•Loading and reducing the isospin amplitudes

result = 1/4 CheckF[dum, ("PiPiEMResult" <> "1111"), NoSave -> True, ForceSave -> False] + 1/4 CheckF[dum, ("PiPiEMResult" <> "1122"), NoSave -> True, ForceSave -> False] - 1/4 CheckF[{dum}, ("PiPiEMResult" <> "1212"), NoSave -> True, ForceSave -> False] + 1/4 CheckF[dum, ("PiPiEMResult" <> "1221"), NoSave -> True, ForceSave -> False] + 1/4 CheckF[dum, ("PiPiEMResult" <> "2112"), NoSave -> True, ForceSave -> False] - 1/4 CheckF[dum, ("PiPiEMResult" <> "2121"), NoSave -> True, ForceSave -> False] + 1/4 CheckF[dum, ("PiPiEMResult" <> "2211"), NoSave -> True, ForceSave -> False] + 1/4 CheckF[dum, ("PiPiEMResult" <> "2222"), NoSave -> True, ForceSave -> False] ;

count = 0 ; result1 = (++ count ; WriteString["stdout", count] ; Simplify (* [# /. If[count =!= 1, ren4rule, {}]]) & *) /@ result ;

123456

LeafCount /@ result1

{152, 4413, 677, 483, 415, 4781}

This result is s-t but not t-u crossing symmetric.

manred[MandelstamU][result1] - manred[MandelstamU][result1] /. {MandelstamS -> MandelstamT, MandelstamT -> MandelstamS} // PaVeOrder // Simplify

{0, 0, 0, 0, 0, 0}

cdtermsFull = Simplify /@ (Simplify /@ Collect[result1[[2]] // ChargedNeutralMassesCancel, {_CouplingConstant, _C0, _D0}]) // Simplify // manred[None] // PaVeOrder // Simplify ;

cdtermsFull1 = manred[MandelstamU][cdtermsFull] // Simplify // manred[None] // Simplify ;

cdtermsFull12 = Simplify /@ Collect[Simplify /@ Collect[Expand[cdtermsFull1], {_C0, _D0}], {_CouplingConstant}] ;

cTerms = FullSimplify /@ Collect[cdtermsFull12 /. _D0 -> 0 // Expand, _C0]

(C _ 0 ( s , (m _ π^+^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 , (m _ γ^(ó  r ))^2 , (m _ γ^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 ) (s - 2 (m _ π^+^(ó  r ))^2) (e^( ))^4)/(2 π^2) + (C _ 0 ( t , (m _ π^+^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 , (m _ γ^(ó  r ))^2 , (m _ γ^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 ) (t - 2 (m _ π^+^(ó  r ))^2) (e^( ))^4)/(2 π^2) - 1/(16 π^2 C^(r ) (f _ π^(ó  ))^2) (C _ 0 ( u , (m _ π^+^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 , (m _ γ^(ó  r ))^2 ) (u - 2 (m _ π^+^(ó  r ))^2) (2 C^(r ) (-4 (e^( ))^2 (f _ π^(ó  ))^2 - 4 (m _ π^+^(ó  r ))^2 + (m _ π^0^(ó  r ))^2 + 2 u) (e^( ))^2 + (f _ π^(ó  ))^2 (-4 (m _ π^+^(ó  r ))^4 + 7 (m _ π^0^(ó  r ))^2 (m _ π^+^(ó  r ))^2 - 3 (m _ π^0^(ó  r ))^4))) + 1/(16 π^2 C^(r ) (f _ π^(ó  ))^2) (C _ 0 ( s , (m _ π^+^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 , (m _ γ^(ó  r ))^2 ) (s - 2 (m _ π^+^(ó  r ))^2) (2 C^(r ) (2 (e^( ))^2 (f _ π^(ó  ))^2 - 4 (m _ π^+^(ó  r ))^2 + (m _ π^0^(ó  r ))^2 + 2 u) (e^( ))^2 + (f _ π^(ó  ))^2 (-4 (m _ π^+^(ó  r ))^4 + 7 (m _ π^0^(ó  r ))^2 (m _ π^+^(ó  r ))^2 - 3 (m _ π^0^(ó  r ))^4))) + 1/(16 π^2 C^(r ) (f _ π^(ó  ))^2) (C _ 0 ( t , (m _ π^+^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 , (m _ γ^(ó  r ))^2 ) (t - 2 (m _ π^+^(ó  r ))^2) (2 C^(r ) (2 (e^( ))^2 (f _ π^(ó  ))^2 - 4 (m _ π^+^(ó  r ))^2 + (m _ π^0^(ó  r ))^2 + 2 u) (e^( ))^2 + (f _ π^(ó  ))^2 (-4 (m _ π^+^(ó  r ))^4 + 7 (m _ π^0^(ó  r ))^2 (m _ π^+^(ó  r ))^2 - 3 (m _ π^0^(ó  r ))^4)))

dTerms = cdtermsFull12 /. _C0 -> 0 // FullSimplify

1/(4 π^2) ((e^( ))^4 (D _ 0 ( s , (m _ π^+^(ó  r ))^2 , t , (m _ π^+^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 , (m _ γ^(ó  r ))^2 , (m _ γ^(ó  r ))^2 ) (s - 2 (m _ π^+^(ó  r ))^2)^2 + D _ 0 ( s , (m _ π^+^(ó  r ))^2 , t , (m _ π^+^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 , (m _ γ^(ó  r ))^2 , (m _ γ^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 ) (t - 2 (m _ π^+^(ó  r ))^2)^2 + (D _ 0 ( s , (m _ π^+^(ó  r ))^2 , u , (m _ π^+^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 , (m _ γ^(ó  r ))^2 , (m _ γ^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 ) + D _ 0 ( t , (m _ π^+^(ó  r ))^2 , u , (m _ π^+^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 , (m _ γ^(ó  r ))^2 , (m _ γ^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 , (m _ π^+^(ó  r ))^2 )) (u - 2 (m _ π^+^(ó  r ))^2)^2))

nonCDterms4CTsFull = (Simplify /@ (Simplify /@ Collect[result1[[3]] // ChargedNeutralMassesCancel, {_CouplingConstant}]) // manred[MandelstamU] // Simplify) // manred[MandelstamU] // FullSimplify // manred[MandelstamU] // FullSimplify ;

nonCDterms4PolysFull = result1[[4]] // manred[MandelstamU] // Simplify // ChargedNeutralMassesCancel // manred[MandelstamU] // Simplify ;

$ExpansionQuantities = Union[$ExpansionQuantities, {ParticleMass[PionPlus | PionZero, a___]}] ;

lowestOrder = ((result1[[1]] // manred[MandelstamU]) // Expand // Simplify) // manred[MandelstamU] // FullSimplify // manred[MandelstamU] // FullSimplify

-1/(3 s t u (f _ π^(ó  ))^4) ((f _ π^(ó  ))^2 (s t u (2 (m _ π^+^(ó  r ))^2 - 2 (m _ π^0^(ó  ))^2 - 3 (m _ π^(1 r ))^2 - 3 (m _ π^(2 r ))^2 + 3 u) - 6 (e^( ))^2 (f _ π^(ó  ))^2 (8 ((m _ π^(1 r ))^2 + (m _ π^(2 r ))^2) (m _ π^+^(ó  r ))^4 - 2 (2 s^2 + 3 t s + 2 t^2 + 2 (-(m _ π^(1 r ))^2 - (m _ π^(2 r ))^2 + u) ((m _ π^(1 r ))^2 + (m _ π^(2 r ))^2)) (m _ π^+^(ó  r ))^2 + (s^2 + t s + t^2) ((m _ π^(1 r ))^2 + (m _ π^(2 r ))^2 - u))) - 16 s t u C^( ) (e^( ))^2)

lowestOrder1 = lowestOrder // ChargeEliminate // Simplify // ChargedNeutralMassesCancel // FullSimplify

-1/(s t u (f _ π^(ó  ))^2) (2 (f _ π^(ó  ))^2 (-8 ((m _ π^(1 r ))^2 + (m _ π^(2 r ))^2) (m _ π^+^(ó  r ))^4 + 2 (2 s^2 + 3 t s + 2 t^2 + 2 (-(m _ π^(1 r ))^2 - (m _ π^(2 r ))^2 + u) ((m _ π^(1 r ))^2 + (m _ π^(2 r ))^2)) (m _ π^+^(ó  r ))^2 + (s^2 + t s + t^2) (-(m _ π^(1 r ))^2 - (m _ π^(2 r ))^2 + u)) (e^( ))^2 - (4 s t u C^(r ) (e^( ))^2)/(f _ π^(ó  ))^2 + s t u (-(m _ π^(1 r ))^2 - (m _ π^(2 r ))^2 + u))

lowestOrder1 /. CouplingConstant[QED[_], ___] -> 0 // manred[MandelstamU] // ChargedMassesEliminate // Simplify

lowestOrder1

low4 = (DiscardOrders[(lowestOrder // CEliminate // MassRenormalize) (2 ffacStrong - 1), PerturbationOrder -> 4] // Simplify // ChargedNeutralMassesCancel) - lowestOrder1 // Expand // Simplify ;

poly0 = low4 /. {CouplingConstant[_[4], ___] -> 0, _Log -> 0, _LeutwylerJBar -> 0} // FullSimplify

-(2 (e^( ))^2 (m _ π^+^(ó  r ))^2)/(3 π^2 (f _ π^(ó  ))^2)

poly1 = nonCDterms4PolysFull // ChargedNeutralMassesCancel // CEliminate // manred[MandelstamU] // FullSimplify // manred[MandelstamU] // FullSimplify // manred[MandelstamU] // FullSimplify

-(-360 (e^( ))^4 (s - 4 (m _ π^+^(ó  r ))^2) (t - 4 (m _ π^+^(ó  r ))^2) (f _ π^(ó  ))^4 + 18 (e^( ))^2 (-4 (-176 (m _ π^+^(ó  r ))^4 + 52 u (m _ π^+^(ó  r ))^2 + 11 s^2 + 11 t^2 + 17 s t) (m _ π^+^(ó  r ))^2 + 12 (s - 4 (m _ π^+^(ó  r ))^2) (4 (m _ π^+^(ó  r ))^2 - t) (m _ π^0^(ó  r ))^2 - 15 s t u) (f _ π^(ó  ))^2 + (s - 4 (m _ π^+^(ó  r ))^2) (4 (m _ π^+^(ó  r ))^2 - t) (280 (m _ π^+^(ó  r ))^4 - 2 (324 (m _ π^0^(ó  r ))^2 + 17 u) (m _ π^+^(ó  r ))^2 + 198 (m _ π^0^(ó  r ))^4 + 23 s^2 + 23 t^2 + 90 u (m _ π^0^(ó  r ))^2 + 20 s t))/(288 π^2 (f _ π^(ó  ))^4 (s - 4 (m _ π^+^(ó  r ))^2) (4 (m _ π^+^(ó  r ))^2 - t))

poly = poly0 + poly1 // FullSimplify // manred[MandelstamU] // FullSimplify

-1/(288 π^2 (f _ π^(ó  ))^4) (360 (e^( ))^4 (f _ π^(ó  ))^4 + 1/((s - 4 (m _ π^+^(ó  r ))^2) (4 (m _ π^+^(ó  r ))^2 - t)) (6 (e^( ))^2 (-4 (-528 (m _ π^+^(ó  r ))^4 + 188 u (m _ π^+^(ó  r ))^2 + 33 s^2 + 33 t^2 + 59 s t) (m _ π^+^(ó  r ))^2 + 36 (s - 4 (m _ π^+^(ó  r ))^2) (4 (m _ π^+^(ó  r ))^2 - t) (m _ π^0^(ó  r ))^2 - 45 s t u) (f _ π^(ó  ))^2) + 280 (m _ π^+^(ó  r ))^4 + 198 (m _ π^0^(ó  r ))^4 + 23 s^2 + 23 t^2 + 90 u (m _ π^0^(ó  r ))^2 + 20 s t - 2 (m _ π^+^(ó  r ))^2 (324 (m _ π^0^(ó  r ))^2 + 17 u))

cts0 = (FullSimplify /@ Collect[Simplify[Numerator[tmp = Together[(low4 - (low4 /. {CouplingConstant[_[4], ___] -> 0}))]]] // manred[MandelstamU] // Expand, {_DecayConstant, CouplingConstant[QED[_], ___], MandelstamS, MandelstamT, MandelstamU, _ParticleMass}])/Denominator[tmp] // manred[MandelstamU] // FullSimplify

-1/(27 (f _ π^(ó  ))^4) (80 (e^( ))^4 (k _ 13^(r ) + 2 k _ 14^(r )) (f _ π^(ó  ))^4 + 4 (e^( ))^2 ((30 k _ 1^(r ) + 30 k _ 2^(r ) - 54 k _ 3^(r ) + 27 k _ 4^(r ) + 2 (5 k _ 5^(r ) + 77 k _ 6^(r ) + k _ 7^(r ) + 72 k _ 8^(r ))) (m _ π^0^(ó  r ))^2 - 40 (k _ 1^(r ) + k _ 2^(r )) (m _ π^+^(ó  r ))^2) (f _ π^(ó  ))^2 + 36 l _ 3^(r ) (m _ π^0^(ó  r ))^4 + 54 l _ 4^(r ) (m _ π^0^(ó  r ))^2 (-4 (m _ π^+^(ó  r ))^2 + 2 (m _ π^0^(ó  r ))^2 + u))

cts1 = FullSimplify /@ Collect[FullSimplify /@ Collect[nonCDterms4CTsFull // Expand, {MandelstamS, MandelstamT, MandelstamU, _ParticleMass, CouplingConstant[QED[_], ___]}], {_DecayConstant, CouplingConstant[QED[_], ___]}]

16/27 (5 k _ 13^(r ) + 37 k _ 14^(r )) (e^( ))^4 + 1/(27 (f _ π^(ó  ))^2) (2 (4 (5 k _ 5^(r ) + 185 k _ 6^(r ) + k _ 7^(r ) + 180 k _ 8^(r )) (m _ π^0^(ó  r ))^2 + 27 (2 k _ 3^(r ) + k _ 4^(r )) (4 (m _ π^+^(ó  r ))^2 - 3 u) - 2 k _ 2^(r ) (100 (m _ π^+^(ó  r ))^2 - 60 (m _ π^0^(ó  r ))^2 + 39 u) + 10 k _ 1^(r ) (3 (4 (m _ π^0^(ó  r ))^2 + u) - 20 (m _ π^+^(ó  r ))^2)) (e^( ))^2) + 1/(3 (f _ π^(ó  ))^4) (16 l _ 3^(r ) (m _ π^0^(ó  r ))^4 + 3 l _ 2^(r ) (-32 (m _ π^+^(ó  r ))^4 + 12 u (m _ π^+^(ó  r ))^2 + 3 s^2 + 3 t^2 + 4 s t) + 6 l _ 1^(r ) (-8 (m _ π^+^(ó  r ))^4 + 4 u (m _ π^+^(ó  r ))^2 + s^2 + t^2))

cts = FullSimplify /@ Collect[FullSimplify /@ Collect[cts0 + cts1 // Expand, {MandelstamS, MandelstamT, MandelstamU, _ParticleMass, CouplingConstant[QED[_], ___]}], {_DecayConstant, CouplingConstant[QED[_], ___]}]

16 k _ 14^(r ) (e^( ))^4 + 1/(9 (f _ π^(ó  ))^2) (2 (18 (2 k _ 3^(r ) - k _ 4^(r ) + 8 (k _ 6^(r ) + k _ 8^(r ))) (m _ π^0^(ó  r ))^2 - 9 (2 k _ 3^(r ) + k _ 4^(r )) (3 u - 4 (m _ π^+^(ó  r ))^2) + 10 k _ 1^(r ) (-4 (m _ π^+^(ó  r ))^2 + 2 (m _ π^0^(ó  r ))^2 + u) + k _ 2^(r ) (-40 (m _ π^+^(ó  r ))^2 + 20 (m _ π^0^(ó  r ))^2 - 26 u)) (e^( ))^2) + 1/(f _ π^(ó  ))^4 (4 (l _ 3^(r ) - l _ 4^(r )) (m _ π^0^(ó  r ))^4 - 2 l _ 4^(r ) (u - 4 (m _ π^+^(ó  r ))^2) (m _ π^0^(ó  r ))^2 + l _ 2^(r ) (-32 (m _ π^+^(ó  r ))^4 + 12 u (m _ π^+^(ó  r ))^2 + 3 s^2 + 3 t^2 + 4 s t) + 2 l _ 1^(r ) (-8 (m _ π^+^(ó  r ))^4 + 4 u (m _ π^+^(ó  r ))^2 + s^2 + t^2))

logsFull0 = (FullSimplify /@ Collect[Numerator[tmp = Together[(low4 - (low4 /. {_Log -> 0}))]] // Expand, {_Log}])/Denominator[tmp]

1/(48 π^2 (f _ π^(ó  ))^4) (2 log((m _ π^+^(ó  r ))^2/μ^2) (12 (e^( ))^2 (f _ π^(ó  ))^2 + 8 (m _ π^+^(ó  r ))^2 - 5 (m _ π^0^(ó  r ))^2) (m _ π^+^(ó  r ))^2 + log((m _ π^0^(ó  r ))^2/μ^2) (m _ π^0^(ó  r ))^2 (-24 (m _ π^+^(ó  r ))^2 + 5 (m _ π^0^(ó  r ))^2 + 6 u))

logsFull1 = FullSimplify /@ ((FullSimplify /@ Collect[result1[[5]] // Expand, _Log]) // manred[MandelstamU] // ChargedNeutralMassesCancel)

-(log((m _ γ^(ó  r ))^2/μ^2) (e^( ))^4)/(2 π^2) - (log((m _ π^0^(ó  r ))^2/μ^2) (16 (m _ π^0^(ó  r ))^4 + 12 (u - 4 (m _ π^+^(ó  r ))^2) (m _ π^0^(ó  r ))^2 + 3 (s^2 + t^2)))/(96 π^2 (f _ π^(ó  ))^4) - 1/(96 π^2 (f _ π^(ó  ))^4) (log((m _ π^+^(ó  r ))^2/μ^2) (24 (e^( ))^4 (f _ π^(ó  ))^4 + 6 (e^( ))^2 (20 (m _ π^+^(ó  r ))^2 + 3 (u - 4 (m _ π^0^(ó  r ))^2)) (f _ π^(ó  ))^2 + 96 (m _ π^+^(ó  r ))^4 + 60 (m _ π^0^(ó  r ))^4 + 5 s^2 + 5 t^2 + 24 u (m _ π^0^(ó  r ))^2 + 8 s t - 4 (m _ π^+^(ó  r ))^2 (53 (m _ π^0^(ó  r ))^2 + u)))

logsFull = FullSimplify[Collect[#, {CouplingConstant[QED[_], ___], MandelstamS, MandelstamT, MandelstamU, _ParticleMass}]] & /@ Collect[logsFull0 + logsFull1, _Log]

-(log((m _ γ^(ó  r ))^2/μ^2) (e^( ))^4)/(2 π^2) - (log((m _ π^0^(ó  r ))^2/μ^2) (2 (m _ π^0^(ó  r ))^4 + s^2 + t^2))/(32 π^2 (f _ π^(ó  ))^4) - 1/(96 π^2 (f _ π^(ó  ))^4) (log((m _ π^+^(ó  r ))^2/μ^2) (24 (e^( ))^4 (f _ π^(ó  ))^4 + 18 (e^( ))^2 (4 (m _ π^+^(ó  r ))^2 - 4 (m _ π^0^(ó  r ))^2 + u) (f _ π^(ó  ))^2 + 64 (m _ π^+^(ó  r ))^4 + 60 (m _ π^0^(ó  r ))^4 + 5 s^2 + 5 t^2 + 24 u (m _ π^0^(ó  r ))^2 + 8 s t - 4 (m _ π^+^(ó  r ))^2 (48 (m _ π^0^(ó  r ))^2 + u)))

jbarsfull = FullSimplify /@ ((FullSimplify /@ Collect[result1[[6]] // Expand, _LeutwylerJBar]) // manred[MandelstamU] // ChargedNeutralMassesCancel)

4 Overscript[J, _] _ (m _ γ^(ó  r ))^2(s) (e^( ))^4 + 4 Overscript[J, _] _ (m _ γ^(ó  r ))^2(t) (e^( ))^4 + (4 Overscript[J, _] _ ((m _ π^+^(ó  r ))^2 (m _ γ^(ó  r ))^2)((m _ π^+^(ó  r ))^2) (-80 u (m _ π^+^(ó  r ))^4 - 8 s t (m _ π^+^(ó  r ))^2 + 6 (s - 4 (m _ π^+^(ó  r ))^2) (t - 4 (m _ π^+^(ó  r ))^2) (m _ π^0^(ó  r ))^2 + 3 s t u) (e^( ))^2)/(3 (f _ π^(ó  ))^2 (s - 4 (m _ π^+^(ó  r ))^2) (4 (m _ π^+^(ó  r ))^2 - t)) + (Overscript[J, _] _ (m _ π^0^(ó  r ))^2(s) (s - (m _ π^0^(ó  r ))^2)^2)/(2 (f _ π^(ó  ))^4) + (Overscript[J, _] _ (m _ π^0^(ó  r ))^2(t) (t - (m _ π^0^(ó  r ))^2)^2)/(2 (f _ π^(ó  ))^4) + (Overscript[J, _] _ (m _ π^+^(ó  r ))^2(u) (-2 (e^( ))^2 (f _ π^(ó  ))^2 - 4 (m _ π^+^(ó  r ))^2 + 2 (m _ π^0^(ó  r ))^2 + u)^2)/(2 (f _ π^(ó  ))^4) + 1/(6 (f _ π^(ó  ))^4 (t - 4 (m _ π^+^(ó  r ))^2)) (Overscript[J, _] _ (m _ π^+^(ó  r ))^2(t) (6 (e^( ))^4 (t - 4 (m _ π^+^(ó  r ))^2) (f _ π^(ó  ))^4 + 6 (e^( ))^2 (-16 (m _ π^+^(ó  r ))^4 + 8 (-2 (m _ π^0^(ó  r ))^2 + 2 s + 3 t) (m _ π^+^(ó  r ))^2 + t (4 (m _ π^0^(ó  r ))^2 - 8 s - 5 t)) (f _ π^(ó  ))^2 + (t - 4 (m _ π^+^(ó  r ))^2) (32 (m _ π^+^(ó  r ))^4 - 4 (12 (m _ π^0^(ó  r ))^2 + s - 2 t) (m _ π^+^(ó  r ))^2 + 24 (m _ π^0^(ó  r ))^4 - 12 t (m _ π^0^(ó  r ))^2 + t (s + 2 t)))) + 1/(6 (f _ π^(ó  ))^4 (s - 4 (m _ π^+^(ó  r ))^2)) (Overscript[J, _] _ (m _ π^+^(ó  r ))^2(s) (6 (e^( ))^4 (s - 4 (m _ π^+^(ó  r ))^2) (f _ π^(ó  ))^4 + 6 (e^( ))^2 (-16 (m _ π^+^(ó  r ))^4 + 8 (-2 (m _ π^0^(ó  r ))^2 + 3 s + 2 t) (m _ π^+^(ó  r ))^2 + s (4 (m _ π^0^(ó  r ))^2 - 5 s - 8 t)) (f _ π^(ó  ))^2 + (s - 4 (m _ π^+^(ó  r ))^2) (s (2 s + t) + 4 (6 (m _ π^0^(ó  r ))^4 - 3 (4 (m _ π^+^(ó  r ))^2 + s) (m _ π^0^(ó  r ))^2 + (m _ π^+^(ó  r ))^2 (8 (m _ π^+^(ó  r ))^2 + 2 s - t)))))

endres = CheckF[{lowestOrder1, poly, cts0, cts1, cts, logsFull0, logsFull1, logsFull, jbarsfull, cTerms, dTerms}, "PiPiEMFullResult", ForceSave -> True] ;

Converted by Mathematica  (July 10, 2003)