KSS2Checks.nb

•Text output

Polynomial contribution:

$textPoly = finPoly /. _RenormalizationState -> Sequence[] /. Pair[Momentum[p_], Momentum[p_]] -> p^2 //. {_Pair -> Sequence[], _DecayConstant -> f, CouplingConstant[ChPTW3[2], 1] -> c2, CouplingConstant[ChPTW3[2], 2] -> c5, CouplingConstant[ChPTW3[4], i_] -> n[i], CouplingConstant[ChPT3[4], i_] -> L[i], MandelstamT -> t, MandelstamS -> s, MandelstamU -> u, ParticleMass[Pion] -> mPi, ParticleMass[Kaon] -> mK, ParticleMass[EtaMeson] -> mEta, LeutwylerJBar[a__, ___Rule] :> Jbar[a], QuarkCondensate[] -> B} // InputForm$

(B*(-3*c2*(mEta^2 + 2*mK^2 - 3*mPi^2)*(-mK^2 + p2^2) +
c5*(-mK^2 + mPi^2)*(3*mEta^2 + 14*mK^2 + mPi^2 - 14*p2^2 - 18*p3^2 + 192*f^2*Pi^2)))/
(24*f^3*(-mK^2 + p2^2)*Pi^2)

Logs:

$textLogs = finLogs /. _RenormalizationState -> Sequence[] /. Pair[Momentum[p_], Momentum[p_]] -> p^2 //. {_Pair -> Sequence[], _DecayConstant -> f, CouplingConstant[ChPTW3[2], 1] -> c2, CouplingConstant[ChPTW3[2], 2] -> c5, CouplingConstant[ChPTW3[4], i_] -> n[i], CouplingConstant[ChPT3[4], i_] -> L[i], MandelstamT -> t, MandelstamS -> s, MandelstamU -> u, ParticleMass[Pion] -> mPi, ParticleMass[Kaon] -> mK, ParticleMass[EtaMeson] -> mEta, LeutwylerJBar[a__, ___Rule] :> Jbar[a], QuarkCondensate[] -> B} // InputForm$

-(B*(2*c5*(23*mK^4 - 70*mK^2*mPi^2 + 11*mPi^4 + 3*(-mK^2 + mPi^2)*p2^2 +
       27*(-mK^2 + mPi^2)*p3^2) + c2*(-23*mK^4 - 8*mK^2*mPi^2 + 4*mPi^4 + 9*p2^4 +
       27*mK^2*p3^2 - 3*p2^2*(-26*mK^2 + 8*mPi^2 + 9*p3^2)))*Log[mEta^2/ScaleMu^2])/
  (288*f^3*(-mK^2 + p2^2)*Pi^2) -
(B*(6*c5*(-mK^2 + mPi^2)*(p2^2 + p3^2) + c2*(p2^4 - 3*p2^2*(-2*mK^2 + p3^2) +
      3*mK^2*(-mK^2 + p3^2)))*Log[mK^2/ScaleMu^2])/(16*f^3*(-mK^2 + p2^2)*Pi^2) +
(B*(-2*c5*(3*mK^4 - 6*mK^2*mPi^2 + 7*mPi^4 + 3*(-mK^2 + mPi^2)*p2^2 +
      3*(-mK^2 + mPi^2)*p3^2) + 3*c2*(mK^4 - 8*mK^2*mPi^2 + 4*mPi^4 + p2^4 +
      3*mK^2*p3^2 + p2^2*(-2*mK^2 + 8*mPi^2 - 3*p3^2)))*Log[mPi^2/ScaleMu^2])/
  (32*f^3*(-mK^2 + p2^2)*Pi^2)

's:

$textJBars = finJBars /. _RenormalizationState -> Sequence[] /. Pair[Momentum[p_], Momentum[p_]] -> p^2 //. {_Pair -> Sequence[], _DecayConstant -> f, CouplingConstant[ChPTW3[2], 1] -> c2, CouplingConstant[ChPTW3[2], 2] -> c5, CouplingConstant[ChPTW3[4], i_] -> n[i], CouplingConstant[ChPT3[4], i_] -> L[i], MandelstamT -> t, MandelstamS -> s, MandelstamU -> u, ParticleMass[Pion] -> mPi, ParticleMass[Kaon] -> mK, ParticleMass[EtaMeson] -> mEta, LeutwylerJBar[a__, ___Rule] :> Jbar[a], QuarkCondensate[] -> B} // InputForm$

(B*(-3*c2*(-mK^2 + p2^2)*((-4*mEta^2 + mK^2 - p2^2 + 3*p3^2)*Jbar[p3^2, mEta^2] -
     2*(3*mK^2 + p2^2 - 3*p3^2)*Jbar[p3^2, mK^2] + 3*(-mK^2 + 4*mPi^2 + p2^2 - 3*p3^2)*
      Jbar[p3^2, mPi^2]) + 2*c5*(-mK^2 + mPi^2)*
    ((-6*mEta^2 - mK^2 - 2*mPi^2 + p2^2 + 9*p3^2)*Jbar[p3^2, mEta^2] +
     18*(-mK^2 + p2^2 + p3^2)*Jbar[p3^2, mK^2] + 9*(-mK^2 + p2^2 + p3^2)*
      Jbar[p3^2, mPi^2])))/(6*f^3*(-mK^2 + p2^2))

$finJBarsKLM /. _RenormalizationState -> Sequence[] /. Pair[Momentum[p_], Momentum[p_]] -> p^2 //. {_DecayConstant -> f, CouplingConstant[ChPTW3[2], 1] -> c2, CouplingConstant[ChPTW3[2], 2] -> c5, CouplingConstant[ChPTW3[4], i_] -> n[i], CouplingConstant[ChPT3[4], i_] -> L[i], MandelstamT -> t, MandelstamS -> s, MandelstamU -> u, ParticleMass[Pion] -> mPi, ParticleMass[Kaon] -> mK, ParticleMass[EtaMeson] -> mEta, LeutwylerJBar[a__, ___Rule] :> Jbar[a], QuarkCondensate[] -> B} // InputForm$

(B*(c2*(-mK^2 + p2^2)*(13*mK^2 - 4*mPi^2 + 3*p2^2 - 9*p3^2) +
    2*c5*(-mK^2 + mPi^2)*(-9*mK^2 + p2^2 + 9*p3^2))*Jbar[p3^2, mEta^2])/
  (6*f^3*(-mK^2 + p2^2)) + (B*(c2*(-mK^2 + p2^2)*(3*mK^2 + p2^2 - 3*p3^2) +
    6*c5*(-mK^2 + mPi^2)*(-mK^2 + p2^2 + p3^2))*Jbar[p3^2, mK^2])/(f^3*(-mK^2 + p2^2)) -
(3*B*(c2*(-mK^2 + p2^2)*(-mK^2 + 4*mPi^2 + p2^2 - 3*p3^2) +
    2*c5*(mK^2 - mPi^2)*(-mK^2 + p2^2 + p3^2))*Jbar[p3^2, mPi^2])/(2*f^3*(-mK^2 + p2^2))

Counterterms:

$textCTs = finCTs /. _RenormalizationState -> Sequence[] /. Pair[Momentum[p_], Momentum[p_]] -> p^2 //. {_DecayConstant -> f, CouplingConstant[ChPTW3[2], 1] -> c2, CouplingConstant[ChPTW3[2], 2] -> c5, CouplingConstant[ChPTW3[4], i_] -> n[i], CouplingConstant[ChPT3[4], i_] -> L[i], MandelstamT -> t, MandelstamS -> s, MandelstamU -> u, ParticleMass[Pion] -> mPi, ParticleMass[Kaon] -> mK, ParticleMass[EtaMeson] -> mEta, LeutwylerJBar[a__, ___Rule] :> Jbar[a], QuarkCondensate[] -> B} // InputForm$

(-8*B*c5*(mK^2 - mPi^2)*(f^2 - 4*(p2^2 - p3^2)*(3*L[4] + L[5]) -
    4*mK^2*(5*L[4] + 2*(L[5] - 6*L[6] - 2*L[8])) - 4*mPi^2*(L[4] - 2*L[5] + 4*L[8])))/
  (f^3*(-mK^2 + p2^2)) + (16*B*c2*(-mK^2 + mPi^2)*
   (2*p2^2*n[10] + (-mK^2 + mPi^2 + 3*p2^2)*n[11] - p2^2*n[21]))/(f^3*(-mK^2 + p2^2))

Full amplitude:

(B*(-3*c2*(mEta^2 + 2*mK^2 - 3*mPi^2)*(-mK^2 + p2^2) +
    c5*(-mK^2 + mPi^2)*(3*mEta^2 + 14*mK^2 + mPi^2 - 14*p2^2 - 18*p3^2 + 192*f^2*Pi^2)))/
  (24*f^3*(-mK^2 + p2^2)*Pi^2) +
(B*(-3*c2*(-mK^2 + p2^2)*((-4*mEta^2 + mK^2 - p2^2 + 3*p3^2)*Jbar[p3^2, mEta^2] -
      2*(3*mK^2 + p2^2 - 3*p3^2)*Jbar[p3^2, mK^2] + 3*(-mK^2 + 4*mPi^2 + p2^2 - 3*p3^2)*
       Jbar[p3^2, mPi^2]) + 2*c5*(-mK^2 + mPi^2)*
     ((-6*mEta^2 - mK^2 - 2*mPi^2 + p2^2 + 9*p3^2)*Jbar[p3^2, mEta^2] +
      18*(-mK^2 + p2^2 + p3^2)*Jbar[p3^2, mK^2] + 9*(-mK^2 + p2^2 + p3^2)*
       Jbar[p3^2, mPi^2])))/(6*f^3*(-mK^2 + p2^2)) -
(8*B*c5*(mK^2 - mPi^2)*(f^2 - 4*(p2^2 - p3^2)*(3*L[4] + L[5]) -
    4*mK^2*(5*L[4] + 2*(L[5] - 6*L[6] - 2*L[8])) - 4*mPi^2*(L[4] - 2*L[5] + 4*L[8])))/
  (f^3*(-mK^2 + p2^2)) -
(B*(2*c5*(23*mK^4 - 70*mK^2*mPi^2 + 11*mPi^4 + 3*(-mK^2 + mPi^2)*p2^2 +
      27*(-mK^2 + mPi^2)*p3^2) + c2*(-23*mK^4 - 8*mK^2*mPi^2 + 4*mPi^4 + 9*p2^4 +
      27*mK^2*p3^2 - 3*p2^2*(-26*mK^2 + 8*mPi^2 + 9*p3^2)))*Log[mEta^2/ScaleMu^2])/
  (288*f^3*(-mK^2 + p2^2)*Pi^2) -
(B*(6*c5*(-mK^2 + mPi^2)*(p2^2 + p3^2) + c2*(p2^4 - 3*p2^2*(-2*mK^2 + p3^2) +
      3*mK^2*(-mK^2 + p3^2)))*Log[mK^2/ScaleMu^2])/(16*f^3*(-mK^2 + p2^2)*Pi^2) +
(B*(-2*c5*(3*mK^4 - 6*mK^2*mPi^2 + 7*mPi^4 + 3*(-mK^2 + mPi^2)*p2^2 +
      3*(-mK^2 + mPi^2)*p3^2) + 3*c2*(mK^4 - 8*mK^2*mPi^2 + 4*mPi^4 + p2^4 +
      3*mK^2*p3^2 + p2^2*(-2*mK^2 + 8*mPi^2 - 3*p3^2)))*Log[mPi^2/ScaleMu^2])/
  (32*f^3*(-mK^2 + p2^2)*Pi^2) +
(16*B*c2*(-mK^2 + mPi^2)*(2*p2^2*n[10] + (-mK^2 + mPi^2 + 3*p2^2)*n[11] - p2^2*n[21]))/
  (f^3*(-mK^2 + p2^2))

Converted by Mathematica (July 10, 2003)