The AFG04 NLO parametrizations are based on a scheme invariant implementation
of the non-perturbative component of the parton distributions in real photon.
This approach is described in ref.  and .
The distributions are the sum of a perturbative pointlike (PL) contribution
and of a non-perturbative contribution inspired by the Vector meson Dominance
distr = PL + Cnp⋅ VDM
where the coefficient Cnp fixes the relative
normalization of the PL and VDM contributions. The pointlike contribution is
characterized by the scale Q02 which is the
starting point of the QCD evolution. The parameters
Cnp and Q02 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 Cnp and
|| AFG04_BF (best fit value)
These choices are commented in ref. . The
AFG04 parametrization also offers the possibility to modify the shape of the
non-perturbative gluon distribution which is described, at
Q2 = 2 GeV2, by the input
x g(x, Q2=2) ∼ (1 −
The choices p10 = 1.0 (hard gluon), p10 =
1.9 (standard gluon) and p10 = 4.0 (soft gluon) are
available to the users.
Besides the distributions xu(x,Q2),
xb(x,Q2), the corresponding structure
function F2(x,Q2) is also
|F2 = Cq
* (q +
||) + Cg * g +
where Cq and
Cg are the Wilson coefficients and
Cgam is the direct term. Although the heavy quark
evolution is massless, the direct term Cgam includes
the effects due to the heavy quark mass. The heavy quark thresholds are
therefore correctly described at the lowest order in
αs. (Details are given in  an ).
The various parametrizations and the photon structure function
F2 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 F2. 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
The source code is available here: afg04.tar.gz
Please send any questions/comments to Michel Fontannaz
- P. Aurenche, M. Fontannaz, J. Ph. Guillet, Z. Phys.
C64 (1994) 621.
- P. Aurenche, M. Fontannaz, J. Ph. Guillet, [hep-ph/0503259].
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