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dvcsamp.f
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dvcsamp.f
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CMM Convolution program for NLO DVCS amplitude see Belitsky et al, hep-ph/9908337
CMM This code takes as input the ODPDFs
CMM see e.g. Golec-Biernat Martin hep-ph/9807497
CMM
CMM We always take quark singlet as the input, in both polarised and unpolarised cases
CMM from the evolution code of A Freund. There is one input file for each skewedness value.
CMM The code convolutes them with the appropriate coefficient functions to produce contributions to
CMM the DVCS amplitude from each flavour. These are stored in the output files
CMM uamp.dat, damp.dat, samp.dat, gamp.dat: the output is of the form
CMM
CMM del(1)
CMM q^2(1) ReA ImA
CMM .
CMM .
CMM q^2(nq) ReA ImA
CMM del(2)
CMM .
CMM .
CMM del(ndel)
CMM q^2(1) ReA ImA
CMM .
CMM .
CMM q^2(1) ReA ImA
CMM
CMM For use by dvcsob.f which includes Bether-Heitler and implements BMNS hep-ph/0004059
CMM
CMM How this code works:
CMM
CMM 1) Subroutine readin(nx,nq,ndel) is called and returns the number of points in X,Q and delta (skewedness)
CMM It stores the values of the ODPDFS to three dimensional
CMM arrays in del' Q' and X' and the values of delta, Q and X in 1D vectors.
CMM This are all passed via common blocks /pdfarray/, /delarray/, /qarray/ and /xarray/
CMM to the main program.
CMM 2) The array in x is extended to have 0 and 1 at either end. Output files are opened.
CMM 3) The calculations are performed in three nested do loops in delta, q and x' respectively.
CMM The delta loop specifies the value of delta from the array and stores it to the output.
CMM The position of the cross over point between DGLAP and ERBL is calculated,
CMM and the array index of the last point in the the ERBL region is stored in iv.
CMM In the Q do loop the value of Q is specified, then the GPDs are extrapolated to
CMM the point x' = delta and then used to set the GPDs at the point x' = 0 using symmetries.
CMM This is achieved using a seven point array around iv and subroutine ratint
CMM Subroutine wcread calculates the coeff functions for the particular delta and Q
CMM (using function tqi tgi and subroutine alpdr to calculate alphas).
CMM Argument n sets the order (1 or 2).
CMM It passes the coeff functions via common block /wcoeff/ tq, tg, tqm, tgm, tqi, tgi
CMM in arrays in x'.
CMM A patten of minus signs is set (via sq,sg) (according to whether we want axial (iknl =2)
CMM or vector(iknl=1) case)
CMM The 'subtracted' integrands are then defined (taking care of the necessary subtractions
CMM (at x' = 0)).
CMM Using pu,pd,ps,pg for ERBL and pu1,..,pg1 for (just ?) DGLAP in integral 0..1
CMM The imaginary piece of the subtracted integrands of the integral del...1 are
CMM stored in pui,...,pgi.
CMM The special point at x' = delta is treated separately using the symmetries of the
CMM coefficient fns.
CMM The special bin between del and x_iv+1 in the del..1 integral is then calculated
CMM and stored in temu1,...temg1 for the real part and temui,...,temgi for the imaginary
CMM part.
CMM Do loop in x' then does the integrations (using gauss) in all the other bins and
CMM adds them cumilatively into temu1...
CMM The arguments of integration routines "gauss" are not the above arrays but
CMM interpolations of them using fintrp.
CMM The counterterms are then calculated using subroutine counterV or counterA as
CMM appropriate to axial (iknl =2) or vector (iknl =1)
CMM Finally, the real and imaginary peices are put together in reau,...,reag, ximau,....,ximag
CMM and sent to the output files together with the value of Q^2.
CMM
subroutine convolution(tw,gpdtype,unpolopol,n,lambda11,lambda21
>,nfl,nx1,ndel1,nq1)
c program convol6
implicit none
real*8 del,qone,mu,reqint,imqint,regint,imgint
integer j,k,ni,li,irt,l
integer mxx,mq,mdel,m,m1,kt,tw
integer k1,ktemp,ktemp1,old1
integer nfl,n,iknl,gpdtype, unpolopol
integer nx,nq,ndel,nx1,nq1,ndel1
real*8 nf,lambda1,lambda2,lambda11,lambda21
real*8 qu,qd,qs,g
real*8 qar,delar,xar,xarb
real*8 pu,pd,ps,pg,pu1,ps1,pd1,pg1
real*8 pui,pdi,psi,pgi
real*8 tq,tg,tqm,tgm,tqi,tgi
integer iv,nc1,nc2,ncut,ntemp,iset,iset1,iset2,iset3
real*8 udel,ddel,sdel,gdel,q2,e,aer,rer,err
real*8 temu,temd,tems,temg,temu1,temd1,tems1,temg1
real*8 temui,temdi,temsi,temgi,tempui,tempdi,tempsi
real*8 gauss,tempu,tempd,temps,tempg,tempgi
real*8 reau,read,reas,reag,dxdzn,dxdz
real*8 ximau,ximad,ximas,ximag
real*8 x0,tem,dz,diffdel,res,comp,comp1
real*8 sq,sg,qm,smpnol,smpnor,smpsna
real*8 temp1qu,temp1qd,temp1qs,temp1g,xtemp
parameter (mxx = 1050, mq = 100, mdel = 100)
CMM arrays of dimension mxx + 1
C maximum number of points in x, 1050, in x_bj, 20 and in Q^2, 20.
C can be adjusted of course
common / pdfarray / qu(mdel,mq,0:mxx),qd(mdel,mq,0:mxx),
> qs(mdel,mq,0:mxx),g(mdel,mq,0:mxx)
common / qarray / qar(mq)
common / delarray / delar(mdel)
common / xarray1 / xarb(2,0:mxx,mdel)
common / xarray / xar(0:mxx)
common / regfunc / pu(mxx), pd(mxx), ps(mxx), pg(mxx),
> pu1(mxx), pd1(mxx), ps1(mxx), pg1(mxx),
> pui(mxx), pdi(mxx), psi(mxx), pgi(mxx)
common / wcoeff / tq(0:mxx), tg(0:mxx), tqm(0:mxx), tgm(0:mxx),
> tqi(0:mxx),tgi(0:mxx)
common / all / nx,nq,ndel
common / clambda / lambda1,lambda2
common / tempar / temp1qu(mdel),temp1qd(mdel),temp1qs(mdel)
> ,temp1g(mdel),xtemp(mdel)
dimension dxdz(mxx)
C
C external functions
C
external alpdr
external spence
external counterV,counterA
external smpnol,smpnor,smpsna,dxdzn
nx = nx1
ndel = ndel1
nq = nq1
lambda1 = lambda11
lambda2 = lambda21
iknl = unpolopol
k1 = gpdtype
C load pdf arrays, x array, del and Q value, number of bins, del's and Q's
CMM Returns values for nx,nq,ndel and
CMM Fills up 3D-arrays qu,qd,qs,g dim (ndel,nq,nx)
CMM and 1D arrays delar(ndel), qar(nq), xar(nx)
CMM define nf as real*8 otherwize dangerous integer division
c do 99 k1 = 1,gpdtype
c do 100 n = 1,2
c do 101 iknl = 1,unpolopol
C
C set number of flavours
C
nf = dble(nfl)
C
C readin GPD data files
C
call readin(k1,n,iknl)
C opening file for the values of the amplitude for the various quarks and the gluon
C output mode: first the q value than in the next line del, Real part of amplitude,
C Imaginary part of the amplitude. various files for the quark species and the gluon.
if (tw.eq.2) then
if (k1.eq.1) then
if (n.eq.1.and.iknl.eq.1) then
open(1,file='luamp.dat',status='unknown')
open(2,file='ldamp.dat',status='unknown')
open(3,file='lsamp.dat',status='unknown')
open(4,file='lgamp.dat',status='unknown')
elseif(n.eq.1.and.iknl.eq.2) then
open(1,file='luamppol.dat',status='unknown')
open(2,file='ldamppol.dat',status='unknown')
open(3,file='lsamppol.dat',status='unknown')
open(4,file='lgamppol.dat',status='unknown')
elseif(n.eq.2.and.iknl.eq.1) then
open(1,file='nlouamp.dat',status='unknown')
open(2,file='nlodamp.dat',status='unknown')
open(3,file='nlosamp.dat',status='unknown')
open(4,file='nlogamp.dat',status='unknown')
elseif(n.eq.2.and.iknl.eq.2) then
open(1,file='nlouamppol.dat',status='unknown')
open(2,file='nlodamppol.dat',status='unknown')
open(3,file='nlosamppol.dat',status='unknown')
open(4,file='nlogamppol.dat',status='unknown')
endif
else
if (n.eq.1.and.iknl.eq.1) then
open(1,file='luampe.dat',status='unknown')
open(2,file='ldampe.dat',status='unknown')
open(3,file='lsampe.dat',status='unknown')
open(4,file='lgampe.dat',status='unknown')
elseif(n.eq.1.and.iknl.eq.2) then
open(1,file='luamppole.dat',status='unknown')
open(2,file='ldamppole.dat',status='unknown')
open(3,file='lsamppole.dat',status='unknown')
open(4,file='lgamppole.dat',status='unknown')
elseif(n.eq.2.and.iknl.eq.1) then
open(1,file='nlouampe.dat',status='unknown')
open(2,file='nlodampe.dat',status='unknown')
open(3,file='nlosampe.dat',status='unknown')
open(4,file='nlogampe.dat',status='unknown')
elseif(n.eq.2.and.iknl.eq.2) then
open(1,file='nlouamppole.dat',status='unknown')
open(2,file='nlodamppole.dat',status='unknown')
open(3,file='nlosamppole.dat',status='unknown')
open(4,file='nlogamppole.dat',status='unknown')
endif
endif
else
if (k1.eq.1) then
if (n.eq.1.and.iknl.eq.1) then
open(1,file='luamptw3.dat',status='unknown')
open(2,file='ldamptw3.dat',status='unknown')
open(3,file='lsamptw3.dat',status='unknown')
open(4,file='lgamptw3.dat',status='unknown')
elseif(n.eq.1.and.iknl.eq.2) then
open(1,file='luamppoltw3.dat',status='unknown')
open(2,file='ldamppoltw3.dat',status='unknown')
open(3,file='lsamppoltw3.dat',status='unknown')
open(4,file='lgamppoltw3.dat',status='unknown')
endif
else
if (n.eq.1.and.iknl.eq.1) then
open(1,file='luampetw3.dat',status='unknown')
open(2,file='ldampetw3.dat',status='unknown')
open(3,file='lsampetw3.dat',status='unknown')
open(4,file='lgampetw3.dat',status='unknown')
elseif(n.eq.1.and.iknl.eq.2) then
open(1,file='luamppoletw3.dat',status='unknown')
open(2,file='ldamppoletw3.dat',status='unknown')
open(3,file='lsamppoletw3.dat',status='unknown')
open(4,file='lgamppoletw3.dat',status='unknown')
endif
endif
endif
C
C loop that runs through the various values of del
C
do 22 k = 1, ndel
del = delar(k)
C
C write the del values in output
C
write(1,*) del
write(2,*) del
write(3,*) del
write(4,*) del
CMM Now determine iv for this delta (corssover point from ERBL to DGLAP)
iv = 0
do 121 j = 1, nx
xar(j) = xarb(k1,j,k)
if (xar(j).le.del) then
iv = iv + 1
else
iv = iv
endif
121 continue
xar(nx+1) = 1.0
C
C initialize jacobain array used in simpson integration!
C
do 144 j = 1,nx+1
dz = 1./nx
x0 = dz*(j-1)
if (j.le.iv) then
dxdz(j) = dxdzn(1,j,nx+1,x0,del)
else
dxdz(j) = dxdzn(2,j,nx+1,x0,del)
endif
IF (J.EQ.IV) DIFFDEL = DXDZN(2,J,NX+1,X0,DEL)
144 continue
C
C outer loop that runs through the various values of q
C
do 11 ni = 1,nq
q2 = qar(ni)
C
C Fill the array with the values of the LO and NLO coefficient functions!
C
C
C Set ratio of factorization to renormalization scale in variable qone!
C
C Default value Q^2/mu^2 =1
C
mu = q2
qone = q2
qm = qone**2/mu**2
call wcread(tw,del,qm,q2,n,iknl,nf,nx,iv)
C
C inner loop that runs through x for the integration
C
e = del/(2.-del)
C
C Set switch for real part of T(2*y/del-1) for y>del in the integrand of
C the integral from del..1
C depending whether vector or axial-vector is used (IKNL=1,2)
C unpol vs pol
C
if (iknl.eq.1) then
sq = -1.
sg = +1.
else if (iknl.eq.2) then
sq = +1.
sg = -1.
else
stop
endif
if (k1.eq.2) then
if (iknl.eq.1) then
qu(k,ni,iv) = -qu(k,ni,1)
qd(k,ni,iv) = -qd(k,ni,1)
qs(k,ni,iv) = -qs(k,ni,1)
g(k,ni,iv) = g(k,ni,1)
else
qu(k,ni,iv) = qu(k,ni,1)
qd(k,ni,iv) = qd(k,ni,1)
qs(k,ni,iv) = qs(k,ni,1)
g(k,ni,iv) = -g(k,ni,1)
endif
endif
CMM defining subtracted integrands for both integrals
CMM tqm is T^q in integrand of integral from del to 1
do 33 l = 1, nx+1
if (l.lt.iv) then
pu(l) = dxdz(l)*tq(l)*4./9.*(qu(k,ni,l)-qu(k,ni,iv))/e
pd(l) = dxdz(l)*1./9.*tq(l)*(qd(k,ni,l)-qd(k,ni,iv))/e
ps(l) = dxdz(l)*1./9.*tq(l)*(qs(k,ni,l)-qs(k,ni,iv))/e
pg(l) = dxdz(l)*1./nf*tg(l)*(g(k,ni,l)-g(k,ni,iv))/(e**2)
elseif(l.gt.iv) then
CMM Same thing but also define the integrands for the second integral.
CMM Combine the original integral
C del..1 with the real part of the integrand T(2*y/del-1)*(q(y)-qdel).
pu1(l-iv+1) = dxdz(l)*(tqm(l)*4./9.*qu(k,ni,l)/e +
> sq*tq(l)*4./9.*(qu(k,ni,l)-qu(k,ni,iv))/e)
pd1(l-iv+1) = dxdz(l)*(1./9.*tqm(l)*qd(k,ni,l)/e +
> sq*1./9.*tq(l)*(qd(k,ni,l)-qd(k,ni,iv))/e)
ps1(l-iv+1) = dxdz(l)*(1./9.*tqm(l)*qs(k,ni,l)/e +
> sq*1./9.*tq(l)*(qs(k,ni,l)-qs(k,ni,iv))/e)
pg1(l-iv+1) = dxdz(l)*(1./nf*tgm(l)*g(k,ni,l)/(e**2) +
> sg*1./nf*tg(l)*(g(k,ni,l)-g(k,ni,iv))/(e**2))
CMM calculate imaginary piece from del...1 in first integral
CMM Subtractions needed here too
pui(l-iv+1) = dxdz(l)*tqi(l)*4./9.*(qu(k,ni,l)- qu(k,ni,iv))/e
pdi(l-iv+1) = dxdz(l)*1./9.*tqi(l)*(qd(k,ni,l)- qd(k,ni,iv))/e
psi(l-iv+1) = dxdz(l)*1./9.*tqi(l)*(qs(k,ni,l)- qs(k,ni,iv))/e
pgi(l-iv+1) = dxdz(l)*1./nf*tgi(l)*(g(k,ni,l)-g(k,ni,iv))/e**2
endif
33 continue
CMM value of integrand at y=del for the integral del..1
CMM Special point...not calculated above
CMM Algabraic expressions for tq(1) are given specially in wcread
CMM See notes for the calculation.
CMM Here we use the fact that tq(1) = tqm(iv), i.e. T(y=0) = Tm (y=del)
CMM To LO T = 1/(1-x) Tm = 1/(1+x), x = 2y/del -1 to T(y=0) = 1/2 =Tm(y=del)
CMM The use of pu1(iv) is just for code convenience, these integrands correspond to yy = del > xar(iv)
C
C Since semi-open simpson is used these points are not directly used in the integration but are still put here
C for bookkeeping purposes!
C
pu1(1) = diffdel*tq(1)*4./9.*qu(k,ni,iv)/e
pd1(1) = diffdel*1./9.*tq(1)*qd(k,ni,iv)/e
ps1(1) = diffdel*1./9.*tq(1)*qs(k,ni,iv)/e
pg1(1) = diffdel*1./nf*tg(1)*g(k,ni,iv)/(e**2)
C
C Values of the integrand for 0..del integral at y=del
C
pu(iv) = 0.0
pd(iv) = 0.0
ps(iv) = 0.0
pg(iv) = 0.0
C
C value of the integrands of the imaginary part in the integral from del..1.
C at y=del.
C
pui(1) = 0.0
pdi(1) = 0.0
psi(1) = 0.0
pgi(1) = 0.0
C
C \int^1_0 dy T(2*y/del-1)*(q(y)-q(del) -/+ \int^1_del dy T(1-2*y/del)*q(y)
C and reverse the sign for the gluon.
C
C
C Set # of points in ERBL and DGLAP region,first ERBL then DGLAP
C
nc1 = iv
nc2 = nx-iv+2
C
C spacing of points
C
dz = 1./nx
C
C do the integration from 0..del
C
temu = smpnor(nc1,dz,pu,err)
temd = smpnor(nc1,dz,pd,err)
tems = smpnor(nc1,dz,ps,err)
if (n.eq.2) then
temg = smpnor(nc1,dz,pg,err)
endif
C
C DO the integration from del..1
C
temu1 = smpnol(nc2,dz,pu1,err)
temd1 = smpnol(nc2,dz,pd1,err)
tems1 = smpnol(nc2,dz,ps1,err)
if (n.eq.2) then
temg1 = smpnol(nc2,dz,pg1,err)
endif
CMM Separate calc for for V and A not needed.
CMM Correct choice made within wcread
C
C Integration for imaginary part. del..1 only!
C
if (n.eq.2) then
temui = smpnol(nc2,dz,pui,err)
temdi = smpnol(nc2,dz,pdi,err)
temsi = smpnol(nc2,dz,psi,err)
temgi = smpnol(nc2,dz,pgi,err)
elseif (n.eq.1.and.tw.eq.3) then
temui = smpnol(nc2,dz,pui,err)
temdi = smpnol(nc2,dz,pdi,err)
temsi = smpnol(nc2,dz,psi,err)
temgi = 0D0
endif
CMM Unpolarized case
C
C Initialize variables
C
reqint = 0.
imqint = 0.
regint = 0.
imgint = 0.
C
C compute value of the counterterms for unpolarized case
C
if (iknl.eq.1) then
call counterV(tw,del,qone,mu,nf,reqint,imqint,regint,imgint,n)
C
C Assemble final value of the real parts
C
reau = temu - temu1 + 4./9.*qu(k,ni,iv)*reqint/e
read = temd - temd1 + 1./9.*qd(k,ni,iv)*reqint/e
reas = tems - tems1 + 1./9.*qs(k,ni,iv)*reqint/e
if (n.eq.2) then
reag = temg + temg1 + 1./(nf*e**2)*g(k,ni,iv)*regint
else
reag = 0D0
endif
C
C Assembly of imaginary part!
C
C
C There are no integrals for the imaginary part in LO (n=1) twist-2
C
If (n.eq.1.and.tw.eq.2) then
temui = 0.0
temdi = 0.0
temsi = 0.0
temgi = 0.0
endif
C
C put together counterterms and result of integral for imaginary part
C
ximau = 4./9.*qu(k,ni,iv)*imqint/e + temui
ximad = 1./9*qd(k,ni,iv)*imqint/e + temdi
ximas = 1./9.*qs(k,ni,iv)*imqint/e + temsi
if (n.eq.2) then
ximag = 1./(nf*e**2)*g(k,ni,iv)*imgint + temgi
else
ximag = 0D0
endif
C
C Same as above but now for the polarized amplitudes
C
else if(iknl.eq.2) then
call counterA(tw,del,qone,mu,nf,reqint,imqint,regint,imgint,n)
reau = temu + temu1 + 4./9.*qu(k,ni,iv)*reqint/e
read = temd + temd1 + 1./9.*qd(k,ni,iv)*reqint/e
reas = tems + tems1 + 1./9.*qs(k,ni,iv)*reqint/e
if (n.eq.2) then
reag = temg - temg1 + 1./(nf*e**2)*g(k,ni,iv)*regint
else
reag = 0D0
endif
if (n.eq.1) then
temui = 0.0
temdi = 0.0
temsi = 0.0
temgi = 0.0
endif
ximau = 4./9.*qu(k,ni,iv)*imqint/e + temui
ximad = 1./9*qd(k,ni,iv)*imqint/e + temdi
ximas = 1./9.*qs(k,ni,iv)*imqint/e + temsi
if (n.eq.2) then
ximag = 1./(nf*e**2)*g(k,ni,iv)*imgint + temgi
else
ximag = 0D0
endif
else
write(6,*) 'iknl not rec. stop'
stop
endif
C
C Write output of final results in files
C
write(1,102) q2**2, reau, ximau
write(2,102) q2**2, read, ximad
write(3,102) q2**2, reas, ximas
write(4,102) q2**2, reag, ximag
11 continue
22 continue
close(28)
close(4)
close(3)
close(2)
close(1)
c 101 continue
c 100 continue
c 99 continue
return
102 FORMAT(3(E15.8,1X))
end
C
C Dick Robert's code for alpha_s
C
real*8 function alpdr(n,nf,q)
implicit none
external alp
integer n,iord
real*8 nf
real*8 qsct,qsdt,alambda,xflav,lambda1,lambda2
common / clambda / lambda1, lambda2
common/alpin/alambda,xflav,qsct,qsdt,iord
real*8 al2,q2,t,alp,q
iord =n-1
xflav = dble(nf)
qsdt = 6.9696D0 !! mc = 1.32 values in PDG 2000
qsct = 73.96D0 !! mb = 4.3
alambda = lambda2
if (iord.eq.0) then
alambda = lambda1
endif
al2=alambda*alambda
q2 = q*q
t=dlog(q2/al2)
alpdr=alp(t)
return
end
real*8 FUNCTION alp(T)
implicit none
REAL*8 alambda,xflav,qsct,qsdt,pi
REAL*8 tol,tt,t,qsdtt,qsctt,al,al2,qs
integer iord,ith
real*8 b0,b1,f,fp,del,alfqc4,alfqc5,alfqs5,alfinv
real*8 x1,x2,as2,as,alfqs3,alfqc3
COMMON/alpin/alambda,xflav,qsct,qsdt,iord
DATA PI/3.141592653589793/
DATA TOL/.00005/
ITH=0
TT=T
qsdtt=qsdt/4.
qsctt=qsct/4.
AL=alambda
AL2=AL*AL
XFLAV=4.
QS=AL2*EXP(T)
if(qs.lt.0.5d0) then !! running stops below 0.5
qs=0.5d0
t=dlog(qs/al2)
tt=t
endif
IF(QS.gt.QSCTT) GO TO 12
IF(QS.lt.QSDTT) GO TO 312
11 CONTINUE
B0=11-2.*XFLAV/3.
X1=4.*PI/B0
IF(IORD.eq.0) then
ALP=X1/T
ELSE
B1=102.-38.*XFLAV/3.
X2=B1/B0**2
AS2=X1/T*(1.-X2*dlog(T)/T)
5 AS=AS2
F=-T+X1/AS-X2*dlog(X1/AS+X2)
FP=-X1/AS**2*(1.-X2/(X1/AS+X2))
AS2=AS-F/FP
DEL=ABS(F/FP/AS)
IF((DEL-TOL).GT.0.) go to 5
ALP=AS2
ENDIF
IF(ITH.EQ.0) RETURN
GO TO (13,14,15) ITH
GO TO 5
12 ITH=1
T=dlog(QSCTT/AL2)
GO TO 11
13 ALFQC4=ALP
XFLAV=5.
ITH=2
GO TO 11
14 ALFQC5=ALP
ITH=3
T=TT
GO TO 11
15 ALFQS5=ALP
ALFINV=1./ALFQS5+1./ALFQC4-1./ALFQC5
ALP=1./ALFINV
RETURN
311 CONTINUE
B0=11-2.*XFLAV/3.
X1=4.*PI/B0
IF(IORD.eq.0) then
ALP=X1/T
ELSE
B1=102.-38.*XFLAV/3.
X2=B1/B0**2
AS2=X1/T*(1.-X2*dlog(T)/T)
35 AS=AS2
F=-T+X1/AS-X2*dlog(X1/AS+X2)
FP=-X1/AS**2*(1.-X2/(X1/AS+X2))
AS2=AS-F/FP
DEL=ABS(F/FP/AS)
IF((DEL-TOL).GT.0.) go to 35
ALP=AS2
endif
IF(ITH.EQ.0) RETURN
GO TO (313,314,315) ITH
312 ITH=1
T=dlog(QSDTT/AL2)
GO TO 311
313 ALFQC4=ALP
XFLAV=3.
ITH=2
GO TO 311
314 ALFQC3=ALP
ITH=3
T=TT
GO TO 311
315 ALFQS3=ALP
ALFINV=1./ALFQS3+1./ALFQC4-1./ALFQC3
ALP=1./ALFINV
RETURN
END
C
C Coefficient functions for LO tq1 and NLO tq2,tq2a,tg2,tg2a
C
CMM See eq.(14-17) in BMNS hep-ph/9908337
real*8 function tq1(xx,qm)
implicit none
real*8 tq2,tq2a,tq3r,tq3i,tq3ar,tq3ai
real*8 tg2,tg2a,tg3r,tg3i,tg3ar,tg3ai
real*8 tq1t3,tq1r,tq1i
real*8 xx, qm
real*8 pi
PARAMETER (pi = 3.141592653589793)
tq1 = 1./(1.-xx)
return
entry tq1t3(xx,qm)
tq1t3 = (log(2.)-log(1.-xx))/(1.+xx)
return
entry tq2(xx,qm)
tq2 = ((2.*log((1.-xx)/2.) + 3.)*(log(qm) +
> log((1.-xx)/2.)/2. - 3./4.) - 27./4.)/(2.*(1.-xx)) -
> 3.*log((1.-xx)/2.)/(2.*(1.+xx))
return
entry tq2a(xx,qm)
tq2a = ((2.*log((1.-xx)/2.) + 3.)*(log(qm) +
> log((1.-xx)/2.)/2. - 3./4.) - 27./4.)/(2.*(1.-xx)) -
> log((1.-xx)/2.)/(2.*(1.+xx))
return
CMM Needed for del....1, i.e. x >1
CMM since xx > 1, t > xi now
CMM take minus sign out of log according to the sign of the +ie prescription
C
C **3*r = real part of coefficient function
C **3*i = imaginary part of coefficient function
C
entry tq1r(xx,qm)
tq1r = (log(2.)-log(xx-1.))/(1.+xx)
return
entry tq1i(xx,qm)
tq1i = pi/(1.+xx)
return
entry tq3r(xx,qm)
tq3r = ((2.*log((xx-1.)/2.) + 3.)*(log(qm) +
> log((xx-1.)/2.)/2. - 3./4.) - 27./4. - pi**2)/(2.*(1.-xx)) -
> 3.*log((xx-1.)/2.)/(2.*(1.+xx))
return
entry tq3i(xx,qm)
tq3i = -pi/2.*(2.*(log(qm)+log((xx-1.)/2.))/(1.-xx) -
> 3./(1.+xx))
return
entry tq3ar(xx,qm)
tq3ar = ((2.*log((xx-1.)/2.) + 3.)*(log(qm) +
> log((xx-1.)/2.)/2. - 3./4.) - 27./4. - pi**2)/(2.*(1.-xx)) -
> log((xx-1.)/2.)/(2.*(1.+xx))
return
entry tq3ai(xx,qm)
tq3ai = -pi/2.*(2.*(log(qm)+log((xx-1.)/2.))/(1.-xx) -
> 1./(1.+xx))
return
entry tg2(xx,qm)
tg2 = -((1./(1.-xx**2) + log((1.-xx)/2.)/(1.+xx)**2)*
> (log(qm) + log((1.-xx)/2.) - 2.) -
> (log((1.-xx)/2.)/(1.+xx))**2/2. )/2. +
> ((log(qm) + log((1.-xx)/2.) - 2.)/(1.-xx) +
> log((1.-xx)/2.)/(1.+xx))/2.
return
entry tg2a(xx,qm)
tg2a = ((1./(1.-xx**2) + log((1.-xx)/2.)/(1.+xx)**2)*
> (log(qm) + log((1.-xx)/2.) - 2.) -
> (log((1.-xx)/2.)/(1.+xx))**2/2.)/2.
return
entry tg3r(xx,qm)
tg3r = -((1./(1.-xx**2) + log((xx-1.)/2.)/(1.+xx)**2)*
> (log(qm) + log((xx-1.)/2.) - 2.) -
> (log((xx-1.)/2.)/(1.+xx))**2/2. - (pi/(1.+xx))**2/2.)/2. +
> ((log(qm) + log((xx-1.)/2.) - 2.)/(1.-xx) +
> log((xx-1.)/2.)/(1.+xx))/2.
return
entry tg3i(xx,qm)
tg3i = -pi*(1./(1.-xx**2) -
> (log(qm) +log((xx-1.)/2.) -2.)/(1.+xx)**2 )/2.
return
entry tg3ar(xx,qm)
tg3ar =((1./(1.-xx**2) + log((xx-1.)/2.)/(1.+xx)**2)*
> (log(qm) + log((xx-1.)/2.) - 2.) -
> (log((xx-1.)/2.)/(1.+xx))**2/2. -
> (pi/(1+xx))**2/2.)/2.
return
entry tg3ai(xx,qm)
tg3ai = -pi*((log(qm) + log((xx-1.)/2.) -2.)/(1.+xx)**2
> + 1./(1.-xx**2))/2.
return
end
C
C subroutine to read in of GPDs, q's and del's
C
subroutine readin(k1,n,iknl)