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sigcollsoft.f
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c subroutines soft, collfsr, softcollfsr, collisrp, collisrm,
c softcollisrp, softcollisrm
c are called by btildereal; they return (1-y) csi^2 R_alr (if kn_emitter
c is >2, i.e. final state) or (1-y^2) csi^2 R (if kn_emitter <=2) in the
c collinear final state (collfsr)
c soft-collinear final state (softcollfsr)
c collinear initial state in the + direction (collisrp)
c collinear initial state in the - direction (collisrm)
c soft-collinear initial state + (softcollisrp)
c soft-collinear initial state - (softcollisrm)
c The soft limit is taken keeping y (i.e. kn_y) fixed
c The collinear limit is taken keeping csitilde (kn_csitilde) fixed
c
c The Born and real phase space must have been set before calling them.
c The subroutine fills the array argument rc(maxalr) with the alr
c contributions that have as emitter the current emitter kn_emitter.
c All the others are set to zero.
c
c
c Functions: collbtl and softbtl are required to compute the damping
c factor in bornzerodamp. They are called by sigreal, and
c sigreal is used by btilde (hence the btl suffix)
c softbtl: computes the same quantity as soft, but does not include
c the luminosity
c
c collbtl: if kn_emitter is in the final state, computes the same quantity as
c collfsr, but does not include the luminosity
c if kn_emitter is 1 or 2 computes the same quantity as
c collisrp or collisrm, without luminosity
c if kn_emitter is 0 computes the average of the return values
c of collisrp and collisrm, weighted with the factors
c (1+y)/2 and (1-y)/2.
c
c
c
c Functions: collrad, softrad are required to compute the damping
c factor in bornzerodamp. They are called by sigreal_rad,
c i.e. they are used in the generation of radiation.
c They compute the same quantities as collbtl and softbtl,
c except that they only fill alr values corresponding to
c the current radiation underlying Born (i.e. the alr list
c rad_alr_list(1...rad_alr_nlist)) and that share the current
c radiation kinematics (i.e. the rad_kinreg value). Furthermore
c they are divided by kn_csi^2(1-kn_y^2) (for initial state
c kinematic regions) or kn_csi^2(1-kn_y) (for final state
c kinematic regions).
subroutine collfsr(rc)
implicit none
include 'nlegborn.h'
include 'pwhg_flst.h'
include 'pwhg_flg.h'
include 'pwhg_kn.h'
include 'pwhg_pdf.h'
real * 8 rc(maxalr)
real * 8 pdf1(-pdf_nparton:pdf_nparton),
1 pdf2(-pdf_nparton:pdf_nparton)
real * 8 rescfac
integer alr
call collfsrnopdf(rc)
if(.not.flg_minlo) then
call pdfcall(1,kn_x1,pdf1)
call pdfcall(2,kn_x2,pdf2)
rescfac=1
endif
do alr=1,flst_nalr
if(flg_minlo) then
call setlocalscales(flst_alr2born(alr),2,rescfac)
call pdfcall(1,kn_x1,pdf1)
call pdfcall(2,kn_x2,pdf2)
endif
rc(alr)=rc(alr)*pdf1(flst_alr(1,alr))*pdf2(flst_alr(2,alr))
1 *rescfac
enddo
end
subroutine collfsrnopdf(rc)
implicit none
include 'nlegborn.h'
include 'pwhg_flst.h'
include 'pwhg_flg.h'
include 'pwhg_kn.h'
real * 8 rc(maxalr)
integer alr,em,kres
real * 8 kperp(0:3),kperp2,q0,xocsi,csi,x,phi
em=kn_emitter
csi=kn_csi
call buildfsrvars(em,q0,xocsi,x,kperp,kperp2)
do alr=1,flst_nalr
if(em.eq.flst_emitter(alr)) then
call collfsralr(alr,csi,xocsi,x,q0,kperp,kperp2,rc(alr))
else
rc(alr)=0
endif
enddo
end
subroutine buildfsrvars(em,q0,xocsi,x,kperp,kperp2)
implicit none
integer em
real * 8 q0,xocsi,x,kperp(0:3),kperp2
include 'nlegborn.h'
include 'pwhg_flst.h'
include 'pwhg_flg.h'
include 'pwhg_kn.h'
integer kres
real * 8 pem(0:3),pres(0:3),phi
real * 8 dotp
external dotp
kres=flst_bornres(em,1)
if(kres.eq.0) then
pres=kn_cmpborn(:,1)+kn_cmpborn(:,2)
pem=kn_cmpborn(:,em)
else
call boost2reson(kn_cmpborn(:,kres),1,kn_cmpborn(:,em),pem)
pres(1:3)=0
pres(0)=sqrt(dotp(kn_cmpborn(:,kres),kn_cmpborn(:,kres)))
endif
q0=pres(0)
xocsi=q0/2/pem(0)
c for fsr csi is y independent
phi=kn_azi
x=kn_csi*xocsi
call buildkperp(phi,pem,kperp,kperp2)
c The correctness of this has not been tested yet in any specific process
c (typically a process with a gluon splitting in resonance decay).
c The question is: should the kperp vector be boosted back from
c the resonance frame to the CM frame?
c if(kres.ne.0) then
c call boost2reson(kn_cmpborn(:,kres),1,kperp,kperp)
c endif
end
subroutine buildkperp(phi,pem,kperp,kperp2)
implicit none
real * 8 phi,pem(0:3),kperp(0:3),kperp2,dir(1:3)
c Construct kperp; First construct a vector in the plane of p_em and
c the third axis, orthogonal to p_em.
c Then rotate it counterclockwise around the em direction
kperp(1)=pem(1)
kperp(2)=pem(2)
kperp(3)=-(pem(2)**2+pem(1)**2)
#/pem(3)
kperp2=(kperp(1)**2+kperp(2)**2+kperp(3)**2)
dir(1)=pem(1)/pem(0)
dir(2)=pem(2)/pem(0)
dir(3)=pem(3)/pem(0)
call mrotate(dir,sin(phi),cos(phi),kperp(1))
kperp(0)=0
end
subroutine softcollfsr(rc)
implicit none
include 'nlegborn.h'
include 'pwhg_flst.h'
include 'pwhg_flg.h'
include 'pwhg_pdf.h'
include 'pwhg_kn.h'
real * 8 rc(maxalr)
real * 8 pdf1(-pdf_nparton:pdf_nparton),
1 pdf2(-pdf_nparton:pdf_nparton)
integer alr
real * 8 tmp,rescfac
tmp=kn_csi
kn_csi=0
call collfsrnopdf(rc)
kn_csi=tmp
if(.not.flg_minlo) then
call pdfcall(1,kn_xb1,pdf1)
call pdfcall(2,kn_xb2,pdf2)
rescfac=1
endif
do alr=1,flst_nalr
if(flg_minlo) then
call setlocalscales(flst_alr2born(alr),2,rescfac)
call pdfcall(1,kn_xb1,pdf1)
call pdfcall(2,kn_xb2,pdf2)
endif
rc(alr)=rc(alr)*pdf1(flst_alr(1,alr))*pdf2(flst_alr(2,alr))
1 *rescfac
enddo
end
subroutine collisrp(rc)
implicit none
include 'nlegborn.h'
include 'pwhg_flst.h'
real * 8 rc(maxalr)
call collisr(1,rc)
end
subroutine collisrm(rc)
implicit none
include 'nlegborn.h'
include 'pwhg_flst.h'
real * 8 rc(maxalr)
call collisr(2,rc)
end
subroutine softcollisrp(rc)
implicit none
include 'nlegborn.h'
include 'pwhg_flst.h'
include 'pwhg_flg.h'
include 'pwhg_pdf.h'
include 'pwhg_kn.h'
real * 8 rc(maxalr)
real * 8 pdf1(-pdf_nparton:pdf_nparton),
1 pdf2(-pdf_nparton:pdf_nparton)
integer alr
real * 8 tmp,rescfac
tmp=kn_csip
kn_csip=0
call collisrnopdf(1,rc)
kn_csip=tmp
if(.not.flg_minlo) then
call pdfcall(1,kn_xb1,pdf1)
call pdfcall(2,kn_xb2,pdf2)
rescfac=1
endif
do alr=1,flst_nalr
if(flg_minlo) then
call setlocalscales(flst_alr2born(alr),2,rescfac)
call pdfcall(1,kn_xb1,pdf1)
call pdfcall(2,kn_xb2,pdf2)
endif
rc(alr)=rc(alr)*pdf1(flst_alr(1,alr))*pdf2(flst_alr(2,alr))
1 *rescfac
enddo
end
subroutine softcollisrm(rc)
implicit none
include 'nlegborn.h'
include 'pwhg_flst.h'
include 'pwhg_flg.h'
include 'pwhg_kn.h'
include 'pwhg_pdf.h'
real * 8 rc(maxalr)
real * 8 pdf1(-pdf_nparton:pdf_nparton),
1 pdf2(-pdf_nparton:pdf_nparton)
integer alr
real * 8 tmp,rescfac
tmp=kn_csim
kn_csim=0
call collisrnopdf(2,rc)
kn_csim=tmp
if(.not.flg_minlo) then
call pdfcall(1,kn_xb1,pdf1)
call pdfcall(2,kn_xb2,pdf2)
rescfac=1
endif
do alr=1,flst_nalr
if(flg_minlo) then
call setlocalscales(flst_alr2born(alr),2,rescfac)
call pdfcall(1,kn_xb1,pdf1)
call pdfcall(2,kn_xb2,pdf2)
endif
rc(alr)=rc(alr)*pdf1(flst_alr(1,alr))*pdf2(flst_alr(2,alr))
1 *rescfac
enddo
end
subroutine collisr(i,rc)
implicit none
integer i
include 'nlegborn.h'
include 'pwhg_flst.h'
include 'pwhg_flg.h'
include 'pwhg_pdf.h'
include 'pwhg_kn.h'
real * 8 rc(maxalr)
real * 8 pdf1(-pdf_nparton:pdf_nparton),
1 pdf2(-pdf_nparton:pdf_nparton),
1 x1,x2
integer alr
real * 8 rescfac
call collisrnopdf(i,rc)
if(i.eq.1) then
x1=kn_xb1/(1-kn_csip)
x2=kn_xb2
elseif(i.eq.2) then
x1=kn_xb1
x2=kn_xb2/(1-kn_csim)
endif
if(.not.flg_minlo) then
call pdfcall(1,x1,pdf1)
call pdfcall(2,x2,pdf2)
rescfac=1
endif
do alr=1,flst_nalr
if(flg_minlo) then
call setlocalscales(flst_alr2born(alr),2,rescfac)
call pdfcall(1,x1,pdf1)
call pdfcall(2,x2,pdf2)
endif
rc(alr)=rc(alr)*pdf1(flst_alr(1,alr))*pdf2(flst_alr(2,alr))
1 *rescfac
enddo
end
subroutine collisrnopdf(i,rc)
implicit none
integer i
include 'nlegborn.h'
include 'pwhg_flst.h'
include 'pwhg_kn.h'
include 'pwhg_math.h'
real * 8 rc(maxalr)
integer alr
real * 8 kperp(0:3),csi,phi
if(i.eq.1) then
csi=kn_csip
else
csi=kn_csim
endif
phi=kn_azi
c Construct kperp
kperp(1)=sin(phi)
kperp(2)=cos(phi)
kperp(3)=0
kperp(0)=0
do alr=1,flst_nalr
if(flst_emitter(alr).eq.kn_emitter) then
call collisralr(alr,i,csi,kperp,rc(alr))
else
rc(alr)=0
endif
enddo
end
subroutine soft(r0)
c blegs: integer, number of legs of born
c bflav(nlegs): integer, flavours of the incoming partons, according to PDG conventions,
c MODIFIED TO HAVE 0 FOR GLUONS (instead of 21)
c p(0:3,nleg): real * 8, momenta, 0 is time component
c softvec(0:3): real * 8, 4-vector of soft gluon normalized to softvec(0)=1
implicit none
include 'nlegborn.h'
include 'pwhg_flst.h'
include 'pwhg_flg.h'
include 'pwhg_kn.h'
include 'pwhg_math.h'
include 'pwhg_st.h'
include 'pwhg_br.h'
include 'pwhg_pdf.h'
real * 8 r0(maxalr)
integer alr,em
real * 8 y
real * 8 pdf1(-pdf_nparton:pdf_nparton),
1 pdf2(-pdf_nparton:pdf_nparton)
real * 8 rescfac
c Boost Born momenta to their rest frame
c find boost velocity
em=kn_emitter
y=kn_y
do alr=1,flst_nalr
call softalr(alr,em,y,r0(alr))
enddo
if(.not.flg_minlo) then
call pdfcall(1,kn_xb1,pdf1)
call pdfcall(2,kn_xb2,pdf2)
rescfac=1
endif
do alr=1,flst_nalr
if(flg_minlo) then
call setlocalscales(flst_alr2born(alr),2,rescfac)
call pdfcall(1,kn_xb1,pdf1)
call pdfcall(2,kn_xb2,pdf2)
endif
r0(alr)=r0(alr)*pdf1(flst_alr(1,alr))*pdf2(flst_alr(2,alr))
1 *rescfac
enddo
end
subroutine collfsralr(alr,csi,xocsi,x,q0,kperp,kperp2,res)
implicit none
include 'nlegborn.h'
include 'pwhg_flst.h'
include 'pwhg_flg.h'
include 'pwhg_kn.h'
include 'pwhg_math.h'
include 'pwhg_st.h'
include 'pwhg_br.h'
include 'pwhg_par.h'
include 'pwhg_em.h'
integer alr
real * 8 csi,xocsi,x,q0,kperp(0:3),kperp2,res
integer iub,em,emflav,raflav,mu,nu,kres
real * 8 gtens(0:3,0:3),ap,q2
data gtens/1d0, 0d0, 0d0, 0d0,
# 0d0,-1d0, 0d0, 0d0,
# 0d0, 0d0,-1d0, 0d0,
# 0d0, 0d0, 0d0,-1d0/
save gtens
real * 8 chargeofparticle
external chargeofparticle
logical is_em
is_em = .false.
iub=flst_alr2born(alr)
em=flst_emitter(alr)
c no collinear subtraction for massive particle
if(kn_masses(em).gt.0) then
res=0
return
endif
kres=flst_bornres(em,iub)
if(kres.eq.0) then
q2=kn_cmpborn(0,em)**2
else
q2= ( kn_cmpborn(0,kres)*kn_cmpborn(0,em)
1 -kn_cmpborn(1,kres)*kn_cmpborn(1,em)
2 -kn_cmpborn(2,kres)*kn_cmpborn(2,em)
3 -kn_cmpborn(3,kres)*kn_cmpborn(3,em) )**2/
4 ( kn_cmpborn(0,kres)**2
5 -kn_cmpborn(1,kres)**2
6 -kn_cmpborn(2,kres)**2
7 -kn_cmpborn(3,kres)**2 )
endif
emflav=flst_alr(em,alr)
raflav=flst_alr(nlegreal,alr)
if(emflav.eq.0.and.raflav.eq.0) then
ap=0
do mu=0,3
do nu=0,3
ap=ap+(-gtens(mu,nu)*(csi*x/(1-x)+(1-x)/xocsi)
#+2*x*(1-x)*csi*
#(kperp(mu)*kperp(nu))/kperp2)*br_bmunu(mu,nu,em,iub)
enddo
enddo
ap=ap*2*ca
c In case of two equal gluon we also supply e E_em^p/(E_em^p+E_rad^p)
c factor, and divide by 2 for the identical particles
c ap=ap*(1-x)**par_2gsupp/((1-x)**par_2gsupp+x**par_2gsupp)
c Commented out: now this is done at the end of the if block
elseif(emflav+raflav.eq.0) then
ap=0d0
do mu=0,3
do nu=0,3
ap=ap+(-gtens(mu,nu)
#-4*x*(1-x)*(kperp(mu)*kperp(nu))/kperp2)*br_bmunu(mu,nu,em,iub)
enddo
enddo
ap=ap*tf*csi
elseif(raflav.eq.0.and.emflav.ne.0) then
ap=cf*(1+(1-x)**2)/xocsi*br_born(iub)
elseif(raflav.ne.0.and.emflav.eq.0) then
ap=cf*(1+x**2)/(1-x)*csi*br_born(iub)
elseif(raflav.eq.22.and.emflav.ne.0) then
is_em = .true.
ap=(1+(1-x)**2)/xocsi*br_born(iub)
1 *chargeofparticle(emflav)**2
elseif(raflav.ne.0.and.emflav.eq.22) then
is_em = .true.
ap=(1+x**2)/(1-x)*csi*br_born(iub)
1 *chargeofparticle(emflav)**2
else
write(*,*) 'coll (fsr): unammissible flavour structure'
call pwhg_exit(-1)
endif
if(flg_doublefsr.or.(emflav.eq.0.and.raflav.eq.0)) then
ap=ap*(1-x)**par_2gsupp/((1-x)**par_2gsupp+x**par_2gsupp)
endif
c 1/(p_em . p_ra) = 1/(p_bar_em(0,em)**2* x * (1-x) * (1-y);
c we multiply everything by (1-y) csi^2; one csi is included
c above; the other here.
res=ap/q2/(xocsi*(1-x))
if(is_em) then
res = res * (4*pi*em_alpha)
else
res = res * (4*pi*st_alpha)
endif
c provide multiplicity of emitter in underlyng Born
res=res*flst_ubmult(alr)
end
subroutine collisralr(alr,i,csi,kperp,res)
implicit none
include 'nlegborn.h'
include 'pwhg_flst.h'
include 'pwhg_kn.h'
include 'pwhg_math.h'
include 'pwhg_st.h'
include 'pwhg_em.h'
include 'pwhg_br.h'
integer alr,i,em
real * 8 csi,kperp(0:3),res
integer iub,emflav,raflav,mu,nu
real * 8 gtens(0:3,0:3),ap,x
data gtens/1d0, 0d0, 0d0, 0d0,
# 0d0,-1d0, 0d0, 0d0,
# 0d0, 0d0,-1d0, 0d0,
# 0d0, 0d0, 0d0,-1d0/
save gtens
real * 8 chargeofparticle
logical is_em
external chargeofparticle
is_em=.false.
x=1-csi
iub=flst_alr2born(alr)
em=flst_emitter(alr)
emflav=flst_alr(i,alr)
raflav=flst_alr(nlegreal,alr)
if(emflav.eq.0.and.raflav.eq.0) then
ap=0
do mu=0,3
do nu=0,3
ap=ap+(-gtens(mu,nu)*(x+x*(1-x)**2)
#+2*(1-x)**2/x*
#(kperp(mu)*kperp(nu)))*br_bmunu(mu,nu,i,iub)
enddo
enddo
ap=ap*2*ca
elseif(raflav-emflav.eq.0) then
ap=0d0
do mu=0,3
do nu=0,3
ap=ap+(-gtens(mu,nu)*x
#+4*(1-x)/x*(kperp(mu)*kperp(nu)))*br_bmunu(mu,nu,i,iub)
enddo
enddo
c gluon radiation case
if(flst_born(i,iub).eq.0) then
ap=ap*cf*(1-x)
c photon radiation case
elseif(flst_born(i,iub).eq.22) then
is_em=.true.
ap=ap*(1-x)*chargeofparticle(emflav)**2
else
write(*,*) ' collisralr: unammissible ub flavour'
call pwhg_exit(-1)
endif
elseif(raflav.eq.0.and.emflav.ne.0) then
ap=cf*(1+x**2)*br_born(iub)
elseif(emflav.eq.0.and.raflav.ne.0) then
ap=tf*(x**2+(1-x)**2)*br_born(iub)*(1-x)
elseif(emflav.ne.0.and.raflav.eq.22) then
c WEW, consider photon emission
is_em=.true.
ap=(1+x**2)*br_born(iub)*chargeofparticle(emflav)**2
elseif(emflav.eq.22.and.raflav.ne.0) then
c WEW, consider emission by photon
is_em=.true.
ap=(x**2+(1-x)**2)*br_born(iub)*(1-x)
+ *3d0*chargeofparticle(raflav)**2
else
write(*,*) 'coll (isr): unammissible flavour structure'
endif
c In the real CM frame:
c 1/(p_ra . p_i)=1/(p^0_ra*p^0_i*(1-y))=1/(p^0_i)^2 /[(1-x)*(1-y)]
c where 1/(p^0_i)^2=1/(p^0_1 * p^0_2)=1/(pborn^0_1 * pborn^0_2/x),
c the last expression being boost invariant.
c Supplying che csi^2 (1-y^2) factor in the collinear limit,
c using csi=1-x we get
if(is_em) then
c WEW, electromagnetic coupling
res=ap/(kn_pborn(0,1)*kn_pborn(0,2)/x) * 2
c ew coupling:
# *(4*pi*em_alpha)
else
res=ap/(kn_pborn(0,1)*kn_pborn(0,2)/x) * 2
c strong coupling:
# *(4*pi*st_alpha)
c The remaining csi=1-x factor has been applied earlier
endif
end
function colcorr(j,iub,res)
c Returns true if parton j, in the underlying Born flavour
c structure iub, belongs to a group of colour correlated particles
c arising from the decay of the resonance res. This group is formed
c by all coloured particles that are sons of the resonance res
c (including eventually other coloured resonances) and by the resonance
c itself if coloured.
c The case res=0 corresponds to the partons produced promptly in the
c hard process.
implicit none
logical colcorr
integer iub,res,j
include 'nlegborn.h'
include 'pwhg_flst.h'
include 'pwhg_flg.h'
logical is_coloured
colcorr= is_coloured(flst_born(j,iub))
colcorr=colcorr .and.
1 (j.eq.res .or. flst_bornres(j,iub).eq.res)
end
function sigma(id,pos)
c WEW, sigma() added
c Returns the sigma of particle id
c + 1 for incoming fermion or outgoing antifermion
c - 1 for incoming antifermion or outgoing fermion
integer sigma
integer id,pos
if (id.gt.0.and.pos.le.2) then
sigma = 1
elseif (id.lt.0.and.pos.gt.2) then
sigma = 1
else
sigma = -1
endif
end
function colcorrem(j,iub,em)
c Returns true if parton j, in the underlying Born flavour structure
c iub, belongs to a group of colour correlated partons relevant for the
c emitter em. This is essentially as the colcorr function, except that
c it deals with the special case em=0 (that in POWHEG means radiation
c from either initial state partons)
implicit none
logical colcorrem
integer iub,em,res,j
include 'nlegborn.h'
include 'pwhg_flst.h'
include 'pwhg_flg.h'
logical colcorr
if(em.eq.0) then
res=0
else
res=flst_bornres(em,iub)
endif
colcorrem=colcorr(j,iub,res)
end
subroutine softalr(alr,em,y,res)
implicit none
include 'nlegborn.h'
include 'pwhg_flst.h'
include 'pwhg_flg.h'
include 'pwhg_kn.h'
include 'pwhg_math.h'
include 'pwhg_st.h'
include 'pwhg_em.h'
include 'pwhg_br.h'
integer alr,em
real * 8 y,res,chj,chk
integer iub,j,k,kres
real * 8 pjsq,sumdijinv,result,q2
real * 8 dotp,chargeofparticle
integer sigma
logical colcorrem
external dotp,chargeofparticle,colcorrem,sigma
if(flst_emitter(alr).eq.em) then
if(flst_alr(nlegreal,alr).eq.0) then
iub=flst_alr2born(alr)
if(em.eq.0) then
kres=0
else
kres=flst_bornres(em,iub)
endif
if(kres.eq.0) then
q2=4*kn_cmpborn(0,1)*kn_cmpborn(0,2)
else
q2=abs(kn_cmpborn(0,kres)**2
1 -kn_cmpborn(1,kres)**2
2 -kn_cmpborn(2,kres)**2
3 -kn_cmpborn(3,kres)**2)
endif
c loop over pairs of coloured particles
result=0
do j=1,nlegborn
if(colcorrem(j,iub,em)) then
do k=j+1,nlegborn
if(colcorrem(k,iub,em)) then
result=result+
#dotp(kn_cmpborn(0,j),kn_cmpborn(0,k))
#/(dotp(kn_cmpborn(0,j),kn_softvec)*
#dotp(kn_cmpborn(0,k),kn_softvec)) * br_bornjk(j,k,iub)
endif
enddo
endif
enddo
c the previous sum should run over all indexes. Since br_bornjk is
c symmetric, multiply by 2
result = result*2
do j=1,nlegborn
if(colcorrem(j,iub,em) .and.
#flst_born(j,iub).ne.0) then
pjsq=kn_cmpborn(0,j)**2-kn_cmpborn(1,j)**2-
#kn_cmpborn(2,j)**2-kn_cmpborn(3,j)**2
result=result-pjsq/dotp(kn_cmpborn(0,j),
#kn_softvec)**2*br_born(iub)*cf
endif
enddo
c having chosen a soft four momentum of energy 1, supply
c 1/esoft^2. Multiply by csi^2, csi=2*esoft/q0, so net
c factor 4/q0^2
if(em.gt.2) then
res=result*4/q2*(1-y)
else
res=result*4/q2*(1-y**2)
endif
c Coupling:
res=res*(4*pi*st_alpha)
elseif(flst_alr(nlegreal,alr).eq.22) then
c WEW: soft photon emission
iub=flst_alr2born(alr)
c loop over pairs of charged particles
result=0
do j=1,nlegborn
chj=chargeofparticle(flst_born(j,iub))
if(chj.ne.0) then
do k=j+1,nlegborn
chk=chargeofparticle(flst_born(k,iub))
if(chk.ne.0) then
result= result+
1 dotp(kn_cmpborn(0,j),kn_cmpborn(0,k))
2 /( dotp(kn_cmpborn(0,j),kn_softvec)*
3 dotp(kn_cmpborn(0,k),kn_softvec) )
4 * chj * chk
5 * sigma(flst_born(j,iub),j)
6 * sigma(flst_born(k,iub),k) * (-1)
endif
enddo
endif
enddo
c symmetric, multiply by 2
result = result*2
do j=1,nlegborn
chj=chargeofparticle(flst_born(j,iub))
if(chj.ne.0.and.kn_masses(j).ne.0) then
pjsq = dotp(kn_cmpborn(0,j),kn_cmpborn(0,j))
result = result
+ -pjsq/dotp(kn_cmpborn(0,j),kn_softvec)**2
+ *chj**2
endif
enddo
result=result * br_born(iub)
c having chosen a soft four momentum of energy 1, supply
c 1/esoft^2. Multiply by csi^2, csi=2*esoft/q0, so net
c factor 4/q0^2
if(em.gt.2) then
res=result*4/
#(4*kn_cmpborn(0,1)*kn_cmpborn(0,2))*(1-y)
else
res=result*4/
#(4*kn_cmpborn(0,1)*kn_cmpborn(0,2))*(1-y**2)
endif
c Coupling:
res=res*(4*pi*em_alpha)
c The case of the emitter being a gluon requires no special treatment here!
c the extra (1-x) factor is simply 1!
else
res=0
endif
else
res=0
endif
c Multiply soft result by (soft limit Sij appropriate factors)
if(res.ne.0) then
sumdijinv=0
do j=1,flst_allreg(1,0,alr)
if(flst_allreg(2,j,alr).eq.nlegreal) then
sumdijinv=sumdijinv
#+1/kn_dijterm_soft(flst_allreg(1,j,alr))
endif
enddo
res=res/kn_dijterm_soft(em)/sumdijinv
endif
res=res*flst_ubmult(alr)
end
subroutine softbtl(r0)
c blegs: integer, number of legs of born
c bflav(nlegs): integer, flavours of the incoming partons, according to PDG conventions,
c MODIFIED TO HAVE 0 FOR GLUONS (instead of 21)
c p(0:3,nleg): real * 8, momenta, 0 is time component
c softvec(0:3): real * 8, 4-vector of soft gluon normalized to softvec(0)=1
implicit none
include 'nlegborn.h'
include 'pwhg_flst.h'
include 'pwhg_kn.h'
include 'pwhg_math.h'
include 'pwhg_st.h'
include 'pwhg_br.h'
real * 8 r0(maxalr)
integer alr,em
real * 8 y
c Boost Born momenta to their rest frame
c find boost velocity
em=kn_emitter
y=kn_y
do alr=1,flst_nalr
call softalr(alr,em,y,r0(alr))
enddo
end
c This returns in rc the collinear approximation to
c the real cross section (multiplied by csi^2(1-y^2) or (1-y))
c to be used to construct the damping factor in the real
c cross section used in Btilde
subroutine collbtl(rc)
implicit none
include 'nlegborn.h'
include 'pwhg_flst.h'
include 'pwhg_kn.h'
real * 8 rc(maxalr)
integer alr,em,i
real * 8 kperp(0:3),kperp2,q0,xocsi,csi,x,phi,r1,r2
em=kn_emitter
if(em.gt.2) then
c for fsr csi is y independent
csi=kn_csi
call buildfsrvars(em,q0,xocsi,x,kperp,kperp2)
do alr=1,flst_nalr
if(em.eq.flst_emitter(alr)) then
call collfsralr(alr,csi,xocsi,x,q0,kperp,kperp2,rc(alr))
else
rc(alr)=0
endif
enddo
else
phi=kn_azi
c Construct kperp
kperp(1)=sin(phi)
kperp(2)=cos(phi)
kperp(3)=0
kperp(0)=0
do alr=1,flst_nalr
if(flst_emitter(alr).eq.em) then
if(em.ne.2) then
i=1
csi=kn_csi*kn_csimaxp/kn_csimax
call collisralr(alr,i,csi,kperp,r1)
endif
if(em.ne.1) then
i=2
csi=kn_csi*kn_csimaxm/kn_csimax
call collisralr(alr,i,csi,kperp,r2)
endif
if(em.eq.0) then
rc(alr)=(r1*(1+kn_y)+r2*(1-kn_y))/2
elseif(em.eq.1) then
rc(alr)=r1
elseif(em.eq.2) then
rc(alr)=r2
endif
else
rc(alr)=0
endif
enddo
endif
end
c This returns in rcs the soft-collinear approximation to
c the real cross section (multiplied by csi^2(1-y^2) or (1-y))
c to be used to construct the damping factor in the real
c cross section used in Btilde
subroutine collsoftbtl(rcs)
implicit none
include 'nlegborn.h'
include 'pwhg_flst.h'
include 'pwhg_kn.h'
real * 8 rcs(maxalr)
integer alr,em,i
real * 8 kperp(0:3),kperp2,q0,xocsi,csi,x,phi,r1,r2,kncsisave
kncsisave = kn_csi
kn_csi = 0
em=kn_emitter
if(em.gt.2) then
c for fsr csi is y independent
csi=kn_csi
call buildfsrvars(em,q0,xocsi,x,kperp,kperp2)
do alr=1,flst_nalr
if(em.eq.flst_emitter(alr)) then
call collfsralr(alr,csi,xocsi,x,q0,kperp,kperp2,rcs(alr))
else
rcs(alr)=0
endif
enddo
else
phi=kn_azi
c Construct kperp
kperp(1)=sin(phi)
kperp(2)=cos(phi)
kperp(3)=0
kperp(0)=0
do alr=1,flst_nalr
if(flst_emitter(alr).eq.em) then
if(em.ne.2) then
i=1
csi=kn_csi*kn_csimaxp/kn_csimax
call collisralr(alr,i,csi,kperp,r1)
endif
if(em.ne.1) then
i=2
csi=kn_csi*kn_csimaxm/kn_csimax
call collisralr(alr,i,csi,kperp,r2)
endif
if(em.eq.0) then
rcs(alr)=(r1*(1+kn_y)+r2*(1-kn_y))/2
elseif(em.eq.1) then
rcs(alr)=r1
elseif(em.eq.2) then
rcs(alr)=r2
endif
else
rcs(alr)=0
endif
enddo
endif
kn_csi = kncsisave
end
c This returns in rc the collinear approximation to
c the real cross section to be used to construct the damping factor
c in the real radiation cross section
subroutine collrad(rc)
implicit none
include 'nlegborn.h'
include 'pwhg_flst.h'
include 'pwhg_kn.h'
include 'pwhg_rad.h'
real * 8 rc(maxalr)
integer alr,em
real * 8 q0,xocsi,csi,phi,x,kperp(0:3),kperp2,r1,r2
integer j
do j=1,rad_alr_nlist
alr=rad_alr_list(j)
em=flst_emitter(alr)
c check if emitter corresponds to current radiation region (i.e. rad_kinreg):
if(rad_kinreg.eq.1.and.em.le.2) then
phi=kn_azi
c Construct kperp
kperp(1)=sin(phi)
kperp(2)=cos(phi)
kperp(3)=0
kperp(0)=0
if(em.ne.2) then
csi=kn_csi*kn_csimaxp/kn_csimax
call collisralr(alr,1,csi,kperp,r1)
endif
if(em.ne.1) then
csi=kn_csi*kn_csimaxm/kn_csimax
call collisralr(alr,2,csi,kperp,r2)
endif
if(em.eq.0) then
rc(alr)=(r1*(1+kn_y)+r2*(1-kn_y))/2
elseif(em.eq.1) then
rc(alr)=r1
elseif(em.eq.2) then
rc(alr)=r2
endif
rc(alr)=rc(alr)/(kn_csi**2*(1-kn_y**2))
elseif(flst_lightpart+rad_kinreg-2.eq.em) then
csi=kn_csi
call buildfsrvars(em,q0,xocsi,x,kperp,kperp2)
call collfsralr(alr,csi,xocsi,x,q0,kperp,kperp2,rc(alr))
rc(alr)=rc(alr)/csi**2/(1-kn_y)
else
rc(alr)=0
endif
enddo
end
subroutine softrad(r0)
implicit none
include 'nlegborn.h'
include 'pwhg_flst.h'
include 'pwhg_kn.h'
include 'pwhg_rad.h'
real * 8 r0(maxalr)
integer alr,em,j
real * 8 y,csi
y=kn_y
csi=kn_csi
do j=1,rad_alr_nlist
alr=rad_alr_list(j)
em=flst_emitter(alr)
if(rad_kinreg.eq.1.and.em.le.2) then
call softalr(alr,em,y,r0(alr))
r0(alr)=r0(alr)/csi**2/(1-y**2)
elseif(flst_lightpart+rad_kinreg-2.eq.em) then
call softalr(alr,em,y,r0(alr))
r0(alr)=r0(alr)/csi**2/(1-y)
else
r0(alr)=0
endif
enddo
end
c This returns in rcs the soft-collinear approximation to