subroutine Aamp_pmp(q,mc,ms,Apmp) c--- u + g -> c + s + d (t-channel single-charm) ************************************************************************ * * * AUTHORS: R. FREDERIX AND F. TRAMONTANO * * DATE : 12/17/2008 * * * ************************************************************************ implicit none include 'constants.f' include 'zprods_com.f' include 'epinv.f' include 'stopf1inc.f' double precision q(mxpart,4),dot,cDs,gDs,cDg,mc,ms, . mc2,ms2,qsq,s,t,u,xsn,xsd,xs double complex trc,trg,trs,trsgc,zpmp,Apmp mc2=mc**2 ms2=ms**2 cDs=dot(q,3,4)+mc2*dot(q,4,2)/2d0/dot(q,3,2) . +ms2*dot(q,3,2)/2d0/dot(q,4,2) cDg=dot(q,3,2) gDs=dot(q,4,2) qsq=mc2+ms2+2d0*cDs+2d0*cDg+2d0*gDs s=ms2+2d0*gDs t=mc2+2d0*cDg u=mc2+ms2+2d0*cDs xsn=(1d0-dsqrt(1d0-4d0*ms*mc/(u-(ms-mc)**2))) xsd=(1d0+dsqrt(1d0-4d0*ms*mc/(u-(ms-mc)**2))) xs=-xsn/xsd trg=2d0*za(5,2)*zb(2,1) trs=2d0*za(5,4)*zb(4,1)+ms**2*za(5,2)*zb(2,1)/gDs trc=2d0*za(5,3)*zb(3,1)+mc**2*za(5,2)*zb(2,1)/cDg trsgc=2d0*zb(1,4)*za(4,2)*zb(2,3)*za(3,5) zpmp=za(2,4)**2*zb(4,3) Apmp = ms2*(trsgc*(gDs*(cDg*(gDs+2*cDs+cDg)-mc2*gDs)-ms2*cDg**2)+ & cDg*gDs*(cDg*(ms2*trg-2*(trs+trc)*gDs)+mc2*trg*gDs))*tr3Xs/(cDg & *gDs**2) Apmp = (mc2*trsgc*(-mc2*gDs**2+cDg**2*(gDs-ms2)+2*cDg*cDs*gDs)-cD & g*gDs*(trg*(-mc2**2*gDs+2*cDg**2*cDs+cDg**3)+2*mc2*trc*cDg*gDs) & )*tr3Xc/cDg**3+Apmp Apmp = Apmp-(cDg**2*(4*trc*gDs**2-2*trsgc*gDs+ms2*trsgc)+mc2*trs & gc*gDs**2-2*cDg*gDs*(mc2*trg*gDs+trsgc*cDs))*tr1Xfs/cDg**2 Apmp = (-4*trc*cDg*gDs-mc2*trsgc*gDs/cDg+2*mc2*trg*gDs-ms2*trsgc* & cDg/gDs+2*trsgc*cDs+2*trsgc*cDg)*tr1Xfc+Apmp Apmp = (cDg**3*(8*mc2*trc*gDs**2+(4*trg*cDs**2+2*mc2*(ms2*(2*trs+ & trg+(4-3*sck)*trc)-2*trsgc))*gDs-mc2*ms2*(-3*sck*trsgc+2*trsgc+ & 2*ms2*trs+3*ms2*trg))+2*mc2*cDg*gDs**2*(ms2*((trg+trc)*(gDs+ms2 & )-trs*(gDs+2*cDs+ms2-mc2))+mc2*trsgc)-mc2*cDg**2*gDs*(-2*(ms2*( & trs+trg+trc)-2*mc2*trg)*gDs+4*trsgc*cDs+ms2*(trsgc+ms2*(trg+trc & )+mc2*(4-3*sck)*trg))-mc2*ms2*(trs+trg+trc)*gDs**3*(2*gDs+2*cDs & +ms2-mc2)+6*trg*cDg**4*cDs*gDs+2*trg*cDg**5*gDs)*lVs/(mc2*cDg** & 3*gDs)/4.0d+0+Apmp Apmp = (2*cDg**3*(2*(trs+trg+trc)*gDs**2+trg*(2*cDs-ms2)*gDs+ms2* & (trsgc+mc2*(trs+trg)))+cDg**2*gDs*(mc2*trc*(2*gDs+ms2)-trsgc*(2 & *gDs+4*cDs+mc2))+mc2*cDg*gDs**2*(-2*(-trs+trg+trc)*gDs+4*trs*cD & s+trsgc-mc2*(2*trs+trg)-2*ms2*(-trs+trg+trc))+mc2*(trs+trg+trc) & *gDs**3*(2*gDs+2*cDs+ms2-mc2)+2*trg*cDg**4*gDs)*lVc/(cDg**3*gDs & )/4.0d+0+Apmp Apmp = ((mc2*(2*trg*cDg-trsgc)/cDg**2/2.0d+0-2*trc)*gDs-ms2*trsgc & /gDs/2.0d+0+trsgc*cDs/cDg+trsgc)*lRs2+Apmp Apmp = epinv*(trsgc*(cDg**2*(gDs*(4*lRs1+4*lRc1-2)-ms2*(2*lRs1+2* & lRc1-2*sck+1))+2*cDg*cDs*gDs*(2*lRs1+2*lRc1-1)+mc2*gDs**2*(-2*l & Rs1-2*lRc1+1))-2*cDg*(2*trc*cDg-mc2*trg)*gDs*(gDs*(2*lRs1+2*lRc & 1-1)+ms2*(sck-1)))/(cDg**2*gDs)/4.0d+0+Apmp Apmp = ((mc2*(2*trg*cDg-trsgc)/cDg**2/2.0d+0-2*trc)*gDs-ms2*trsgc & /gDs/2.0d+0+trsgc*cDs/cDg+trsgc)*lRc2+Apmp Apmp = (cDg**3*(32*mc2*(2*trs+3*trc)*gDs**4+4*mc2*(36*trg*cDs-12* & trsgc+ms2*(16*trs-12*trg+(41-15*sck)*trc))*gDs**3+(-72*trg*cDs* & *3+36*mc2*ms2*(-trs+4*trg+trc)*cDs+2*mc2*ms2*(15*sck*trsgc+ms2* & (11*trs-9*trg-15*sck*trc+13*trc)+10*mc2*trs+19*mc2*trg))*gDs**2 & +ms2*(-36*trg*cDs**3+18*mc2*(trsgc+ms2*(-trs+3*trg+trc))*cDs+mc & 2*ms2*(15*(sck+2)*trsgc+ms2*(6*(trs+trg)-16*trc)+mc2*(10*trs+37 & *trg)))*gDs+9*mc2*ms2**2*(trsgc*(cDs+ms2)+ms2*trg*(cDs+mc2)))-m & c2*cDg**2*gDs*(2*gDs+ms2)*(4*(trs+8*trg+17*trc)*gDs**3+cDs*(36* & (trc-trs)*gDs**2+(54*trsgc+26*ms2*trg+8*ms2*trc)*gDs+9*ms2*(trs & gc+mc2*trg))+2*(-9*trsgc+5*mc2*trs-3*ms2*(-trs+6*trg+3*trc)+12* & mc2*trg)*gDs**2-ms2*(-18*trsgc+mc2*(18*trs+(15*sck-44)*trg+23*t & rc)+3*ms2*(trg+trc))*gDs+9*mc2*ms2*(trsgc+ms2*trg))-mc2*cDg*gDs & **2*(2*gDs+ms2)*(2*(-9*trsgc+2*mc2*(7*trs+2*trg+11*trc)+3*ms2*( & -trs+trg+trc))*gDs**2+3*cDs*(3*mc2*(trsgc+ms2*trg)-2*(3*trsgc+m & c2*(trs+3*trg-3*trc)+2*ms2*trs)*gDs)+(-mc2*(45*trsgc+ms2*(-12*t & rs+49*trg+22*trc))+10*mc2**2*trs+6*ms2**2*(-trs+trg+trc))*gDs+9 & *mc2*ms2*(trsgc+mc2*trg))+mc2*gDs**3*(2*gDs+ms2)*(-6*(mc-ms)*(m & s+mc)*(trs+trg+trc)*gDs**2+cDs*(9*mc2*(trsgc+mc2*trg)-6*(mc-ms) & *(ms+mc)*(trs+trg+trc)*gDs)+(3*mc2*(3*trsgc-2*ms2*(trs+trg+trc) & )+3*ms2**2*(trs+trg+trc)+mc2**2*(-7*trs+4*trg-5*trc))*gDs+9*mc2 & **2*(trsgc+ms2*trg))+cDg**4*(2*gDs+ms2)*(36*mc2*trg*gDs**2-2*(4 & 5*trg*cDs**2+mc2*ms2*(17*trs-trg+trc))*gDs+mc2*ms2*(9*trsgc+ms2 & *(-8*trs+trg-10*trc)))-72*trg*cDg**5*cDs*gDs*(2*gDs+ms2)-18*trg & *cDg**6*gDs*(2*gDs+ms2))/(mc2*cDg**3*gDs**2*(2*gDs+ms2))/1.2d+1 & +Apmp Apmp = 2*LsA*(mc2**2*trsgc*gDs**4-cDg**3*gDs*(cDs*(4*trc*gDs**2-2 & *trsgc*gDs+3*ms2*trsgc)+ms2*(trsgc+mc2*trg)*gDs)+ms2*cDg**4*(2* & (trs+trc)*gDs**2-(trsgc+ms2*trg)*gDs+ms2*trsgc)+cDg**2*gDs**2*( & 2*mc2*trc*gDs**2+mc2*(2*trg*cDs-trsgc)*gDs+2*trsgc*(cDs**2+mc2* & ms2))-mc2*cDg*gDs**3*(mc2*trg*gDs+3*trsgc*cDs))/(cDg**3*gDs**2) & +Apmp Apmp = B0cgsf*(cDg**3*(-4*mc2*(trg+2*trc)*gDs**3+(mc2*(2*(2*trg*c & Ds+trsgc)+ms2*(-2*trs-3*trg+trc))-4*trg*cDs**2)*gDs**2+(-4*trg* & cDs**3+2*mc2*ms2*(-trs+2*trg+trc)*cDs+mc2*ms2*(ms2*(2*trs+3*trg & -2*trc)+mc2*trg))*gDs+mc2*ms2*(trsgc*(cDs+ms2)+ms2*trg*(cDs+mc2 & )))-mc2*cDg**2*gDs*(4*(trg+2*trc)*gDs**3+cDs*(4*(trc-trs)*gDs** & 2-2*trsgc*gDs+ms2*(3*trg+trc)*gDs+ms2*(trsgc+mc2*trg))+(-4*trsg & c+2*mc2*(trs-trg+trc)-ms2*(-2*trs+3*trg+trc))*gDs**2-(mc2*(trsg & c+2*ms2*(trs-trg+trc))+ms2*(ms2*(trg+trc)-trsgc))*gDs+mc2*ms2*( & trsgc+ms2*trg))-cDg**4*(mc2*(-2*trg*gDs**2+ms2*(4*trs*gDs-trsgc & )+ms2**2*(trs+trc))+2*trg*cDs*gDs*(3*gDs+5*cDs))-mc2*cDg*gDs**2 & *(2*(-trsgc+2*mc2*(trs+trc)+ms2*(-trs+trg+trc))*gDs**2+cDs*(2*( & -trsgc+mc2*(trs-trg+trc)-2*ms2*trs)*gDs+mc2*(trsgc+ms2*trg))-(m & c2*(2*trsgc+ms2*(-4*trs+7*trg+4*trc))-2*ms2**2*(-trs+trg+trc)+m & c2**2*trg)*gDs+mc2*ms2*(trsgc+mc2*trg))+mc2*gDs**3*(-2*(mc-ms)* & (ms+mc)*(trs+trg+trc)*gDs**2+cDs*(mc2*(trsgc+mc2*trg)-2*(mc-ms) & *(ms+mc)*(trs+trg+trc)*gDs)+(mc2*(trsgc-2*ms2*(trs+trg+trc))+ms & 2**2*(trs+trg+trc)+mc2**2*trg)*gDs+mc2**2*(trsgc+ms2*trg))-2*tr & g*cDg**5*gDs*(gDs+4*cDs)-2*trg*cDg**6*gDs)/(mc2*cDg**3*gDs**2)/ & 4.0d+0+Apmp Apmp = tr3c00fs*(cDg*(-mc2*cDs*(8*trg*gDs**2+2*ms2*(-trs+2*trg+tr & c)*gDs+ms2*(trsgc+ms2*trg))-mc2*ms2*(-8*trc*gDs**2+(2*trsgc+mc2 & *trg-6*ms2*trc)*gDs+ms2*(trsgc+mc2*trg))+4*trg*cDs**3*gDs)+cDg* & *2*(-4*mc2*trg*gDs**2+2*(5*trg*cDs**2+mc2*ms2*(4*trs+2*trg+trc) & )*gDs+mc2*ms2*(ms2*(3*trs+2*(trg+trc))-trsgc))+mc2*ms2*gDs*(mc2 & *(trg*(2*gDs+cDs+ms2)+trs*gDs)+trsgc*(cDs+mc2))+8*trg*cDg**3*cD & s*gDs+2*trg*cDg**4*gDs)/(mc2*cDg*gDs**2)+Apmp Apmp = ls*(-cDg*((8*trg*cDs**2+4*mc2*ms2*(trg-trc))*gDs**2+2*ms2* & (2*trg*cDs**2+mc2*(trsgc-ms2*(trs-trg+trc)))*gDs+mc2*ms2**2*(tr & sgc+ms2*trg))-6*trg*cDg**2*cDs*gDs*(2*gDs+ms2)-2*trg*cDg**3*gDs & *(2*gDs+ms2)-mc2*ms2*(trsgc+mc2*trg)*gDs*(2*gDs+ms2))/(mc2*cDg* & (2*gDs+ms2)**2)/2.0d+0+Apmp Apmp = tr3s001ft*(3*ms2*(trg+trc)*cDg*(cDg*(cDs-3*gDs)-2*mc2*gDs) & -3*trs*(2*cDg+mc2)*((2*cDg+mc2)*gDs**2+ms2*cDg**2))/cDg**3+Apm & p Apmp = Apmp-tr3s00ft*(cDg*(2*(trsgc+mc2*(3*trs+trg-trc))*gDs**2- & cDs*(-2*trsgc*gDs+2*mc2*(-trs-trg+trc)*gDs+mc2*(trsgc+ms2*trg)) & +mc2*(4*trsgc+9*ms2*trg+6*ms2*trc)*gDs-mc2*ms2*(trsgc+mc2*trg)) & +cDg**2*(-4*(trc-2*trs)*gDs**2-cDs*(4*(trc-trs)*gDs+4*trsgc+5*m & s2*trg+3*ms2*trc)+(2*trsgc+6*mc2*trs+11*ms2*trg+9*ms2*trc)*gDs+ & ms2*(-2*trsgc+3*mc2*trs-3*mc2*trg+2*mc2*trc))+mc2**2*gDs*(trg*( & gDs+cDs+ms2)+trs*gDs)+3*cDg**3*(4*trs*gDs+ms2*(2*trs-trg+trc))+ & mc2*trsgc*gDs*(gDs+cDs+mc2))/cDg**3 Apmp = 3*ms2*tr3c001fs*(mc2*(trs+trg)*gDs**2+2*trc*cDg*gDs*(2*gDs & +ms2)+(trs+trg)*cDg**2*(2*gDs+ms2))/(cDg*gDs**2)+Apmp Apmp = 3*ms2*tr3c002fs*(mc2*trc*gDs**2+trc*cDg**2*(2*gDs+ms2)+2*m & c2*(trs+trg)*cDg*gDs)/(cDg*gDs**2)+Apmp Apmp = BfunX*(cDg**2*gDs**2*((trg+trc)*(4*gDs*(gDs+cDs)+ms2*(gDs- & cDs)-ms2**2)-2*trs*gDs*(2*(gDs+cDs)+ms2))+2*cDg*gDs**3*(2*(gDs+ & cDs)+ms2)*(ms2*(-trs+trg+trc)-2*trs*(gDs+cDs))-(trs+trg+trc)*gD & s**4*(2*(gDs+cDs)+ms2)**2-ms2*cDg**3*gDs*((4*trs+5*trg+trc)*gDs & +4*(trs+trg)*cDs+2*ms2*(trs+trg-trc))+ms2*cDg**4*(2*(-trs-trg+t & rc)*gDs+ms2*(trs+trg+trc)))/(cDg**3*gDs**2)/4.0d+0+Apmp Apmp = lc*((2*cDg+mc2)*(cDg*(2*(-trs-trg+trc)*gDs+ms2*trg)-mc2*tr & g*gDs)-trsgc*(-mc2*gDs+cDg*(mc2-2*gDs)+4*cDg**2))/(cDg*(2*cDg+m & c2))/2.0d+0+Apmp Apmp = epinv**2*((mc2*(2*trg*cDg-trsgc)/cDg**2/2.0d+0-2*trc)*gDs- & ms2*trsgc/gDs/2.0d+0+trsgc*cDs/cDg+trsgc)+Apmp Apmp = Apmp-3*tr3s002ft*(2*cDg+mc2)**2*gDs*((trg+trc)*gDs+2*trs* & cDg)/cDg**3 Apmp=Apmp/zpmp return end