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. [1] and [2].

The distributions are the sum of a perturbative pointlike (PL) contribution and of a non-perturbative contribution inspired by the Vector meson Dominance Model (VDM)
distr = PL + CnpVDM ,

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 Q02.

Q02     Cnp     
.34 GeV2     .60     AFG04_LW
.70 GeV2     .78     AFG04_BF (best fit value)
.97 GeV2     .84     AFG04_HG

These choices are commented in ref. [2]. 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 − x)p10 .

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), xd(x,Q2), xs(x,Q2), xc(x,Q2) and xb(x,Q2), the corresponding structure function F2(x,Q2) is also calculated

F2 = Cq * (q +
) + Cg * g + Cgam ,

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 [1] an [2]).

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 Q2.

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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