A Modification of the Saturation Model: DGLAP Evolution

We propose to modify the saturation model of Golec-Biernat and Wüsthoff by including DGLAP evolution. We find considerable improvement for the total deep inelastic cross section, in particular in the large Q region. The successful description of DIS diffraction is preserved. The saturation model [1, 2, 3] has provided a successful description of HERA deep inelastic scattering data, in particular for the transition from the perturbative region to the nonperturbative photoproduction region. This includes both the total γ∗p cross section and the DIS diffractive cross section. Whereas the formulae are particularly appealing through their simplicity, they also have an attractive theoretical background, namely the idea of saturation. Despite its success, the model suffers from shortcomings which should be cured. In particular, the model does not include logarithmic scaling violations, i.e. at larger values of Q2 it does not exactly match with QCD evolution (DGLAP). This becomes clearly visible in the energy dependence of σ p tot in the region Q 2 > 20 GeV2 where the model predictions are below the data. One expects that QCD evolution should enhance the cross section in this region. It is the purpose of this letter to propose a modification of the saturation model. We attempt to preserve the success of the model in the low-Q2 and in the transition region, while incorporating DGLAP evolution in the large-Q2 domain. Since the energy dependence in the large-Q2 region is mainly due to the behaviour of the dipole cross section at small dipole sizes r, our changes will affect mostly the small-r region. At the same time, particular attention will be given to DIS diffraction for which the saturation model correctly describes the energy dependence. Since the inclusive diffractive cross section mostly depends upon the large-r behaviour of the dipole cross section, we attempt to leave the dipole cross section unchanged in this region. A recent attempt [4] along the same lines indicates that, in fact, diffraction provides a highly nontrivial restriction on possible modifications of the saturation model.