6 + (-6 (m _ K^(ó  ))^4 + 6 t (m _ K^(ó  ))^2 + t (u - 7 t)) (m _ π^(ó  ))^4 - 2 (-(m _ K^(ó  ))^6 + 17 t (m _ K^(ó  ))^4 + t (u - 26 t) (m _ K^(ó  ))^2 + t^2 (16 t + u)) (m _ π^(ó  ))^2 + t (t - (m _ K^(ó  ))^2) (-10 (m _ K^(ó  ))^4 + (11 t - u) (m _ K^(ó  ))^2 + t (23 t + u)) - 2 p _ 2^2 (-(m _ π^(ó  ))^6 + 3 ((m _ K^(ó  ))^2 + 2 t) (m _ π^(ó  ))^4 + (-3 (m _ K^(ó  ))^4 + 4 t (m _ K^(ó  ))^2 - 9 t^2) (m _ π^(ó  ))^2 + (m _ K^(ó  ))^6 - 10 t (m _ K^(ó  ))^4 + 4 t^3 + 5 t^2 (m _ K^(ó  ))^2)) u^2 + t (3 u (-(t + u) (m _ π^(ó  ))^6 + (20 (t + u) (m _ K^(ó  ))^2 - 54 t u) (m _ π^(ó  ))^4 - (19 (t + u) (m _ K^(ó  ))^4 - 322 t u (m _ K^(ó  ))^2 + 111 t u (t + u)) (m _ π^(ó  ))^2 + 54 t u p _ 2^4 + t u (182 (m _ K^(ó  ))^4 - 285 (t + u) (m _ K^(ó  ))^2 + 84 t^2 + 84 u^2 + 174 t u) + p _ 2^2 ((t + u) (m _ π^(ó  ))^4 + (82 t u - 20 (t + u) (m _ K^(ó  ))^2) (m _ π^(ó  ))^2 + 19 (t + u) (m _ K^(ó  ))^4 + 230 t u (m _ K^(ó  ))^2 - 138 t u (t + u))) + 8 t π^2 Jll(u, (m _ K^(ó  ))^2, (m _ η^(ó  ))^2) (-10 (m _ π^(ó  ))^8 + (30 (m _ K^(ó  ))^2 - 50 u) (m _ π^(ó  ))^6 + (-30 (m _ K^(ó  ))^4 + 186 u (m _ K^(ó  ))^2 + (5 t - 71 u) u) (m _ π^(ó  ))^4 + 2 (5 (m _ K^(ó  ))^6 - 81 u (m _ K^(ó  ))^4 + u (122 u - 5 t) (m _ K^(ó  ))^2 + 3 (5 t - 2 u) u^2) (m _ π^(ó  ))^2 + u (26 (m _ K^(ó  ))^6 + (5 t + 151 u) (m _ K^(ó  ))^4 - 30 u (7 t + 8 u) (m _ K^(ó  ))^2 + 9 u^2 (5 t + 7 u)) - 2 p _ 2^2 (-5 (m _ π^(ó  ))^6 + (15 (m _ K^(ó  ))^2 - 16 u) (m _ π^(ó  ))^4 + (-15 (m _ K^(ó  ))^4 + 62 u (m _ K^(ó  ))^2 + 3 u^2) (m _ π^(ó  ))^2 + 5 (m _ K^(ó  ))^6 - 46 u (m _ K^(ó  ))^4 + 18 u^3 - 57 u^2 (m _ K^(ó  ))^2)) + 72 t π^2 Jll(u, (m _ π^(ó  ))^2, (m _ K^(ó  ))^2) (-2 (m _ π^(ó  ))^8 + 6 ((m _ K^(ó  ))^2 + 3 u) (m _ π^(ó  ))^6 + (-6 (m _ K^(ó  ))^4 + 6 u (m _ K^(ó  ))^2 + (t - 7 u) u) (m _ π^(ó  ))^4 - 2 (-(m _ K^(ó  ))^6 + 17 u (m _ K^(ó  ))^4 + (t - 26 u) u (m _ K^(ó  ))^2 + u^2 (t + 16 u)) (m _ π^(ó  ))^2 + u (u - (m _ K^(ó  ))^2) (-10 (m _ K^(ó  ))^4 - (t - 11 u) (m _ K^(ó  ))^2 + u (t + 23 u)) - 2 p _ 2^2 (-(m _ π^(ó  ))^6 + 3 ((m _ K^(ó  ))^2 + 2 u) (m _ π^(ó  ))^4 + (-3 (m _ K^(ó  ))^4 + 4 u (m _ K^(ó  ))^2 - 9 u^2) (m _ π^(ó  ))^2 + (m _ K^(ó  ))^6 - 10 u (m _ K^(ó  ))^4 + 4 u^3 + 5 u^2 (m _ K^(ó  ))^2)))))

Using the expansion of the Overscript[J, _]'s we see that this is indeed the case for the polynomial part:

probJ /. {MandelstamS -> s, MandelstamT -> t, MandelstamU -> u} /. u -> -s - t + ParticleMass[Kaon]^2 + Pair[Momentum[p2], Momentum[p2]] + 2 ParticleMass[Pion]^2 /. Jll -> Jl /. _Log -> 0 /. gellmannOkubo // Simplify

1/(2304 π^2 (f _ ϕ^(ó  ))^4 ((m _ π^(ó  ))^2 - (m _ K^(ó  ))^2)^2) (i t^2 c _ 2^( ) (2 (m _ π^(ó  ))^2 + (m _ K^(ó  ))^2 - s - t + p _ 2^2)^2 (128 (m _ π^(ó  ))^8 - 6 (-111 (m _ K^(ó  ))^2 + 57 s + 5 p _ 2^2) (m _ π^(ó  ))^6 + 6 (416 (m _ K^(ó  ))^4 - 2 (137 s + 147 t) (m _ K^(ó  ))^2 + 5 p _ 2^4 + 2 s (12 s + 5 t) + p _ 2^2 (377 (m _ K^(ó  ))^2 - 11 s - 14 t)) (m _ π^(ó  ))^4 - (1271 (m _ K^(ó  ))^6 + 15 (91 s + 106 t) (m _ K^(ó  ))^4 - 9 (135 s^2 + 236 t s + 98 t^2) (m _ K^(ó  ))^2 - 9 p _ 2^6 + 3 s (s^2 + 10 t s + 10 t^2) + 21 p _ 2^4 (-45 (m _ K^(ó  ))^2 + s + 2 t) - 3 p _ 2^2 (-53 (m _ K^(ó  ))^4 - 264 (3 s + 2 t) (m _ K^(ó  ))^2 + 5 s^2 + 14 t^2 + 24 s t)) (m _ π^(ó  ))^2 + 3 (m _ K^(ó  ))^2 (29 (m _ K^(ó  ))^6 + (223 s - 118 t) (m _ K^(ó  ))^4 + (25 s^2 + 320 t s + 118 t^2) (m _ K^(ó  ))^2 + 39 p _ 2^6 - s (85 s^2 + 202 t s + 202 t^2) + p _ 2^4 (5 (m _ K^(ó  ))^2 - 163 s - 110 t) + p _ 2^2 (155 (m _ K^(ó  ))^4 + 6 (s - 38 t) (m _ K^(ó  ))^2 + 209 s^2 + 110 t^2 + 312 s t))))

This is the potentially problematic logarithmic piece coming from the expansion of the Overscript[J, _]'s:

tmp1 = ((((probJ /. {MandelstamS -> s, MandelstamT -> t, MandelstamU -> u} /. Jll -> Jl) - (probJ /. {MandelstamS -> s, MandelstamT -> t, MandelstamU -> u} /. Jll -> Jl /. _Log -> 0)) /. gellmannOkubo // Expand) /. (t)^(_ ? ((# > 1) &)) (u)^(_ ? ((# > 1) &)) -> 0 /. cancelLogs // Simplify) /. cancelLogs // Simplify

-(i t u (t + u) c _ 2^( ) (p _ 2^2 - (m _ π^(ó  ))^2) (m _ K^(ó  ))^2 ((log((m _ π^(ó  ))^2/μ^2) + 5 log(4/3 - (m _ π^(ó  ))^2/(3 (m _ K^(ó  ))^2)) - log((m _ K^(ó  ))^2/μ^2)) (m _ π^(ó  ))^2 - 20 log(4/3 - (m _ π^(ó  ))^2/(3 (m _ K^(ó  ))^2)) (m _ K^(ó  ))^2))/(384 π^2 (f _ ϕ^(ó  ))^4)

Converted by Mathematica  (July 10, 2003)