double complex function A1phiAQggmpmmL(k1,k2,k3,k4,za,zb) c--- This is an implementation of Eq. (5.2) in c--- S.~Badger, John.~M.~Campbell, R.~Keith Ellis and Ciaran Williams c--- "Analytic results for the one-loop NMHV H-qbar-q-g-g amplitude." c--- preprint DESY 09-180, FERMILAB-PUB-09-505-T, IPPP/09/86 c--- arXiv: 0910.4481 [hep-ph] implicit none include 'constants.f' include 'zprods_decl.f' include 'sprods_com.f' include 'scale.f' include 'epinv.f' include 'deltar.f' integer j,k1,k2,k3,k4 double complex V1L,A0phiAQggmpmm,lnrat,zab2,Lsm1,Lsm1_2mht double complex sum,l23,l34,l41,l12,coef3m1234,coef3m1423, & S1,S2,K1DK2,a1,a2,a3,a4,gamma,factor,I3m, & BGRL1,BGRL2hat,BGRL3hat double precision s12,s13,s14,s23,s24,s34,s123,s234,s124,s134,mhsq zab2(k1,k2,k3,k4)=za(k1,k2)*zb(k2,k4)+za(k1,k3)*zb(k3,k4) s12=s(k1,k2) s13=s(k1,k3) s14=s(k1,k4) s23=s(k2,k3) s24=s(k2,k4) s34=s(k3,k4) mhsq=s12+s13+s14+s23+s24+s34 s123=s12+s13+s23 s124=s12+s14+s24 s134=s13+s14+s34 s234=s23+s24+s34 l12=lnrat(musq,-s12) l23=lnrat(musq,-s23) l34=lnrat(musq,-s34) l41=lnrat(musq,-s14) V1L= . -epinv**2-epinv*l23-0.5d0*l23**2 . -epinv**2-epinv*l34-0.5d0*l34**2 . -epinv**2-epinv*l41-0.5d0*l41**2 . +13d0/6d0*(epinv+l12)+119d0/18d0-deltar/6d0 A1phiAQggmpmmL=A0phiAQggmpmm(k1,k2,k3,k4,za,zb)*V1L sum= & -s134**2/(zb(k4,k1)*zb(k3,k4)*zab2(k2,k1,k4,k3)) & *Lsm1(-s14,-s134,-s34,-s134) & -zab2(k1,k3,k4,k2)**2/(zab2(k1,k2,k3,k4)*zb(k2,k3)*zb(k3,k4)) & *Lsm1(-s34,-s234,-s23,-s234) & +(mhsq**2*za(k1,k4)**2*za(k2,k4) & /(za(k1,k2)*zab2(k2,k1,k4,k3)*zab2(k4,k1,k2,k3)*s124) & -zab2(k3,k1,k4,k2)**3 & /(zb(k1,k2)*zb(k2,k4)*zab2(k3,k1,k2,k4)*s124)) & *Lsm1(-s14,-s124,-s12,-s124) & +(zb(k2,k3)**2*zab2(k4,k2,k3,k1)**3 & /(zb(k1,k2)*zb(k1,k3)**3*zab2(k4,k1,k2,k3)*s123) & -mhsq**2*za(k1,k3)**3 & /(za(k1,k2)*zab2(k1,k2,k3,k4)*zab2(k3,k1,k2,k4)*s123)) & *Lsm1(-s12,-s123,-s23,-s123) & +za(k3,k4)*s134**2 & /(zb(k3,k4)*za(k3,k4)*zb(k1,k4)*zab2(k2,k1,k4,k3)) & *Lsm1_2mht(s12,s134,s34,mhsq) & -zab2(k1,k3,k4,k2)**2 & /(zb(k3,k4)*zb(k2,k3)*zab2(k1,k2,k3,k4)) & *Lsm1_2mht(s12,s234,s34,mhsq) & +(zab2(k4,k1,k3,k2)**3 & /(zb(k1,k2)*zb(k2,k3)*zab2(k4,k1,k2,k3)*s123) & -mhsq**2*za(k1,k3)**3 & /(za(k1,k2)*zab2(k1,k2,k3,k4)*zab2(k3,k1,k2,k4)*s123)) & *Lsm1_2mht(s34,s123,s12,mhsq) & +(mhsq**2*za(k1,k4)**2*za(k2,k4) & /(za(k1,k2)*zab2(k2,k1,k4,k3)*zab2(k4,k1,k2,k3)*s124) & -zab2(k3,k2,k4,k1)*zab2(k3,k1,k4,k2)**2 & /(zab2(k3,k1,k2,k4)*zb(k1,k4)*zb(k1,k2)*s124)) & *Lsm1_2mht(s34,s124,s12,mhsq) & +(zab2(k4,k1,k3,k2)**3 & /(zb(k1,k2)*zb(k2,k3)*zab2(k4,k1,k2,k3)*s123) & -mhsq**2*za(k1,k3)**3 & /(za(k1,k2)*zab2(k1,k2,k3,k4)*zab2(k3,k1,k2,k4)*s123)) & *Lsm1_2mht(s14,s123,s23,mhsq) & +(mhsq**2*za(k2,k4)*za(k1,k4)**2 & /(za(k1,k2)*zab2(k2,k1,k4,k3)*zab2(k4,k1,k2,k3)*s124) & -zab2(k3,k1,k4,k2)**2*zab2(k3,k2,k4,k1) & /(zb(k1,k2)*zb(k1,k4)*zab2(k3,k1,k2,k4)*s124)) & *Lsm1_2mht(s23,s124,s14,mhsq) C-----Now for three mass triangles C-----Deal with the 12-34 case first C-----K1=-(p1+p2+p3+p4) C-----K2=-(p1+p2) C K1flat=gamma/(gamma**2-S1*S2)*(gamma*K1-S1*K2) C K1flat=gamma/(gamma**2-S1*S2)*((S1-gamma)*(p1+p2)-gamma*((p3+p4)) C----solve for gamma_+ and gamma_- S1=dcmplx(mhsq) S2=dcmplx(s12) K1DK2=dcmplx(s12+0.5d0*(s13+s14+s23+s24)) C-gamma+ = K1DK2+sqrt(K1DK2**2-S1*S2) C-gamma- = K1DK2-sqrt(K1DK2**2-S1*S2) coef3m1234=czip gamma=K1DK2+sqrt(K1DK2**2-S1*S2) do j=1,2 C -- calculate the projections of K1 flat on k1,k2,k3,k4 called a1,a2,a3,a4 factor=gamma/(gamma**2-S1*S2) a1=factor*(S1-gamma) a2=a1 a3=-factor*gamma a4=a3 C=-- The result for the 12-34 coefficient is c + iza(k1,k2)*iza(k3,k1f)*iza(k4,k1f) * ( c + za(k1,k1f)^2*za(k3,k4)^3*ga^-1*S1^2*[ga-S1]^-1); c which we can rewrite as c + iza(k1,k2) * ( c + 1/4*za(k3,k4)^3*zab2(k1,k1f,k3)*zab2(k1,k1f,k4)*k3.k1f^-1* c k4.k1f^-1*ga^-1*S1^2*[ga-S1]^-1); coef3m1234=coef3m1234 & +mhsq**2*za(k3,k4)**3/(za(k1,k2)*gamma*(gamma-mhsq)) & *(a2*za(k1,k2)*zb(k2,k3)+a4*za(k1,k4)*zb(k4,k3)) ! zab2(k1,k1f,k3) & *(a2*za(k1,k2)*zb(k2,k4)+a3*za(k1,k3)*zb(k3,k4)) ! zab2(k1,k1f,k4) * /(a1*s13+a2*s23+a4*s34) ! (2*k3.k1f)^-1* * /(a1*s14+a2*s24+a3*s34) ! (2*k4.k1f)^-1* C----switch to other solution gamma=2*K1DK2-gamma enddo C-----Now deal with the 14-23 case C-----K1=-(p1+p2+p3+p4) C-----K2=-(p1+p4) C K1flat=gamma/(gamma**2-S1*S2)*(gamma*K1-S1*K2) C K1flat=gamma/(gamma**2-S1*S2)*((S1-gamma)*(p1+p4)-gamma*((p2+p3)) C----solve for gamma_+ and gamma_- S1=dcmplx(mhsq) S2=dcmplx(s14) K1DK2=dcmplx(s14+0.5d0*(s12+s13+s24+s34)) C-gamma+ = K1DK2+sqrt(K1DK2**2-S1*S2) C-gamma- = K1DK2-sqrt(K1DK2**2-S1*S2) coef3m1423=czip gamma=K1DK2+sqrt(K1DK2**2-S1*S2) do j=1,2 C -- calculate the projections of K1 flat on k1,k2,k3,k4 called a1,a2,a3,a4 factor=gamma/(gamma**2-S1*S2) a1=factor*(S1-gamma) a4=a1 a3=-factor*gamma a2=a3 C=-- The result for the 14-23 coefficient is c -za(k1,k4)^2*za(k3,k1f)^2*ga^-1*S1^2*[ga-S1]^-1 c + iza(k1,k1f)*iza(k2,k1f) * c which we can rewrite as c -za(k1,k4)^2*zab2(k3,k1f,k1)*zab2(k3,k1f,k2)*S1^2 c /(2*k1.k1f^-1)/*2*k2.k1f^-1*ga^-1*[ga-S1]^-1 coef3m1423=coef3m1423 & -mhsq**2*za(k1,k4)**2/(2d0*gamma*(gamma-mhsq)) & *(a2*za(k3,k2)*zb(k2,k1)+a4*za(k3,k4)*zb(k4,k1)) ! *zab2(k3,k1f,k1) & *(a1*za(k3,k1)*zb(k1,k2)+a4*za(k3,k4)*zb(k4,k2)) ! *zab2(k3,k1f,k2) * /(a2*s12+a3*s13+a4*s14) ! (2*k1.k1f)^-1* * /(a1*s12+a3*s23+a4*s24) ! (2*k2.k1f)^-1* C----switch to other solution gamma=2*K1DK2-gamma enddo sum=sum-coef3m1234*I3m(mhsq,s12,s34) . -coef3m1423*I3m(mhsq,s14,s23) sum=sum & -2d0/3d0*za(k1,k3)**2*za(k3,k4)*zab2(k4,k1,k2,k3)*zb(k1,k2) & *BGRL3hat(s123,s12) & +1d0/6d0*za(k3,k4)*za(k1,k3) & *(zab2(k4,k1,k3,k2)*zb(k1,k3)-3d0*zab2(k4,k2,k3,k1)*zb(k2,k3)) & /zb(k1,k3) * *BGRL2hat(s123,s12) & +za(k1,k3) & *(0.5d0*zab2(k4,k1,k3,k2)*zab2(k4,k1,k2,k3)*zb(k1,k2)*zb(k1,k3) & -zab2(k4,k2,k3,k1)**2*zb(k2,k3)**2 & -8d0/3d0*zab2(k4,k1,k3,k2)**2*zb(k1,k3)**2) & /(s123*zb(k1,k3)**2*zb(k2,k3)) & *BGRL1(s123,s12) & -2d0/3d0*s124*za(k3,k4)**2*za(k1,k4)*zb(k4,k2) & *BGRL3hat(s124,s12) & +za(k3,k4)*za(k1,k4) & *(1d0/3d0*zab2(k3,k1,k4,k2)*zb(k1,k4) * -0.5d0*zab2(k3,k1,k2,k4)*zb(k1,k2))/zb(k1,k4) & *BGRL2hat(s124,s12) & +zab2(k3,k1,k4,k2)*(3d0/2d0*s124*za(k3,k4) & +11d0/3d0*zab2(k3,k1,k4,k2)*za(k4,k2))/(s124*zb(k1,k4)) & *BGRL1(s124,s12) & +0.5d0*za(k1,k4)*za(k1,k3)*zab2(k4,k2,k3,k1)*zb(k1,k2)/zb(k3,k1) & *BGRL2hat(s123,s23) &-za(k1,k3)*zab2(k4,k2,k3,k1)*(3d0/2d0*zab2(k4,k1,k3,k2)*zb(k1,k3) &+zab2(k4,k2,k3,k1)*zb(k2,k3))/(s123*zb(k1,k3)**2) & *BGRL1(s123,s23) & +0.5d0*s234*za(k1,k4)*za(k3,k4)*zb(k4,k2)/zb(k4,k3) & *BGRL2hat(s234,s23) & +3d0/2d0*za(k3,k4)*zab2(k1,k3,k4,k2)/zb(k4,k3) & *BGRL1(s234,s23) A1phiAQggmpmmL=A1phiAQggmpmmL+sum c--- now add the rational pieces sum= . za(k3,k4)*zab2(k3,k1,k4,k2) . *(2d0*za(k2,k4)*zb(k4,k2)-za(k1,k2)*zb(k2,k1)) . /(12d0*s124*za(k1,k2)*zb(k2,k1)*zb(k4,k1)) . +(za(k2,k3)*zab2(k4,k1,k3,k2)**2*( . 3d0*za(k1,k2)*zb(k2,k1)-2d0*za(k2,k3)*zb(k3,k2)) . -2d0*za(k1,k3)**2*za(k2,k4)*zab2(k4,k2,k3,k1) . *zb(k2,k1)*zb(k3,k2)) . /(12d0*s123*za(k1,k2)*za(k2,k3)*zb(k2,k1)*zb(k3,k1)*zb(k3,k2)) . +5d0*za(k3,k4)**2/(12d0*za(k2,k3)*zb(k3,k1)) . +5d0*za(k3,k4)*zab2(k4,k1,k3,k2) . /(6d0*za(k2,k3)*zb(k3,k1)*zb(k3,k2)) . +zab2(k4,k1,k3,k2)**2 . /(6d0*za(k1,k2)*zb(k2,k1)*zb(k3,k1)*zb(k3,k2)) . -za(k1,k3)*za(k1,k4)*za(k2,k4)*zb(k2,k1) . /(3d0*za(k1,k2)*za(k2,k3)*zb(k3,k1)*zb(k3,k2)) . -za(k1,k3)*za(k3,k4)/(12d0*za(k1,k2)*zb(k4,k1)) . -za(k3,k4)**2*zb(k4,k2)/(6d0*za(k1,k2)*zb(k2,k1)*zb(k4,k1)) . +za(k1,k3)*za(k2,k4)*zab2(k4,k1,k3,k4) . /(4d0*za(k1,k2)*za(k2,k3)*zb(k3,k1)*zb(k4,k3)) . -za(k1,k3)*zab2(k4,k1,k3,k4)/(3d0*za(k1,k2)*zb(k4,k1)*zb(k4,k3)) . -5d0*za(k1,k4)**2*zb(k4,k1)/(12d0*za(k1,k2)*zb(k3,k1)*zb(k4,k3)) . +za(k1,k4)**2*zb(k4,k2)/(6d0*za(k1,k2)*zb(k3,k2)*zb(k4,k3)) A1phiAQggmpmmL=A1phiAQggmpmmL+sum return end double complex function A1phiAQggmpmmR(k1,k2,k3,k4,za,zb) c--- This is an implementation of Eq. (5.10) in c--- S.~Badger, John.~M.~Campbell, R.~Keith Ellis and Ciaran Williams c--- "Analytic results for the one-loop NMHV H-qbar-q-g-g amplitude." c--- preprint DESY 09-180, FERMILAB-PUB-09-505-T, IPPP/09/86 c--- arXiv: 0910.4481 [hep-ph] implicit none include 'constants.f' include 'zprods_decl.f' include 'sprods_com.f' include 'scale.f' include 'epinv.f' include 'deltar.f' integer j,k1,k2,k3,k4 double complex VR,A0phiAQggmpmm,lnrat,zab2,Lsm1,Lsm1_2mht double complex sum,l12,coef3m1423, & S1,S2,K1DK2,a1,a2,a3,a4,gamma,factor,I3m, & BGRL1,BGRL2hat double precision s12,s13,s14,s23,s24,s34,s123,s234,s124,s134,mhsq zab2(k1,k2,k3,k4)=za(k1,k2)*zb(k2,k4)+za(k1,k3)*zb(k3,k4) s12=s(k1,k2) s13=s(k1,k3) s14=s(k1,k4) s23=s(k2,k3) s24=s(k2,k4) s34=s(k3,k4) mhsq=s12+s13+s14+s23+s24+s34 s123=s12+s13+s23 s124=s12+s14+s24 s134=s13+s14+s34 s234=s23+s24+s34 l12=lnrat(musq,-s12) VR=-epinv**2-epinv*l12-0.5d0*l12**2 . -3d0/2d0*(epinv+l12)-7d0/2d0-deltar/2d0 A1phiAQggmpmmR=A0phiAQggmpmm(k1,k2,k3,k4,za,zb)*VR sum= & +zb(k1,k2)**2*zab2(k4,k1,k2,k3)**2/(zb(k1,k3)**3*zb(k2,k3)*s123) & *Lsm1(-s12,-s123,-s23,-s123) & +zab2(k3,k1,k4,k2)**2/(zb(k1,k4)*zb(k2,k4)*s124) & *Lsm1(-s14,-s124,-s12,-s124) & -zab2(k1,k3,k4,k2)**2/(zb(k2,k3)*zb(k3,k4)*zab2(k1,k2,k3,k4)) & *Lsm1_2mht(s14,s234,s23,mhsq) & +s134**2/(zb(k1,k4)*zb(k3,k4)*zab2(k2,k1,k4,k3)) & *Lsm1_2mht(s23,s134,s14,mhsq) C-----Now deal with the 14-23 case C-----K1=-(p1+p2+p3+p4) C-----K2=-(p1+p4) C K1flat=gamma/(gamma**2-S1*S2)*(gamma*K1-S1*K2) C K1flat=gamma/(gamma**2-S1*S2)*((S1-gamma)*(p1+p4)-gamma*((p2+p3)) C----solve for gamma_+ and gamma_- S1=dcmplx(mhsq) S2=dcmplx(s14) K1DK2=dcmplx(s14+0.5d0*(s12+s13+s24+s34)) C-gamma+ = K1DK2+sqrt(K1DK2**2-S1*S2) C-gamma- = K1DK2-sqrt(K1DK2**2-S1*S2) coef3m1423=czip gamma=K1DK2+sqrt(K1DK2**2-S1*S2) do j=1,2 C -- calculate the projections of K1 flat on k1,k2,k3,k4 called a1,a2,a3,a4 factor=gamma/(gamma**2-S1*S2) a1=factor*(S1-gamma) a4=a1 a3=-factor*gamma a2=a3 C=-- The result for the 14-23 coefficient is c -za(k1,k4)^2*za(k3,k1f)^2*ga^-1*S1^2*[ga-S1]^-1 c + iza(k1,k1f)*iza(k2,k1f) * c which we can rewrite as c -za(k1,k4)^2*zab2(k3,k1f,k1)*zab2(k3,k1f,k2)*S1^2 c /(2*k1.k1f^-1)/*2*k2.k1f^-1*ga^-1*[ga-S1]^-1 C---- NB Factor of 1/2 added over and above the form, to get numerical agreement coef3m1423=coef3m1423 & -mhsq**2*za(k1,k4)**2/(2d0*gamma*(gamma-mhsq)) & *(a2*za(k3,k2)*zb(k2,k1)+a4*za(k3,k4)*zb(k4,k1)) ! *zab2(k3,k1f,k1) & *(a1*za(k3,k1)*zb(k1,k2)+a4*za(k3,k4)*zb(k4,k2)) ! *zab2(k3,k1f,k2) * /(a2*s12+a3*s13+a4*s14) ! (2*k1.k1f)^-1* * /(a1*s12+a3*s23+a4*s24) ! (2*k2.k1f)^-1* C----switch to other solution gamma=2*K1DK2-gamma enddo sum=sum-coef3m1423*I3m(mhsq,s14,s23) sum=sum & -0.5d0*(za(k1,k4)*zb(k1,k2)*zab2(k3,k1,k2,k4))**2 & /(zb(k1,k4)*zb(k2,k4)*s124) & *BGRL2hat(s124,s12) & +2d0*za(k3,k4)*zab2(k3,k1,k4,k2)/zb(k1,k4) & *BGRL1(s124,s12) & +0.5d0*zab2(k3,k1,k4,k2)**2/(zb(k1,k4)*zb(k2,k4)*s124) & *lnrat(-s124,-s12) & -0.5d0*(za(k1,k4)*zb(k2,k4)*s234)**2 & /(zb(k2,k3)*zb(k3,k4)*zab2(k1,k2,k3,k4)) & *BGRL2hat(s234,s23) & -2d0*za(k3,k4)*zab2(k1,k3,k4,k2)/zb(k3,k4) & *BGRL1(s234,s23) & +0.5d0*zab2(k1,k3,k4,k2)**2 & /(zb(k2,k3)*zb(k3,k4)*zab2(k1,k2,k3,k4)) & *lnrat(-s234,-s23) &-0.5d0*(za(k1,k2)*zb(k1,k2)*zab2(k4,k2,k3,k1))**2*zb(k2,k3) & /(zb(k1,k3)**3*s123) & *BGRL2hat(s123,s23) & +2d0*za(k1,k3)*zb(k1,k2)*zab2(k4,k1,k2,k3)*zab2(k4,k2,k3,k1) & /(za(k2,k3)*zb(k1,k3)**2*zb(k2,k3)) & *BGRL1(s123,s23) & +(-2d0*za(k1,k3)*zb(k1,k2)*zab2(k4,k1,k2,k3)*zab2(k4,k2,k3,k1) & /(zb(k1,k3)**2*za(k2,k3)*zb(k2,k3)*s123) & +0.5d0*zab2(k4,k2,k3,k1)**2*zb(k2,k3) & /(zb(k1,k3)**3*s123)) & *lnrat(-s123,-s23) & -0.5d0*(za(k1,k3)*zb(k1,k2)*zab2(k4,k1,k2,k3))**2 & /(zb(k1,k3)*zb(k2,k3)*s123) & *BGRL2hat(s123,s12) & +za(k3,k4)*zb(k1,k2)*zab2(k4,k1,k2,k3) & *(-2d0*za(k1,k3)*zb(k1,k3)-za(k2,k3)*zb(k2,k3)) & /(za(k2,k3)*zb(k1,k3)**2*zb(k2,k3)) & *BGRL1(s123,s12) & +zb(k1,k2)*zab2(k4,k1,k2,k3) & *(za(k2,k3)*zab2(k4,k1,k3,k2)+2d0*za(k1,k3)*zab2(k4,k2,k3,k1)) & /(zb(k1,k3)**2*za(k2,k3)*zb(k2,k3)*s123) & *lnrat(-s123,-s12) A1phiAQggmpmmR=A1phiAQggmpmmR+sum c--- now add the rational pieces sum= .-(za(k2,k4)**2*zb(k2,k1)**2)/(2d0*za(k2,k3)*zb(k3,k1)**3) .+(zab2(k4,k1,k2,k3)**2*zb(k2,k1)**2) . /(2d0*s123*zb(k3,k1)**3*zb(k3,k2)) .-(za(k1,k4)**2*zb(k2,k1))/(2*za(k1,k2)*zb(k3,k1)*zb(k3,k2)) .+(zb(k2,k1)*(za(k1,k3)**2*za(k2,k3) . *zab2(k4,k1,k2,k3)**2*zb(k3,k1)**2 .+za(k1,k2)**3*zab2(k4,k2,k3,k1)**2*zb(k2,k1)*zb(k3,k2))) . /(4d0*s123**2*za(k1,k2)*za(k2,k3)*zb(k3,k1)**3*zb(k3,k2)) .+zab2(k3,k1,k4,k2)**2/(2d0*s124*zb(k4,k1)*zb(k4,k2)) .-(za(k1,k3)**2*zb(k2,k1))/(2d0*za(k1,k2)*zb(k4,k1)*zb(k4,k2)) .+(za(k1,k4)**2*zab2(k3,k1,k2,k4)**2*zb(k2,k1)) . /(4d0*s124**2*za(k1,k2)*zb(k4,k1)*zb(k4,k2)) .-(za(k1,k3)*za(k1,k4)*zb(k4,k2))/(2d0*zab2(k1,k2,k3,k4)*zb(k4,k3)) .-(s234*za(k1,k4)**2*zb(k4,k2)**2) . /(4d0*za(k2,k3)*zab2(k1,k2,k3,k4)*zb(k3,k2)**2*zb(k4,k3)) .-(za(k1,k4)**2*zb(k4,k2)**2) . /(2d0*zab2(k1,k2,k3,k4)*zb(k3,k2)*zb(k4,k3)) A1phiAQggmpmmR=A1phiAQggmpmmR+sum return end double complex function A1phiAQggmpmmF(k1,k2,k3,k4,za,zb) c--- This is an implementation of Eq. (5.13) in c--- S.~Badger, John.~M.~Campbell, R.~Keith Ellis and Ciaran Williams c--- "Analytic results for the one-loop NMHV H-qbar-q-g-g amplitude." c--- preprint DESY 09-180, FERMILAB-PUB-09-505-T, IPPP/09/86 c--- arXiv: 0910.4481 [hep-ph] implicit none include 'constants.f' include 'zprods_decl.f' include 'sprods_com.f' include 'scale.f' include 'epinv.f' integer k1,k2,k3,k4 double complex A0phiAQggmpmm,lnrat double complex l12,zab2,BGRL1,BGRL2hat,BGRL3hat double precision s12,s13,s14,s23,s24,s123,s124 zab2(k1,k2,k3,k4)=za(k1,k2)*zb(k2,k4)+za(k1,k3)*zb(k3,k4) s12=s(k1,k2) s13=s(k1,k3) s14=s(k1,k4) s23=s(k2,k3) s24=s(k2,k4) s123=s12+s13+s23 s124=s12+s14+s24 l12=lnrat(musq,-s12) A1phiAQggmpmmF=A0phiAQggmpmm(k1,k2,k3,k4,za,zb) . *(-2d0/3d0*(epinv+l12)-10d0/9d0) & +2d0/3d0*za(k1,k3)*zab2(k4,k1,k3,k2)**2 & /(za(k1,k2)*zb(k1,k2)*zb(k2,k3)*s123)*lnrat(-s123,-s12) & -2d0/3d0*(s24-s124)*zab2(k3,k1,k4,k2)**2 & /(za(k1,k2)*zb(k1,k4)*zb(k2,k4)*zb(k1,k2)*s124)*lnrat(-s124,-s12) & -2d0/3d0*za(k1,k3)*zab2(k4,k1,k3,k2)**2 & /(za(k1,k2)*zb(k2,k3)*zb(k1,k2))*BGRL1(s123,s12) & +2d0/3d0*za(k1,k4)*zab2(k3,k1,k4,k2)**2 & /(za(k1,k2)*zb(k2,k4)*zb(k1,k2))*BGRL1(s124,s12) & +za(k1,k3)*za(k3,k4)*zab2(k4,k1,k3,k2)/3d0*BGRL2hat(s123,s12) & +za(k1,k4)*za(k3,k4)*zab2(k3,k1,k4,k2)/3d0*BGRL2hat(s124,s12) & +2d0/3d0*za(k1,k3)**2*za(k3,k4)*zb(k1,k2)*zab2(k4,k1,k2,k3) & *BGRL3hat(s123,s12) & +2d0/3d0*za(k1,k4)**2*za(k3,k4)*zb(k1,k2)*zab2(k3,k1,k2,k4) & *BGRL3hat(s124,s12) A1phiAQggmpmmF=A1phiAQggmpmmF & -za(k1,k3)*za(k3,k4)*zab2(k4,k1,k3,k2) & /(6d0*za(k1,k2)*zb(k1,k2)*s123) & -za(k1,k4)*za(k3,k4)*zab2(k3,k1,k4,k2) & /(6d0*za(k1,k2)*zb(k1,k2)*s124) & +( & -za(k1,k3)*za(k1,k4)*zb(k1,k2)*zb(k3,k4)) & /(3d0*za(k1,k2)*zb(k1,k2)*zb(k3,k4)**2) return end