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*(c2*(-mK^2 + p2^2)*(3*mK^2 + p2^2 - 3*p3^2) +
2*c5*((mK^2 - mPi^2)*(-mK^2 + p2^2 + p3^2) + 64*f^2*(-2*mK^2 + mPi^2 + p2^2)*Pi^2)))/
(32*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*(-4*mK^2 + mPi^2)*(2*c5*(-mK^2 + mPi^2)*(7*mK^2 - 11*mPi^2 + 4*p2^2 - 9*p3^2) +
    c2*(-29*mK^4 + 24*mK^2*mPi^2 - 4*mPi^4 + 3*p2^4 + 9*mK^2*p3^2 +
      p2^2*(10*mK^2 - 4*mPi^2 - 9*p3^2)))*Log[mEta^2/ScaleMu^2])/
  (576*f^3*(mK^2 - mPi^2)*(-mK^2 + p2^2)*Pi^2) -
(B*(-2*c5*(-5*mK^4 + 2*mK^2*mPi^2 + (2*mK^2 + mPi^2)*p2^2 + (-mK^2 + mPi^2)*p3^2) +
    c2*(-11*mK^4 + p2^4 + 3*mK^2*p3^2 - 3*p2^2*(-2*mK^2 + p3^2)))*Log[mK^2/ScaleMu^2])/
  (32*f^3*(-mK^2 + p2^2)*Pi^2) +
(B*mPi^2*(-2*c5*(-mK^2 + mPi^2)*(-9*mK^2 + 7*mPi^2 + 2*p2^2 + 3*p3^2) +
    c2*(mK^4 - 16*mK^2*mPi^2 + 12*mPi^4 + p2^4 + 3*mK^2*p3^2 +
      p2^2*(-2*mK^2 + 4*mPi^2 - 3*p3^2)))*Log[mPi^2/ScaleMu^2])/
  (64*f^3*(mK^2 - mPi^2)*(-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*(2*c5*(-mK^2 + mPi^2)*p3^2*(-9*(-mK^2 + p2^2 + p3^2)*Jbar[p3^2, mK^2] +
     2*(3*mEta^2 + 5*mK^2 + mPi^2 + 3*p2^2 - 9*p3^2)*Jbar[p3^2, mPi^2, mEta^2]) +
   3*c2*(-mK^2 + p2^2)*(3*p3^2*(3*mK^2 + p2^2 - 3*p3^2)*Jbar[p3^2, mK^2] +
     2*(2*mK^2*(mEta^2 - mPi^2) - (-4*mEta^2 + mK^2)*p3^2 - 3*p3^4 +
       p2^2*(-2*mEta^2 + 2*mPi^2 + p3^2))*Jbar[p3^2, mPi^2, mEta^2])))/
(18*f^3*(-mK^2 + p2^2)*p3^2)

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

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

Counterterms:

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

(-4*B*c5*(f^2*(-2*mK^2 + mPi^2 + p2^2) -
    4*((2*mK^2 + mPi^2)*(-2*mK^2 + mPi^2 + p2^2)*L[4] +
      (-3*mK^4 + mPi^2*(-2*mPi^2 + p2^2 - p3^2) + mK^2*(4*mPi^2 + p3^2))*L[5] +
      4*(-mK^2 + mPi^2)^2*L[8])))/(f^3*(-mK^2 + p2^2)) -
(2*B*c2*(4*(2*(-mK^4 + mPi^2*p2^2)*n[10] + (2*mK^2 + mPi^2)*(-2*mK^2 + mPi^2 + p2^2)*
       n[11]) - 2*(p2^4 + mK^2*(-mK^2 + p3^2) - p2^2*(2*mK^2 - 2*mPi^2 + p3^2))*n[21] +
    (-mK^2 + p2^2)*(-mK^2 + p2^2 + p3^2)*n[22]))/(f^3*(-mK^2 + p2^2))

Full amplitude:

-(B*(c2*(-mK^2 + p2^2)*(3*mK^2 + p2^2 - 3*p3^2) +
     2*c5*((mK^2 - mPi^2)*(-mK^2 + p2^2 + p3^2) + 64*f^2*(-2*mK^2 + mPi^2 + p2^2)*
        Pi^2)))/(32*f^3*(-mK^2 + p2^2)*Pi^2) +
(B*(2*c5*(-mK^2 + mPi^2)*p3^2*(-9*(-mK^2 + p2^2 + p3^2)*Jbar[p3^2, mK^2] +
      2*(3*mEta^2 + 5*mK^2 + mPi^2 + 3*p2^2 - 9*p3^2)*Jbar[p3^2, mPi^2, mEta^2]) +
    3*c2*(-mK^2 + p2^2)*(3*p3^2*(3*mK^2 + p2^2 - 3*p3^2)*Jbar[p3^2, mK^2] +
      2*(2*mK^2*(mEta^2 - mPi^2) - (-4*mEta^2 + mK^2)*p3^2 - 3*p3^4 +
        p2^2*(-2*mEta^2 + 2*mPi^2 + p3^2))*Jbar[p3^2, mPi^2, mEta^2])))/
  (18*f^3*(-mK^2 + p2^2)*p3^2) -
(4*B*c5*(f^2*(-2*mK^2 + mPi^2 + p2^2) -
    4*((2*mK^2 + mPi^2)*(-2*mK^2 + mPi^2 + p2^2)*L[4] +
      (-3*mK^4 + mPi^2*(-2*mPi^2 + p2^2 - p3^2) + mK^2*(4*mPi^2 + p3^2))*L[5] +
      4*(-mK^2 + mPi^2)^2*L[8])))/(f^3*(-mK^2 + p2^2)) +
(B*(-4*mK^2 + mPi^2)*(2*c5*(-mK^2 + mPi^2)*(7*mK^2 - 11*mPi^2 + 4*p2^2 - 9*p3^2) +
    c2*(-29*mK^4 + 24*mK^2*mPi^2 - 4*mPi^4 + 3*p2^4 + 9*mK^2*p3^2 +
      p2^2*(10*mK^2 - 4*mPi^2 - 9*p3^2)))*Log[mEta^2/ScaleMu^2])/
  (576*f^3*(mK^2 - mPi^2)*(-mK^2 + p2^2)*Pi^2) -
(B*(-2*c5*(-5*mK^4 + 2*mK^2*mPi^2 + (2*mK^2 + mPi^2)*p2^2 + (-mK^2 + mPi^2)*p3^2) +
    c2*(-11*mK^4 + p2^4 + 3*mK^2*p3^2 - 3*p2^2*(-2*mK^2 + p3^2)))*Log[mK^2/ScaleMu^2])/
  (32*f^3*(-mK^2 + p2^2)*Pi^2) +
(B*mPi^2*(-2*c5*(-mK^2 + mPi^2)*(-9*mK^2 + 7*mPi^2 + 2*p2^2 + 3*p3^2) +
    c2*(mK^4 - 16*mK^2*mPi^2 + 12*mPi^4 + p2^4 + 3*mK^2*p3^2 +
      p2^2*(-2*mK^2 + 4*mPi^2 - 3*p3^2)))*Log[mPi^2/ScaleMu^2])/
  (64*f^3*(mK^2 - mPi^2)*(-mK^2 + p2^2)*Pi^2) -
(2*B*c2*(4*(2*(-mK^4 + mPi^2*p2^2)*n[10] + (2*mK^2 + mPi^2)*(-2*mK^2 + mPi^2 + p2^2)*
       n[11]) - 2*(p2^4 + mK^2*(-mK^2 + p3^2) - p2^2*(2*mK^2 - 2*mPi^2 + p3^2))*n[21] +
    (-mK^2 + p2^2)*(-mK^2 + p2^2 + p3^2)*n[22]))/(f^3*(-mK^2 + p2^2))

Converted by Mathematica (July 10, 2003)