•L A T E X output

low = DiscardOrders[ampfinalren /. {CouplingConstant[_[4], ___] -> 0, _Log -> 0, _LeutwylerJBar -> 0}, PerturbationOrder -> 2] // Simplify

((t - (m _ π^(ó  r ))^2) δ _ (i _ 1 i _ 4)^(2) δ _ (i _ 2 i _ 3)^(2) + (u - (m _ π^(ó  r ))^2) δ _ (i _ 1 i _ 3)^(2) δ _ (i _ 2 i _ 4)^(2) + (s - (m _ π^(ó  r ))^2) δ _ (i _ 1 i _ 2)^(2) δ _ (i _ 3 i _ 4)^(2))/(f _ π^(ó  r ))^2

poly = ampfinalren - low /. {CouplingConstant[_[4], ___] -> 0, _Log -> 0, _LeutwylerJBar -> 0} // FullSimplify

-1/(288 π^2 (f _ π^(ó  r ))^4) ((-21 (m _ π^(ó  r ))^4 + 8 t (m _ π^(ó  r ))^2 + 3 s^2 + 10 t^2 + 3 u^2 - 4 s u) δ _ (i _ 1 i _ 4)^(2) δ _ (i _ 2 i _ 3)^(2) + (-21 (m _ π^(ó  r ))^4 + 8 u (m _ π^(ó  r ))^2 + 3 s^2 + 3 t^2 + 10 u^2 - 4 s t) δ _ (i _ 1 i _ 3)^(2) δ _ (i _ 2 i _ 4)^(2) + (-21 (m _ π^(ó  r ))^4 + 8 s (m _ π^(ó  r ))^2 + 10 s^2 + 3 t^2 + 3 u^2 - 4 t u) δ _ (i _ 1 i _ 2)^(2) δ _ (i _ 3 i _ 4)^(2))

cts = FullSimplify /@ Collect[ampfinalren - (ampfinalren /. {CouplingConstant[_[4], ___] -> 0}), _SU2Delta]

1/(f _ π^(ó  r ))^4 (4 (4 (L _ 3^(r ) - 2 L _ 4^(r ) - L _ 5^(r ) + 2 L _ 6^(r ) + L _ 8^(r )) (m _ π^(ó  r ))^4 - 2 t (2 L _ 3^(r ) - 2 L _ 4^(r ) - L _ 5^(r )) (m _ π^(ó  r ))^2 + 2 L _ 1^(r ) (t - 2 (m _ π^(ó  r ))^2)^2 + t^2 L _ 3^(r ) + L _ 2^(r ) (8 (m _ π^(ó  r ))^4 - 4 t (m _ π^(ó  r ))^2 + t^2 - 2 s u)) δ _ (i _ 1 i _ 4)^(2) δ _ (i _ 2 i _ 3)^(2)) + 1/(f _ π^(ó  r ))^4 (4 (4 (2 L _ 2^(r ) + L _ 3^(r ) - 2 L _ 4^(r ) - L _ 5^(r ) + 2 L _ 6^(r ) + L _ 8^(r )) (m _ π^(ó  r ))^4 - 2 u (2 (L _ 2^(r ) + L _ 3^(r ) - L _ 4^(r )) - L _ 5^(r )) (m _ π^(ó  r ))^2 + 2 L _ 1^(r ) (u - 2 (m _ π^(ó  r ))^2)^2 - 2 s t L _ 2^(r ) + u^2 (L _ 2^(r ) + L _ 3^(r ))) δ _ (i _ 1 i _ 3)^(2) δ _ (i _ 2 i _ 4)^(2)) + 1/(f _ π^(ó  r ))^4 (4 (4 (L _ 3^(r ) - 2 L _ 4^(r ) - L _ 5^(r ) + 2 L _ 6^(r ) + L _ 8^(r )) (m _ π^(ó  r ))^4 - 2 s (2 L _ 3^(r ) - 2 L _ 4^(r ) - L _ 5^(r )) (m _ π^(ó  r ))^2 + 2 L _ 1^(r ) (s - 2 (m _ π^(ó  r ))^2)^2 + s^2 L _ 3^(r ) + L _ 2^(r ) (8 (m _ π^(ó  r ))^4 - 4 s (m _ π^(ó  r ))^2 + s^2 - 2 t u)) δ _ (i _ 1 i _ 2)^(2) δ _ (i _ 3 i _ 4)^(2))

jbars = ampfinalren - (ampfinalren /. {_LeutwylerJBar -> 0}) // FullSimplify

1/(6 (f _ π^(ó  r ))^4) (-Overscript[J, _] _ (m _ π^(ó  r ))^2(u) ((-2 (m _ π^(ó  r ))^4 + (-3 s + t + 3 u) (m _ π^(ó  r ))^2 + (s - u) u) δ _ (i _ 1 i _ 4)^(2) δ _ (i _ 2 i _ 3)^(2) + 3 ((m _ π^(ó  r ))^4 - u^2) δ _ (i _ 1 i _ 3)^(2) δ _ (i _ 2 i _ 4)^(2) + (-2 (m _ π^(ó  r ))^4 + (s - 3 t + 3 u) (m _ π^(ó  r ))^2 + (t - u) u) δ _ (i _ 1 i _ 2)^(2) δ _ (i _ 3 i _ 4)^(2)) + Overscript[J, _] _ (m _ π^(ó  r ))^2(s) ((2 (m _ π^(ó  r ))^4 - (3 s + t - 3 u) (m _ π^(ó  r ))^2 + s (s - u)) δ _ (i _ 1 i _ 4)^(2) δ _ (i _ 2 i _ 3)^(2) + (2 (m _ π^(ó  r ))^4 - (3 s - 3 t + u) (m _ π^(ó  r ))^2 + s (s - t)) δ _ (i _ 1 i _ 3)^(2) δ _ (i _ 2 i _ 4)^(2) + 3 (s^2 - (m _ π^(ó  r ))^4) δ _ (i _ 1 i _ 2)^(2) δ _ (i _ 3 i _ 4)^(2)) + Overscript[J, _] _ (m _ π^(ó  r ))^2(t) (3 (t^2 - (m _ π^(ó  r ))^4) δ _ (i _ 1 i _ 4)^(2) δ _ (i _ 2 i _ 3)^(2) + (2 (m _ π^(ó  r ))^4 - (-3 s + 3 t + u) (m _ π^(ó  r ))^2 + t (t - s)) δ _ (i _ 1 i _ 3)^(2) δ _ (i _ 2 i _ 4)^(2) + (2 (m _ π^(ó  r ))^4 - (s + 3 t - 3 u) (m _ π^(ó  r ))^2 + t (t - u)) δ _ (i _ 1 i _ 2)^(2) δ _ (i _ 3 i _ 4)^(2)))

logs = ampfinalren - (ampfinalren /. {_Log -> 0}) // Simplify

-1/(96 π^2 (f _ π^(ó  r ))^4) (log((m _ π^(ó  r ))^2/μ^2) ((-7 (m _ π^(ó  r ))^4 + 4 t (m _ π^(ó  r ))^2 + s^2 + 3 t^2 + u^2 - 2 s u) δ _ (i _ 1 i _ 4)^(2) δ _ (i _ 2 i _ 3)^(2) + (-7 (m _ π^(ó  r ))^4 + 4 u (m _ π^(ó  r ))^2 + s^2 + t^2 + 3 u^2 - 2 s t) δ _ (i _ 1 i _ 3)^(2) δ _ (i _ 2 i _ 4)^(2) + (-7 (m _ π^(ó  r ))^4 + 4 s (m _ π^(ó  r ))^2 + 3 s^2 + (t - u)^2) δ _ (i _ 1 i _ 2)^(2) δ _ (i _ 3 i _ 4)^(2)))

low /. {i1 -> 1, i2 -> 1, i3 -> 2, i4 -> 2} // FullSimplify // PhiToLaTeX

(-m_{\rm \pi}^2 + s)/f^2

poly /. {i1 -> 1, i2 -> 1, i3 -> 2, i4 -> 2} // FullSimplify // PhiToLaTeX

-(-21 m_{\rm \pi}^4 + 8 m_{\rm \pi}^2 s + 10 s^2 + 3 t^2 - 4 t u + 3 u^2)/(288 f^4 \\pi^2)

cts /. {i1 -> 1, i2 -> 1, i3 -> 2, i4 -> 2} // FullSimplify // PhiToLaTeX

(4 (4 (L_{3} - 2 L_{4} - L_{5} + 2 L_{6} + L_{8}) m_{\rm \pi}^4 - 2 (2 L_{3} - 2 L_{4}
- L_{5}) m_{\rm \pi}^2 s + L_{3} s^2 + 2 L_{1} (-2 m_{\rm \pi}^2 + s)^2 + L_{2} (8
m_{\rm \pi}^4 - 4 m_{\rm \pi}^2 s + s^2 - 2 t u)))/f^4

logs /. {i1 -> 1, i2 -> 1, i3 -> 2, i4 -> 2} // FullSimplify // PhiToLaTeX

-((-7 m_{\rm \pi}^4 + 4 m_{\rm \pi}^2 s + 3 s^2 + (t - u)^2) \log(m_{\rm \\pi}^2/\mu^2))/ (96 f^4 \pi^2)

jbars /. {i1 -> 1, i2 -> 1, i3 -> 2, i4 -> 2} // FullSimplify // PhiToLaTeX

(3 (-m_{\rm \pi}^4 + s^2) \overline{J}(s, m_{\rm \pi}^2) + (2 m_{\rm \pi}^4 - m_{\rm \\pi}^2 (s + 3 t - 3 u) + t (t - u)) \overline{J}(t, m_{\rm \pi}^2) + (2 m_{\rm \pi}^4
+ u (-t + u) - m_{\rm \pi}^2 (s - 3 t + 3 u)) \overline{J}(u, m_{\rm \pi}^2))/(6 f^4)

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Converted by Mathematica  (July 10, 2003)