<<HighEnergyPhysics`FeynCalc`

Loading FeynCalc from C:\Archivos de programa\Wolfram Research\Mathematica\8.0\AddOns\Applications\HighEnergyPhysics

FeynCalc 8.1.0 For help, type ?FeynCalc, open FeynCalcRef8.nb or visit www.feyncalc.org

Loading FeynArts, see www.feynarts.de for documentation

FeynArts 3.4 patched for use with FeynCalc

SetMandelstam[s,t,u,p1,p2,-p3,-p4,m,m,0,0];

M1=g^2*Spinor[-p2,m].GA[ν].(GS[p1-p3]+m).GA[μ].Spinor[p1,m]*Conjugate[PolarizationVector[p3,μ]]*Conjugate[PolarizationVector[p4,ν]]/(SP[p1-p3,p1-p3]-m^2);
M1A=ComplexConjugate[M1] /. μ-> μ2 /.  ν-> ν2;
F1=1/9*SUNTrace[SUNT[a3,a4,a4,a3]] /. SUNN-> 3;
T11=(1/(16Pi s^2)*F1/4*(M1A  M1 // DoPolarizationSums // Contract // FermionSpinSum) /. DiracTrace->TR // Simplify )/. g->Sqrt[4 Pi α];
T11exp=1/(16Pi s^2)*g^4*(2^5/3^3)*(t*u+m^2*(s-2t-3m^2))/(t-m^2)^2  /. g->Sqrt[4 Pi α];
TrickMandelstam[T11-T11exp,{s,t,u,2m^2}]

M2=g^2*Spinor[-p2,m].GA[ν].(GS[p1-p4]+m).GA[μ].Spinor[p1,m]*Conjugate[PolarizationVector[p4,μ]]*Conjugate[PolarizationVector[p3,ν]]/(SP[p1-p4,p1-p4]-m^2);
M2A=ComplexConjugate[M2] /. μ-> μ2 /.  ν-> ν2;
F2=1/9*SUNTrace[SUNT[a4,a3,a3,a4]] /. SUNN-> 3;
T22=(1/(16Pi s^2)*F2/4*(M2A  M2 // DoPolarizationSums // Contract // FermionSpinSum) /. DiracTrace->TR // Simplify )/. g->Sqrt[4 Pi α];
T22exp=1/(16Pi s^2)*g^4*(2^5/3^3)*(t*u+m^2*(s-2u-3m^2))/(u-m^2)^2  /. g->Sqrt[4 Pi α];
TrickMandelstam[T22-T22exp,{s,t,u,2m^2}]

F12=1/9*SUNTrace[SUNT[a3,a4,a3,a4]] /. SUNN-> 3;
T12=(1/(16Pi s^2)*F12/4*(M1A  M2 // DoPolarizationSums // Contract // FermionSpinSum) /. DiracTrace->TR // Simplify )/. g->Sqrt[4 Pi α];
T12exp=-4/27/(16Pi s^2)*g^4*m^2*(s-4m^2)/(t-m^2)/(u-m^2) /. g->Sqrt[4 Pi α];
TrickMandelstam[T12-T12exp,{s,t,u,2m^2}]

M3=I g^2*Spinor[-p2,m].GA[μ].Spinor[p1,m]*Conjugate[PolarizationVector[p3,ν]]*Conjugate[PolarizationVector[p4,σ]]*((MT[μ,ν] (FV[p,σ]-FV[q,σ])+MT[ν,σ] (FV[q,μ]-FV[r,μ])+MT[μ,σ] (FV[r,ν]-FV[p,ν])))/SP[p3+p4,p3+p4]/.FV[q,i_]->-FV[p3,i]/.FV[r,i_]->-FV[p4,i]/.FV[p,i_]->FV[p3,i]+FV[p4,i];
M3A=ComplexConjugate[M3] /. μ-> μ2 /.  ν-> ν2 /.σ->σ2;
F3=SUNSimplify[1/9*SUNF[b2,a3,a4]*SUNF[b,a3,a4]*SUNTrace[SUNT[b,b2]],SUNNToCACF->False] /. SUNN-> 3;
T33=(1/(16Pi s^2)*F3/4*(M3A  M3 // DoPolarizationSums // Contract // FermionSpinSum) /. DiracTrace->TR // Simplify )/. g->Sqrt[4 Pi α];
T33exp=1/(16Pi s^2)*g^4*(-2/3)*(s^2+7*(t^2+u^2)+4t*u+34m^2 s-18m^4)/s^2  /. g->Sqrt[4 Pi α];
TrickMandelstam[T33-T33exp,{s,t,u,2m^2}]

F13=SUNSimplify[CalcColorFactor[1/9*SUNF[b,a3,a4]*SUNTrace[SUNT[a3,a4,b]]],SUNNToCACF->False] /. SUNN-> 3;
T13=(1/(16Pi s^2)*F13/4*(M1A  M3 // DoPolarizationSums // Contract // FermionSpinSum) /. DiracTrace->TR // Simplify )/. g->Sqrt[4 Pi α];
T13exp=-4/3/(16Pi s^2)*g^4*(t^2+m^2*(m^2+s-2t))/(t-m^2)/s /. g->Sqrt[4 Pi α];
TrickMandelstam[T13-T13exp,{s,t,u,2m^2}]

F23=SUNSimplify[CalcColorFactor[1/9*SUNF[b,a3,a4]*SUNTrace[SUNT[a4,a3,b]]],SUNNToCACF->False] /. SUNN-> 3;
T23=(1/(16Pi s^2)*F23/4*(M2A  M3 // DoPolarizationSums // Contract // FermionSpinSum) /. DiracTrace->TR // Simplify )/. g->Sqrt[4 Pi α];
T23exp=-4/3/(16Pi s^2)*g^4*(u^2+m^2*(m^2+s-2u))/(u-m^2)/s /. g->Sqrt[4 Pi α];
TrickMandelstam[T23-T23exp,{s,t,u,2m^2}]

G=-I g^2*Spinor[-p2,m].GS[p3].Spinor[p1,m]/s;
Ga=ComplexConjugate[G];
FG=SUNSimplify[1/9*SUNF[b2,a3,a4]*SUNF[b,a3,a4]*SUNTrace[SUNT[b2,b]],SUNNToCACF->False] /. SUNN-> 3;
TG=-(1/(16Pi s^2)*FG/4*(Ga G // Contract // FermionSpinSum) /. DiracTrace->TR // Simplify )/. g->Sqrt[4 Pi α];
TGexp=-1/(16Pi s^2)*g^4*(2/3)*(m^2-t)*(m^2-u)/s^2  /. g->Sqrt[4 Pi α];
TrickMandelstam[TG-TGexp,{s,t,u,2m^2}]

fin=1/(16Pi s^2)*2^5*g^4/3^3*((t*u+m^2*(s-2t-3m^2))/(t-m^2)^2+(t*u+m^2*(s-2u-3m^2))/(u-m^2)^2+m^2*(m^2+2*s)/(t-m^2)/(u-m^2)-9/4*(t^2+u^2+6m^2s-2m^4)/s^2)/. g->Sqrt[4 Pi α]

finb=T11+T22+2*T12exp+2*T13exp+2*T23exp+T33exp+2*TGexp

TrickMandelstam[fin-finb,{s,t,u,2m^2}]