Theory of Small x Deep Inelastic Scattering : NLO Evaluations , and low Q 2 Analysis

We calculate structure functions at small x both under the assumption of a hard singularity (essentially, a power behaviour x −λ , λ positive, for x → 0) or that of a soft-Pomeron dominated behaviour, also called double scaling limit, for the singlet component. 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, 10 GeV 2 ≤ Q 2 ≤ 1 500 GeV 2. We get reasonable fits, with a chi-squared/d.o.f. around two unities, with only three-four parameters for both assumptions, but none of the assumptions is by itself able to give a fully satisfactory description of the data. The results improve substantially if combining a soft and a hard component; in this case it is even possible to extend the analysis, phenomenologically, to small values of Q 2 , 0.31 GeV 2 ≤ Q 2 ≤ 8.5 GeV 2 , and in the x range 6 × 10 −6 < ∼ x < ∼ 0.04, with the same hard plus soft Pomeron hypothesis by assuming a saturating expression for the strong coupling, ˜ αs(Q 2) = 4π/β0 log[(Q 2 + Λ 2 eff)/Λ 2 eff ]. The description for low Q 2 implies self-consistent values for the parameters in the exponents of x both for singlet and nonsinglet components. One has to have, for the Regge intercepts, αρ(0) = 0.48 and αP (0) = 1.470 [λ = 0.470], in uncanny agreement with other determinations of these parameters, and in particular the results of the large Q 2 fits. The fit to data is so good that we may look (at large Q 2) for signals of a " triple Pomeron " vertex, for which some evidence is found. The quality of the calculations of F2, and 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.