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

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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 F 2, F Glue and the longitudinal one F L in ep scattering, and for χF 3 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 Q2 ⩽ 1500 GeV 2. 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 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, α s (Q2) = 4π / β 0 log[ (Q2 + Γ eff 2) / Γ eff 2 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, α ϱ (0) = 0.48 and α ϱ (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 F 2, and of the predictions for F Glue, F L is only marred by the very large size of the NLO corrections for the singlet part of F 2. This, in particular, forbids a truly reliable determination of the QCD parameter, A.