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240 lines
12 KiB
240 lines
12 KiB
!
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! SPDX-License-Identifier: GPL-3.0-or-later
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! Copyright (C) 2019-2022, respective authors of MCFM.
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!
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function virt_mm(mQ,ig,is,ie,in,ic,p)
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implicit none
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include 'types.f'
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complex(dp):: virt_mm
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c***********************************************************************
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c Author: F. Tramontano *
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c December, 2008 *
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c***********************************************************************
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c---- One-loop -- helicity amplitude for W+c production
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c---- hQ=-1 with Q(mu)=Q1(mu)+mQ^2/2/Q.g*g(mu)
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c---- hg=-1 with s(mu) as gauge vector
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c for nwz=+1
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c f(-p1)+f(-p2)--> W^+(n(p3)+e^+(p4)) + Qbar(p5)
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c For nwz=-1
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c f(-p1)+f(-p2)--> W^-(e^-(p3)+nbar(p4))+ Q(p5)
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c----
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include 'constants.f'
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include 'mxpart.f'
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include 'epinv.f'
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include 'epinv2.f'
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include 'b0.f'
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include 'scheme.f'
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include 'scale.f'
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include 'zprods_decl.f'
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include 'nwz.f'
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integer:: is,ig,ic,ie,in,nu,jpart
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real(dp):: p(mxpart,4),q(mxpart,4)
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real(dp):: dot,taucg,taugs,taucs,msq,mQ
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real(dp):: qsq,tcg,tcs,qsqhat,qgs,qcg,qcs,cgs1
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real(dp):: ddilog,epin,epin2,xlog
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complex(dp):: smm,lomm
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complex(dp):: amm1,amm2,amm3,amm4,amm5
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complex(dp):: fq2m2,fc002,fc00,ffc00,ffc002,fI3me
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complex(dp):: ffcg1,ffcg3,ffcs1,ffcs2,fun1,fun2,fun4
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complex(dp):: fL6m1,fL6m2,fL6m3,L6m1,L6m2,L6m3
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complex(dp):: lnrat,C0fa2m,C0fb2m,I3me
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c scheme='dred'
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msq=mQ**2
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xlog=log(musq/msq)
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epin=epinv+xlog
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epin2=epinv*epinv2+epinv*xlog+half*xlog**2
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taugs=+two*dot(p,is,ig)
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taucs=+two*dot(p,ic,is)
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taucg=+two*dot(p,ic,ig)
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qsqhat=taucs+taucg+taugs
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qsq=qsqhat+msq
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tcg=taucg+msq
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tcs=taucs+msq
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qgs=qsqhat-taugs
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qcg=qsqhat-taucg
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qcs=qsqhat-taucs
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cgs1=taucs-msq*taugs/taucg
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fq2m2=-msq/qsq+lnrat(-qsqhat,msq)*msq*qsqhat/qsq**2
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ffcs1=fun4(tcs,qsq,msq)
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ffcg1=fun1(tcg,qsq,msq)
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ffcg3=fun2(qsq,tcg,msq)
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ffcs2=fun2(tcs,qsq,msq)
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fL6m1=L6m1(taucg,taucs,taugs,msq,qsq)
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fL6m2=L6m2(taucg,taucs,taugs,msq,qsq)
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fL6m3=L6m3(taucg,taucs,taugs,msq,qsq)
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fI3me=I3me(msq,taugs,qsq)
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ffc00=fc00(msq,taugs,qsq)
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ffc002=fc002(msq,taugs,qsq)
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do nu=1,4
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do jpart=1,5
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q(jpart,nu)=p(jpart,nu)
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if (jpart==ic) q(ic,nu)=p(ic,nu)-msq/taucg*p(ig,nu)
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enddo
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enddo
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if (nwz == -1) then
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call spinoru(5,q,za,zb)
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else
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call spinoru(5,q,zb,za)
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endif
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amm1=za(ig,ie)*zb(ig,in)/za(is,ic)/zb(ig,ic)**2
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amm2=za(ig,ie)*zb(is,in)/zb(ig,ic)
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amm3=za(is,ie)*zb(is,in)/za(is,ic)/zb(ig,ic)**2
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amm4=za(ie,ic)*zb(is,in)*zb(is,ic)/zb(ig,is)/zb(ig,ic)
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amm5=-amm1-amm3
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smm= - 1.D0/2.D0*taucs*taucg**(-2)*mQ**2*xn**(-1)*qcs*qcg*
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& cgs1**(-1)*amm1*fL6m1 - 1.D0/2.D0*taucs*taucg**(-2)*mQ**2*
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& xn**(-1)*qcs*cgs1**(-1)*amm2*fL6m1 - 1.D0/2.D0*taucs*
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& taucg**(-2)*mQ**2*xn**(-1)*qcs**2*cgs1**(-1)*amm3*fL6m1 - 1.D0
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& /2.D0*taucs*taucg**(-1)*taugs**(-1)*xn**(-1)*qcs*amm2*fL6m1
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& - 1.D0/2.D0*taucs*taucg**(-1)*taugs**(-1)*xn**(-1)*qcs**2*
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& amm3*fL6m1 - 1.D0/2.D0*taucs*taucg**(-1)*qsqhat*xn**(-1)*amm1
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& *fL6m1 + taucs*taucg*taugs**(-1)*cf*amm3 + 1.D0/2.D0*taucs*
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& taucg*taugs**(-1)*xn*amm3*fL6m3 + 1.D0/2.D0*taucs*taugs**(-1)
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& *mQ**2*xn**(-1)*amm1*fL6m2 + taucs*taugs**(-1)*cf*qcs*amm5*
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& fq2m2 + 1.D0/2.D0*taucs*taugs**(-1)*cf*qcg*amm5*fq2m2 - 4.D0*
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& taucs*qsq**(-1)*mQ**2*cf*amm1 - 2.D0*taucs*qsq**(-1)*mQ**2*
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& xn**(-1)*amm1 + 2.D0*taucs*qsq**(-1)*mQ**2*xn*amm1 + 4.D0*
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& taucs*qsq**(-1)*cf*cgs1*amm1 + 2.D0*taucs*qsq**(-1)*xn**(-1)*
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& cgs1*amm1 - 2.D0*taucs*qsq**(-1)*xn*cgs1*amm1 - 4.D0*taucs*cf
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& *amm1*fq2m2
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smm = smm + 3.D0*taucs*cf*amm1 + taucs*cf*amm3 - 2.D0*taucs*
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& xn**(-1)*amm1*ffcs2 - 2.D0*taucs*xn**(-1)*amm1*fq2m2 + 2.D0*
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& taucs*xn*amm1*fq2m2 - taucs*xn*amm1 - 1.D0/2.D0*taucs**2*
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& taugs**(-1)*cf*amm1 - 1.D0/2.D0*taucs**2*taugs**(-1)*cf*amm3
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& + 2.D0*taucg**(-1)*taugs*mQ**2*cf*amm3*ffcg3 - 2.D0*
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& taucg**(-1)*mQ**2*cf*amm2*ffcg3 - taucg**(-1)*mQ**2*xn*amm2*
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& fL6m3 - 1.D0/2.D0*taucg*taugs**(-1)*tcs*xn**(-1)*amm3*fL6m2
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& - 1.D0/2.D0*taucg*taugs**(-1)*xn**(-1)*amm2*fL6m2 - taucg*
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& qsq**(-1)*mQ**2*cf*amm3*ffcg3 + 1.D0/2.D0*taugs**(-1)*qsq*
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& xn**(-1)*amm2*fL6m2 + 1.D0/2.D0*taugs**(-1)*mQ**2*xn**(-1)*
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& qcs*amm3*fL6m2 + taugs**(-1)*cf*cgs1*amm2 - taugs**(-1)*
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& xn**(-1)*cgs1*amm2*fL6m2 + 1.D0/2.D0*taugs**(-1)*xn*qcg*amm2*
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& fL6m3 + taugs*tcs*xn**(-1)*amm1*ffcs1 + taugs*qsq**(-1)*mQ**2
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& *cf*amm3*ffcg1 - 2.D0*taugs*qsq**(-1)*mQ**2*cf*amm3*ffcg3 +
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& taugs*xn**(-1)*amm1*ffcs2 + tcg**(-1)*mQ**4*cf*amm3 -
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& qsq**(-1)*mQ**2*cf*amm2*ffcg3
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smm = smm - mQ**2*cf*amm1 - 2.D0*mQ**2*cf*amm3*ffcg3 - 3.D0*mQ**2
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& *cf*amm3 - mQ**2*xn**(-1)*amm1*ffcs2 - mQ**2*xn**(-1)*amm3*
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& ffcg3 - 1.D0/2.D0*mQ**2*xn*qcs*cgs1**(-1)*amm3*fL6m3 - 1.D0/2.
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& D0*mQ**2*xn*qcg*cgs1**(-1)*amm1*fL6m3 - 1.D0/2.D0*mQ**2*xn*
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& cgs1**(-1)*amm2*fL6m3 + 1.D0/2.D0*mQ**2*xn*amm1*fL6m3 - mQ**2
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& *xn*amm3*fL6m3 - xlog*b0*amm2 - xlog*b0*amm4 + 3.D0/2.D0*epin
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& *cf*amm2 + 3.D0/2.D0*epin*cf*amm4 + epin*b0*amm2 + epin*b0*
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& amm4 - 1.D0/2.D0*epin*xn**(-1)*amm2 - 1.D0/2.D0*epin*xn**(-1)
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& *amm4 + 1.D0/2.D0*epin*xn*amm2 + 1.D0/2.D0*epin*xn*amm4 - 1.D0
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& /2.D0*epin2*xn**(-1)*amm2 - 1.D0/2.D0*epin2*xn**(-1)*amm4 + 3.
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& D0/2.D0*epin2*xn*amm2 + 3.D0/2.D0*epin2*xn*amm4 + 1.D0/2.D0*
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& cf*qcs*amm5*fq2m2 + 5.D0/2.D0*cf*amm2 + 5.D0/2.D0*cf*amm4 - 1.
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& D0/2.D0*xn**(-1)*pisqo6*amm2 - 1.D0/2.D0*xn**(-1)*pisqo6*amm4
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& - xn**(-1)*amm2*ffcs2 - xn**(-1)*amm2*fL6m2 - xn**(-1)*amm2
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& + 1.D0/2.D0*xn*pisqo6*amm2
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smm=smm+ 1.D0/2.D0*xn*pisqo6*amm4 - ddilog(
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& msq**(-1)*tcs)*xn**(-1)*amm2 - ddilog(msq**(-1)*tcs)*xn**(-1)*
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& amm4 + ddilog(msq**(-1)*tcg)*xn*amm2 + ddilog(msq**(-1)*tcg)*
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& xn*amm4 - lnrat( - taucs,msq)*taucs*tcs**(-1)*mQ**2*xn**(-1)*
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& amm1 - 2.D0*lnrat( - taucs,msq)*taucs**2*tcs**(-1)*xn**(-1)*
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& amm1 + lnrat( - taucs,msq)*tcs**(-1)*mQ**2*xn**(-1)*amm2 -
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& lnrat( - taucs,msq)*tcs*xn**(-1)*amm3 + lnrat( - taucs,msq)*
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& epin*xn**(-1)*amm2 + lnrat( - taucs,msq)*epin*xn**(-1)*amm4
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& - lnrat( - taucs,msq)**2*xn**(-1)*amm2 - lnrat( - taucs,msq)
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& **2*xn**(-1)*amm4 - 2.D0*lnrat( - taucg,msq)*taucg*tcg**(-1)*
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& mQ**2*cf*amm1 - lnrat( - taucg,msq)*taucg*tcg**(-1)*mQ**2*
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& xn**(-1)*amm1 + lnrat( - taucg,msq)*taucg**2*tcg**(-2)*mQ**2*
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& cf*amm3 - 2.D0*lnrat( - taucg,msq)*tcg**(-1)*mQ**2*cf*qcs*
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& amm3 - 2.D0*lnrat( - taucg,msq)*tcg**(-1)*mQ**4*cf*amm1 -
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& lnrat( - taucg,msq)*tcg**(-1)*mQ**4*xn**(-1)*amm1 - lnrat( -
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& taucg,msq)*epin*xn*amm2 - lnrat( - taucg,msq)*epin*xn*amm4 +
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& lnrat(
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& - taucg,msq)**2*xn*amm2 + lnrat( - taucg,msq)**2*xn*amm4 -
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& lnrat( - taugs,msq)*taucs*taugs**(-1)*cf*amm2 + lnrat( -
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& taugs,msq)*taucs*cf*amm5 + lnrat( - taugs,msq)*taucs*xn**(-1)
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& *amm3 + lnrat( - taugs,msq)*taucs**2*taugs**(-1)*cf*amm3 + 1.D
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& 0/2.D0*lnrat( - taugs,msq)*taucs**2*mQ**(-2)*cf*amm5 + 1.D0/2.
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& D0*lnrat( - taugs,msq)*taugs*cf*amm5 - lnrat( - taugs,msq)*
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& mQ**2*cf*amm3 - lnrat( - taugs,msq)*mQ**2*cf*amm5 - lnrat( -
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& taugs,msq)*epin*xn*amm2 - lnrat( - taugs,msq)*epin*xn*amm4 +
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& 1.D0/2.D0*lnrat( - taugs,msq)*xn**(-1)*qcg*amm5 - lnrat( -
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& taugs,msq)*xn*amm2 + 1.D0/2.D0*lnrat( - taugs,msq)**2*xn*amm2
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& + 1.D0/2.D0*lnrat( - taugs,msq)**2*xn*amm4 - 3.D0*lnrat( -
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& qsqhat,msq)*taucs*taucg*taugs**(-1)*qsq**(-1)*qsqhat*cf*amm3
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& - 2.D0*lnrat( - qsqhat,msq)*taucs*taugs**(-1)*qsq**(-1)*
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& mQ**2*qsqhat*cf*amm3 + 3.D0*lnrat( - qsqhat,msq)*taucs*
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& qsq**(-1)*qsqhat*cf*amm3 + 2.D0*lnrat( - qsqhat,msq)*taucs*
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& qsq**(-1)*qsqhat*cf*amm5
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smm = smm + 3.D0/2.D0*lnrat( - qsqhat,msq)*taucs*qsq**(-1)*qsqhat
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& *xn*amm1 - lnrat( - qsqhat,msq)*taucs**2*taugs**(-1)*qsq**(-1)*
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& qsqhat*cf*amm3 - 1.D0/2.D0*lnrat( - qsqhat,msq)*taucs**2*
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& taugs**(-1)*qsq**(-1)*qsqhat*cf*amm5 - 1.D0/2.D0*lnrat( -
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& qsqhat,msq)*taucs**2*qsq**(-1)*mQ**(-2)*qsqhat*cf*amm5 +
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& lnrat( - qsqhat,msq)*taucg**(-1)*taugs*qsq**(-1)*mQ**2*qsqhat
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& *cf*amm3 - lnrat( - qsqhat,msq)*taugs**(-1)*qsq**(-1)*qsqhat*
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& cf*qcg*amm2 - lnrat( - qsqhat,msq)*taugs**(-1)*qsq**(-1)*
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& qsqhat*cf*cgs1*amm2 - lnrat( - qsqhat,msq)*taugs*qsq**(-1)*
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& qsqhat*cf*amm3 - 3.D0/2.D0*lnrat( - qsqhat,msq)*taugs*
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& qsq**(-1)*qsqhat*cf*amm5 - 1.D0/2.D0*lnrat( - qsqhat,msq)*
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& taugs*qsq**(-1)*qsqhat*xn*amm1 + 2.D0*lnrat( - qsqhat,msq)*
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& qsq**(-1)*mQ**2*qsqhat*cf*amm3 - 3.D0*lnrat( - qsqhat,msq)*
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& qsq**(-1)*mQ**2*qsqhat*cf*amm5 + 3.D0/2.D0*lnrat( - qsqhat,
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& msq)*qsq**(-1)*mQ**2*qsqhat*xn**(-1)*amm1 - 1.D0/2.D0*lnrat(
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& - qsqhat,msq)*qsq**(-1)*mQ**2*qsqhat*xn*amm1
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smm = smm + lnrat( - qsqhat,msq)*qsq**(-1)*qsqhat*xn**(-1)*qcg*
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& amm1 + 1.D0/2.D0*lnrat( - qsqhat,msq)*qsq**(-1)*qsqhat*xn**(-1)*
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& qcg*amm3 + lnrat( - qsqhat,msq)*qsq**(-1)*qsqhat*xn**(-1)*
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& amm2 - 2.D0*C0fb2m(tcg,msq)*taucs**(-1)*taucg**(-1)*taugs*
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& mQ**4*xn**(-1)*amm2 + C0fb2m(tcg,msq)*taucs**(-1)*taucg*mQ**2
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& *xn**(-1)*cgs1*amm3 + C0fb2m(tcg,msq)*taucs**(-1)*mQ**2*
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& xn**(-1)*qcg*amm2 - C0fb2m(tcg,msq)*taucs**(-1)*mQ**4*
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& xn**(-1)*amm2 + 2.D0*C0fa2m(tcs,qsq,msq)*taucs**(-1)*
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& taucg**(-2)*mQ**4*xn**(-1)*qcs**2*amm2 - C0fa2m(tcs,qsq,msq)*
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& taucs**(-1)*taucg**(-1)*mQ**2*xn**(-1)*qcs**2*amm2 - C0fa2m(
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& tcs,qsq,msq)*taucs**(-1)*taucg**(-1)*mQ**4*xn**(-1)*qcs*amm2
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& - C0fa2m(tcs,qsq,msq)*taucs**(-1)*mQ**2*xn**(-1)*qcs*cgs1*
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& amm3 + C0fa2m(tcs,qsq,msq)*taucs**(-1)*mQ**2*xn**(-1)*qcs*
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& amm2 - 2.D0*C0fa2m(tcs,qsq,msq)*taucs*mQ**2*xn**(-1)*amm1 +
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& C0fa2m(tcs,qsq,msq)*taucg**(-1)*taugs*mQ**4*xn**(-1)*amm1 - 2.
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& D0*C0fa2m(tcs,qsq,msq)*taucg**(-1)*mQ**2*xn**(-1)*qcs*amm2
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smm = smm - C0fa2m(tcs,qsq,msq)*mQ**2*xn**(-1)*amm2 - 18.D0*
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& ffc002*taucs*taugs**(-1)*cf*qcs*amm5 + 6.D0*ffc002*taucs**2*
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& taugs**(-1)*mQ**(-2)*cf*qgs*amm5 + 6.D0*ffc002*taucg*
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& taugs**(-1)*cf*qcg*amm5 + 12.D0*ffc002*mQ**2*cf*amm5 + 24.D0*
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& ffc00*taucs*taucg*taugs**(-1)*cf*amm3 + 4.D0*ffc00*taucs*
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& taugs**(-2)*cf*qgs*amm2 + 4.D0*ffc00*taucs*taugs**(-1)*tcs*cf
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& *amm1 + 16.D0*ffc00*taucs*taugs**(-1)*mQ**2*cf*amm3 + 12.D0*
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& ffc00*taucs*taugs**(-1)*cf*qcs*amm1 + 8.D0*ffc00*taucs*
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& taugs**(-1)*cf*amm2 + 12.D0*ffc00*taucs*cf*amm3 - 4.D0*ffc00*
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& taucs**2*taugs**(-2)*qsqhat*cf*amm3 + 8.D0*ffc00*taucs**2*
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& taugs**(-1)*cf*amm3 + 12.D0*ffc00*taucg*taugs**(-1)*mQ**2*cf*
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& amm1 - 8.D0*ffc00*taucg*taugs**(-1)*mQ**2*cf*amm3 - 4.D0*
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& ffc00*taucg*taugs**(-1)*cf*amm2 - 16.D0*ffc00*taugs**(-1)*
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& mQ**2*cf*qcs*amm1 - 8.D0*ffc00*taugs**(-1)*mQ**2*cf*amm2 + 2.D
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& 0*ffc00*taugs**(-1)*xn**(-1)*qgs*qcg*amm5 - 4.D0*ffc00*tcg*
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& xn**(-1)*amm5
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smm = smm - 28.D0*ffc00*mQ**2*cf*amm3 + fI3me*taucs*mQ**2*
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& xn**(-1)*amm3 - 3.D0*fI3me*taucs*mQ**2*xn*amm3 - fI3me*taucs*
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& xn*amm2 - fI3me*taucg**(-1)*taugs*mQ**4*xn*amm1 + 2.D0*fI3me*
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& taucg**(-1)*taugs*mQ**4*xn*amm3 - 2.D0*fI3me*taucg**(-1)*
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& mQ**2*xn*cgs1*amm2 - fI3me*taucg*mQ**2*xn**(-1)*amm3 - fI3me*
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& taugs*mQ**2*xn**(-1)*amm1 - 2.D0*fI3me*taugs*mQ**2*xn**(-1)*
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& amm3 + 2.D0*fI3me*mQ**2*cf*amm2 - fI3me*mQ**2*xn*amm2 + fI3me
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& *xn*cgs1*amm2
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lomm =-(za(ig,ie)*zb(ig,is)+za(ie,ic)*zb(is,ic))*zb(is,in)
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& /zb(ig,is)/zb(ig,ic)
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c--- include finite counterterm to go from DR to MSbar scheme
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c--- alphas(DR) = alphas(MSbar) * (1+ (Nc / 6) * alphas(MSbar) / (2*pi))
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smm=smm + lomm * xn/six
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c--- include finite counterterm due to FDH scheme
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c--- gw = gw * ( 1 - 2 * cf * alphas(MSbar) / (2*pi))
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smm=smm - lomm * cf * two
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if (scheme == 'tH-V') then
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smm = smm - lomm * (cf/two + xn/six)
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endif
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virt_mm=smm
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return
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end
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