. THEORY OF SMALL x DEEP INELASTIC SCATTERING : NLO EVALUATIONS

We calculate structure functions at small x both under the assumption of a hard singularity (essentially, a power behaviour for x → 0), and that of a soft-Pomeron dominated behaviour (also called double scaling limit). A full next to leading order (NLO) analysis is carried for the functions F2, F Glue and the longitudinal one FL in ep scattering, and for xF3 in neutrino scattering. The results of the calculations are compared with experimental data, particularly the recent ones from HERA, in the range x ≤ 0.032, 12 GeV 2 ≤ Q 2 ≤ 1 200 GeV 2. We get a very good description of the data, with a chi-sqared/d.o.f. near unity, with only three-four parameters for both assumptions. The quality of the results , and in particular of the predictions for F Glue , FL is only marred by the very large size of the NLO corrections for the singlet part of F2. This, in particular, forbids a truly reliable determination of the QCD parameter, Λ.