Theory of small x deep inelastic scattering: NLO evaluations, and low Q2 analysis

We calculate structure functions at small x both under the assumption of a hard singularity (essentially, a power behaviour χ−λ, A positive, for x → 0) and 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 out for the functions F2, FGlue and the longitudinal one FL in ep scattering, and for χF3 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 GeV2 Q2 ⩽ 1500 GeV2. We get reasonable fits, with a chi-squared per degree of freedom around two units, with only three-four parameters in both cases. However, none of the assumptions is by itself able to give a fully satisfactory description of the data. The results improve substantially when combining a soft and a hard component; in this case it is even possible to extend the analysis, phenomenologically, to small values of Q2, 0.31 GeV2 ⩽ Q2 ⩽ 8.5 GeV2, 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 (Q2) = 4π / β0 log[ (Q2 + Γeff2) / Γeff2 1. The formulation for low Q2 implies self-consistent values for the parameters in the exponents of x both for singlet and non-singlet components. One has to have, for the Regge intercepts, αϱ(0) = 0.48 and αϱ(0) = 1.470 [λ = 0.470], in uncanny agreement with other determinations of these parameters, and in particular the results of the large Q2 fits. The fit to data is so good that we may look (at large Q2) 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 FGlue, 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, A.