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sigsoftvirt.f
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subroutine btildevirt(resvirt)
implicit none
include 'nlegborn.h'
include 'pwhg_flst.h'
include 'pwhg_kn.h'
include 'pwhg_br.h'
include 'pwhg_math.h'
include 'pwhg_st.h'
include 'pwhg_em.h'
include 'pwhg_flg.h'
include 'pwhg_par.h'
include 'pwhg_pdf.h'
real * 8 resvirt(flst_nborn)
real * 8 c(-6:6),gamma(-6:6),gammap(-6:6),gammatilde(-6:6)
integer j,jb,fl1,fl2,fl,leg,legi,legj,jres,kres
real * 8 Q,I,s,etot,e,eij,virt_arr(flst_nborn),tot,kij,arglog,
1 loglog,pborn(0:3,nlegborn)
real * 8 pdfb1(-pdf_nparton:pdf_nparton),
1 pdfb2(-pdf_nparton:pdf_nparton)
logical ini
data ini/.true./
real * 8 ddilog,dotp
external ddilog,dotp
save c,gamma,gammap,gammatilde,ini
real * 8 tiny
parameter (tiny=1d-14)
real * 8 ll,llew,rescfac
real * 8 Intm_ep,Int0m_0,Int0m_ep,Intmm_0,Intmm_ep
external Intm_ep,Int0m_0,Int0m_ep,Intmm_0,Intmm_ep
real * 8 tmp,tmpew,Qem,Iem,ch_i,ch_j,ch1,ch2
logical pwhg_isfinite
real * 8 chargeofparticle
external pwhg_isfinite,chargeofparticle
integer sigma
external sigma
logical is_charged, is_coloured
external is_charged, is_coloured
c if virtual.f, will not do smartsig when this flag is active
if (flg_novirtual) then
resvirt = 0d0
return
endif
c from 2.100 of FNO2007
if(ini) then
do j=-6,6
if(j.eq.0) then
c(j)=ca
gamma(j)=(11*ca-4*tf*st_nlight)/6
gammap(j)=(67d0/9-2*pi**2/3)*ca-23d0/9*tf*st_nlight
gammatilde(j)=ca/6d0
else
c(j)=cf
gamma(j)=3d0/2*cf
gammap(j)=(13d0/2-2*pi**2/3)*cf
gammatilde(j)=cf/2
endif
enddo
ini=.false.
endif
if(.not.flg_minlo) then
c get pdfs
call pdfcall(1,kn_xb1,pdfb1)
call pdfcall(2,kn_xb2,pdfb2)
endif
tot=0
call sigvirtual(virt_arr)
c Strong Q contribution
Q = 0
c EW Q contribution
Qem = 0
do jres=1,flst_nreson
kres=flst_reslist(jres)
if(kres.ne.0) then
call boost2reson(kn_cmpborn(:,kres),nlegborn,
1 kn_cmpborn,pborn)
etot=pborn(0,kres)
else
pborn=kn_cmpborn
etot=2*kn_cmpborn(0,1)
endif
s=etot**2
if(.not.flg_minlo) then
ll = log(par_csicut**2*s/st_muren2)
if(flg_with_em) llew = log(par_csicut**2*s/em_muren2)
rescfac = 1
endif
do jb=1,flst_nborn
c Strong Q contribution
Q = 0
c EW Q contribution
Qem = 0
if(flg_minlo) then
call setlocalscales(jb,2,rescfac)
ll = log(par_csicut**2*s/st_muren2)
if(flg_with_em) llew = log(par_csicut**2*s/em_muren2)
c get pdfs
call pdfcall(1,kn_xb1,pdfb1)
call pdfcall(2,kn_xb2,pdfb2)
endif
fl1=flst_born(1,jb)
fl2=flst_born(2,jb)
c initial-state parton contribution
if(kres.eq.0) then
if(is_coloured(fl1)) then
Q=Q-log(st_mufact2/st_muren2)*(gamma(fl1)+2*c(fl1)*
1 log(par_csicut))
if(flg_drscheme) then
Q=Q-gammatilde(fl1)
endif
endif
if(is_coloured(fl2)) then
Q=Q-log(st_mufact2/st_muren2)*
1 (gamma(fl2)+2*c(fl2)*log(par_csicut))
if(flg_drscheme) then
Q=Q-gammatilde(fl2)
endif
endif
c EW photonic contribution
ch1=chargeofparticle(fl1)
ch2=chargeofparticle(fl2)
if (flg_with_em.and.ch1.ne.0) then
Qem=Qem-log(st_mufact2/em_muren2)*(
1 (1.5d0+2*log(par_csicut))*ch1**2)
endif
if (flg_with_em.and.ch2.ne.0) then
Qem=Qem-log(st_mufact2/em_muren2)*(
3 + (1.5d0+2*log(par_csicut))*ch2**2)
endif
endif
c loop on final-state massless partons
do leg=3,nlegborn
if(leg.ne.kres.and.flst_bornres(leg,jb).ne.kres) cycle
fl=flst_born(leg,jb)
if(is_coloured(fl)) then
if(kn_masses(leg).eq.0) then
if(flg_drscheme) then
Q=Q-gammatilde(fl)
endif
e=pborn(0,leg)
Q=Q+gammap(fl)
1 -log(s/st_muren2)*(gamma(fl)-2*c(fl)
3 *log(2*e/(par_csicut*etot)))
3 +2*c(fl)*(log(2*e/etot)**2-log(par_csicut)**2)
4 -2*gamma(fl)*log(2*e/etot)
else
Q = Q - c(flst_born(leg,jb))*
1 (ll-0.5*Intm_ep(pborn(0,leg)))
endif
endif
c WEW
if (flg_with_em.and.chargeofparticle(fl).ne.0) then
if(kn_masses(leg).eq.0) then
write(*,*) ' not prepared to handle this!'
call pwhg_exit(-1)
else
Qem = Qem -
1 (llew-0.5*Intm_ep(kn_cmpborn(0,leg)))
2 * chargeofparticle(fl)**2
endif
endif
enddo
Q=Q*br_born(jb)
Qem=Qem*br_born(jb)
Iem=0
I=0
do legi=1,nlegborn
if(legi.ne.kres.and.flst_bornres(legi,jb).ne.kres)
1 cycle
do legj=legi+1,nlegborn
if(legj.ne.kres.and.flst_bornres(legj,jb).ne.kres)
1 cycle
c both particles are colored
if(is_coloured(flst_born(legi,jb)).and.
1 is_coloured(flst_born(legj,jb)) ) then
c massless-massless case
if (kn_masses(legi).eq.0.and.kn_masses(legj).eq.0)
1 then
kij=dotp(pborn(0,legi),pborn(0,legj))
eij=pborn(0,legi)*pborn(0,legj)
arglog = abs(1-kij/(2*eij))
if (arglog.lt.tiny) then
loglog = 0d0
else
loglog = log(arglog)*log(kij/(2*eij))
endif
I=I+(1d0/2*ll**2
1 +ll*log(kij/(2*eij))
2 -ddilog(kij/(2*eij))
3 +1d0/2*log(kij/(2*eij))**2
4 -loglog)*
5 br_bornjk(legi,legj,jb)
endif
c massless-massive case
if (kn_masses(legi).eq.0.and.kn_masses(legj).gt.0)
1 then
I = I + (0.5*(0.5*ll**2 - pi**2/6)
1 +0.5*Int0m_0(pborn(0,legi),pborn(0,legj))*ll
2 -0.5*Int0m_ep(pborn(0,legi),pborn(0,legj)))*
3 br_bornjk(legi,legj,jb)
endif
c massive-massless case
if (kn_masses(legi).gt.0.and.kn_masses(legj).eq.0)
1 then
I = I + (0.5*(0.5*ll**2 - pi**2/6)
1 +0.5*Int0m_0(pborn(0,legj),pborn(0,legi))*ll
2 -0.5*Int0m_ep(pborn(0,legj),pborn(0,legi)))*
3 br_bornjk(legj,legi,jb)
endif
c massive-massive case
if (kn_masses(legi).gt.0.and.kn_masses(legj).gt.0)
1 then
I = I + (0.5*ll*
1 Intmm_0(pborn(0,legi),pborn(0,legj))
2 -0.5*Intmm_ep(pborn(0,legi),pborn(0,legj)))
3 *br_bornjk(legi,legj,jb)
endif
endif
ch_i=chargeofparticle(flst_born(legi,jb))
ch_j=chargeofparticle(flst_born(legj,jb))
c both particles are charged
if (flg_with_em.and.ch_i.ne.0.and.ch_j.ne.0) then
c massless-massless case
if (kn_masses(legi).eq.0.and.kn_masses(legj).eq.0)
1 then
kij=dotp(kn_cmpborn(0,legi),kn_cmpborn(0,legj))
eij=kn_cmpborn(0,legi)*kn_cmpborn(0,legj)
arglog = abs(1-kij/(2*eij))
if (arglog.lt.tiny) then
loglog = 0d0
else
loglog = log(arglog)*log(kij/(2*eij))
endif
Iem=Iem+(1d0/2*llew**2
1 +llew*log(kij/(2*eij))
2 -ddilog(kij/(2*eij))+1d0/2*log(kij/(2*eij))**2
3 -loglog)*
4 br_born(jb)*ch_i*ch_j*(-1)*
5 sigma(flst_born(legi,jb),legi)*
6 sigma(flst_born(legj,jb),legj)
endif
c massless-massive case
if (kn_masses(legi).eq.0.and.kn_masses(legj).gt.0)
1 then
Iem = Iem + (0.5*(0.5*llew**2 - pi**2/6)
1 +0.5*Int0m_0(kn_cmpborn(0,legi),kn_cmpborn(0,legj))*llew
2 -0.5*Int0m_ep(kn_cmpborn(0,legi),kn_cmpborn(0,legj)))*
3 br_born(jb)*ch_i*ch_j*(-1)*
4 sigma(flst_born(legi,jb),legi)*
5 sigma(flst_born(legj,jb),legj)
endif
c massive-massless case
if (kn_masses(legi).gt.0.and.kn_masses(legj).eq.0)
1 then
Iem = Iem + (0.5*(0.5*llew**2 - pi**2/6)
1 +0.5*Int0m_0(kn_cmpborn(0,legj),kn_cmpborn(0,legi))*llew
2 -0.5*Int0m_ep(kn_cmpborn(0,legj),kn_cmpborn(0,legi)))*
3 br_born(jb)*ch_i*ch_j*(-1)*
4 sigma(flst_born(legi,jb),legi)*
5 sigma(flst_born(legj,jb),legj)
endif
c massive-massive case
if (kn_masses(legi).gt.0.and.kn_masses(legj).gt.0)
1 then
Iem = Iem + (0.5*llew*
1 Intmm_0(kn_cmpborn(0,legi),kn_cmpborn(0,legj))
2 -0.5*Intmm_ep(kn_cmpborn(0,legi),kn_cmpborn(0,legj)))*
3 br_born(jb)*ch_i*ch_j*(-1)*
4 sigma(flst_born(legi,jb),legi)*
5 sigma(flst_born(legj,jb),legj)
endif
endif
enddo
enddo
I=I*2
c WEW
Iem=Iem*2
if(jres.eq.1) then
c first time
resvirt(jb)=( (Q+I+virt_arr(jb))*st_alpha
1 + (Qem+Iem)*em_alpha )/(2*pi)
2 *pdfb1(fl1)*pdfb2(fl2)*kn_jacborn * rescfac
else
c others
resvirt(jb)=resvirt(jb)+( (Q+I)*st_alpha
1 + (Qem+Iem)*em_alpha )/(2*pi)
2 *pdfb1(fl1)*pdfb2(fl2)*kn_jacborn * rescfac
endif
tot=tot+resvirt(jb)
enddo
enddo
if (.not.pwhg_isfinite(tot)) then
do jb=1,flst_nborn
resvirt(jb)=0d0
enddo
endif
end
c I_ep(k,m)
function Int0m_ep(k,m)
c / [ ]
c | d phi [ k.m k0 ]
c Int0m_ep = -2 | d cos th ----- log(sin th sin phi) l0^2 [ ------- - ------ ]
c | pi [ k.l m.l k.l l0 ]
c / [ ]
c the range in phi is 0<phi<pi.
implicit none
real * 8 Int0m_ep, k(0:3),m(0:3)
real * 8 kh(0:3),mh(0:3),khmh,b
integer j
real * 8 ddilog,dotp
external ddilog,dotp
do j=0,3
kh(j)=k(j)/k(0)
mh(j)=m(j)/m(0)
enddo
b=sqrt(1-dotp(mh,mh))
khmh=dotp(kh,mh)
Int0m_ep=-2*(log((1-b)/(1+b))**2/4+log(khmh/(1+b))*log(khmh/(1-b))
# +ddilog(1-khmh/(1+b))+ddilog(1-khmh/(1-b)))
end
c I_0(k,m)
c / [ ]
c | d phi [ k.m k0 ]
c I_0 = | d cos th ----- l0^2 [ ------- - ------ ]
c | pi [ k.l m.l k.l l0 ]
c / [ ]
c the range in phi is 0<phi<pi.
function Int0m_0(k,m)
implicit none
real * 8 Int0m_0, k(0:3),m(0:3)
real * 8 kh(0:3),mh(0:3)
integer j
real * 8 dotp
external ddilog,dotp
do j=0,3
kh(j)=k(j)/k(0)
mh(j)=m(j)/m(0)
enddo
Int0m_0=log( dotp(kh,mh)**2/dotp(mh,mh) )
end
function Intm_ep(p)
c / 2
c | d phi p
c Intm_ep = -2 | d cos th ----- log(sin th sin phi) l0^2 -------
c | pi (p.l)^2
c /
c the range in phi is 0<phi<pi.
implicit none
real * 8 p(0:3),Intm_ep
real * 8 beta2,beta
integer j
beta2=0
do j=1,3
beta2=beta2+(p(j)/p(0))**2
enddo
beta=sqrt(beta2)
if(beta.lt.1d-4) then
Intm_ep=2*(2+2*beta**2/3+2*beta**4/5+2*beta**6/7)
else
Intm_ep=2*log((1+beta)/(1-beta))/beta
endif
end
function Intmm_ep(p1,p2)
c /
c | d phi p1.p2
c Intmm_ep= -2 | d cos th ----- log(sin th sin phi) k0^2 ----------
c | pi p1.k p2.k
c /
c p1^2>0, p2^2>0.
c The range in phi is 0<phi<pi.
implicit none
real * 8 p1(0:3),p2(0:3), intmm_ep
real * 8 i,z,zm,zmob,zp,z1,z1ob,z2,a,b,x1,x2,bv1(3),bv2(3),
1 bb1,bb2,b1b2,b2
integer j
real * 8 ddilog,tmp
external ddilog
i(z)=-1d0/2*log((z-zm)*(zp-z)/((zp+z)*(z+zm)))**2
# -2*ddilog(2*zm/(zp-zm)*(zp-z)/(zm+z))
# -2*ddilog(-2*zp/(zp-zm)*(zm+z)/(zp-z))
do j=1,3
bv1(j)=p1(j)/p1(0)
bv2(j)=p2(j)/p2(0)
enddo
bb1=0
bb2=0
b1b2=0
do j=1,3
bb1=bb1+bv1(j)**2
bb2=bb2+bv2(j)**2
b1b2=b1b2+bv1(j)*bv2(j)
enddo
if(bb1.gt.bb2) then
tmp=bb1
bb1=bb2
bb2=tmp
endif
a=bb1+bb2-2*b1b2
x1=bb1-b1b2
x2=bb2-b1b2
b=bb1*bb2-b1b2**2
zp=sqrt(a)+sqrt(a-b)
zm=sqrt(a)-sqrt(a-b)
c zm over b (introduce to handle back-to-back case without generating 0/0)
zmob=1/zp
z1=sqrt(x1**2+b)-x1
z2=sqrt(x2**2+b)+x2
if(bb1.eq.0) then
c handle limiting case, b1=0
b2=sqrt(bb2)
Intmm_ep=(-0.5d0*log((1-b2)/(1+b2))**2
1 +2*ddilog(0d0)-2*ddilog(-2*b2/(1-b2)))
1 * (1-b1b2)/sqrt(a-b)
else
c z1 over b (same as before
z1ob=1/(sqrt(x1**2+b)+x1)
Intmm_ep=(i(z2)
1 +1d0/2*log((z1ob-zmob)*(zp-z1)/((zp+z1)*(z1ob+zmob)))**2
2 +2*ddilog(2*zmob/(zp-zm)*(zp-z1)/(zmob+z1ob))
3 +2*ddilog(-2*zp/(zp-zm)*(zm+z1)/(zp-z1)) )
4 *(1-b1b2)/sqrt(a-b)
endif
end
function Intmm_0(p1,p2)
c /
c | d phi p1.p2
c Intmm_0 = | d cos th ----- k0^2 ----------
c | pi p1.k p2.k
c /
c the range in phi is 0<phi<pi.
implicit none
real * 8 p1(0:3),p2(0:3), Intmm_0
real * 8 kh(3),gh(3),k2,g2,kg,beta,ombeta2
integer j
do j=1,3
kh(j)=p1(j)/p1(0)
gh(j)=p2(j)/p2(0)
enddo
k2=0
g2=0
kg=0
do j=1,3
k2=k2+kh(j)**2
g2=g2+gh(j)**2
kg=kg+kh(j)*gh(j)
enddo
ombeta2=(1-k2)*(1-g2)/(1-kg)**2
beta=sqrt(1-ombeta2)
c Intmm_0=log((1+beta)/(1-beta))/beta
c Equivalent:
Intmm_0=log((1+beta)**2/ombeta2)/beta
end