afg04
The AFG04 NLO parametrizations are based on a scheme invariant implementation
of the nonperturbative component of the parton distributions in real photon.
This approach is described in ref. [1] and [2].
The distributions are the sum of a perturbative pointlike (PL) contribution
and of a nonperturbative contribution inspired by the Vector meson Dominance
Model (VDM)
distr = PL + C_{np}⋅ VDM
,
where the coefficient C_{np} fixes the relative
normalization of the PL and VDM contributions. The pointlike contribution is
characterized by the scale Q_{0}^{2} which is the
starting point of the QCD evolution. The parameters
C_{np} and Q_{0}^{2} are
determined by a fit to LEP data.
The values obtained by this fit are somehow scattered and the AFG04
parametrization takes this fact into account by offering the choice between
several values of C_{np} and
Q_{0}^{2}.
Q_{0}^{2} 
C_{np} 




.34 GeV^{2} 
.60 
AFG04_LW 
.70 GeV^{2} 
.78 
AFG04_BF (best fit value) 
.97 GeV^{2} 
.84 
AFG04_HG 
These choices are commented in ref. [2]. The
AFG04 parametrization also offers the possibility to modify the shape of the
nonperturbative gluon distribution which is described, at
Q^{2} = 2 GeV^{2}, by the input
x g(x, Q^{2}=2) ∼ (1 −
x)^{p10} .
The choices p_{10} = 1.0 (hard gluon), p_{10} =
1.9 (standard gluon) and p_{10} = 4.0 (soft gluon) are
available to the users.
Besides the distributions xu(x,Q^{2}),
xd(x,Q^{2}),
xs(x,Q^{2}),
xc(x,Q^{2}) and
xb(x,Q^{2}), the corresponding structure
function F_{2}(x,Q^{2}) is also
calculated
F_{2} = C_{q}
* (q + 

) + C_{g} * g +
C_{gam} , 
where C_{q} and
C_{g} are the Wilson coefficients and
C_{gam} is the direct term. Although the heavy quark
evolution is massless, the direct term C_{gam} includes
the effects due to the heavy quark mass. The heavy quark thresholds are
therefore correctly described at the lowest order in
α_{s}. (Details are given in [1] an [2]).
The various parametrizations and the photon structure function
F_{2} are obtained by a call to SUBROUTINE AFG04(iflag, if2,
x, q2, xu, xd, xs, xc, xb, xglu, f2m) in which the flag “iflag”
allows the users to choose the desired distributions and the flag
“if2” enables to switch on/off the calculation of the structure
function F_{2}. This subroutine is contained in the FORTRAN program
AFG04.f. This interpolation program reads the different files
outpol_mc_fin.34, outpol_mc_fin.7, outpol_mc_fin.97, outvdm_fin1.0,
outvdm_fin1.0_glu1.0 and outvdm_fin1.0_glu4.0 and gives the quark and gluon
distributions in real photon as functions of x and
Q^{2}.
The source code is available here: afg04.tar.gz
Please send any questions/comments to Michel Fontannaz
References
 [1]
 P. Aurenche, M. Fontannaz, J. Ph. Guillet, Z. Phys.
C64 (1994) 621.
 [2]
 P. Aurenche, M. Fontannaz, J. Ph. Guillet, [hepph/0503259].
This document was translated from L^{A}T_{E}X by
H^{E}V^{E}A.