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(-lambda), lamb da positive, for x --> 0) and that of a soft-pomeron dominated behavio ur, also called double scaling limit, for the singlet component. A ful l next to leading order (NLO) analysis is carried out for the function s F-2, F-Glue and the longitudinal one F-L in ep scattering, and for x F(3) in neutrino scattering. The results of the calculations are compa red with experimental data, particularly the recent ones from HERA, in the range x less than or equal to 0.032, 10 GeV2 less than or equal t o Q(2) less than or equal to 1500 GeV2. We get reasonable fits, with a chi-squared per degree of freedom around two units, with only three-f our parameters in both cases. However, none of the assumptions is by i tself able to give a fully satisfactory description of the data. The r esults improve substantially when combining a soft and a hard componen t; in this case it is even possible to extend the analysis, phenomenol ogically, to small values of Q(2), 0.31 GeV2 less than or equal to Q(2 ) less than or equal to 8.5 GeV2, and in the x range 6 x 10(-6) less t han or similar to x less than or similar to 0.04, with the same hard p lus soft pomeron hypothesis by assuming a saturating expression for th e strong coupling, <(alpha)over tilde>(S)(Q(2)) = 4 pi/beta(0)log[(Q(2 ) + Lambda(eff)(2))/Lambda(eff)(2)]. The formulation for Low Q(2) impl ies serf-consistent values for the parameters in the exponents of x bo th for singlet and non-singlet components. One has to have, for the Re gge intercepts, alpha(p)(0) = 0.48 and alpha(p)(0) = 1.470 [lambda = 0 .470], in uncanny agreement with other determinations of these paramet ers, and in particular the results of the large Q(2) fits. The fit to data is so good that we may look fat large Q(2)) for signals of a ''tr iple pomeron'' vertex, for which some evidence is found. The quality o f the calculations of F-2, and of the predictions for F-Glue, F-L is o nly marred by the very large size of the NLO corrections for the singl et part of F-2. This, in particular, forbids a truly reliable determin ation of the QCD parameter, Lambda. (C) 1997 Elsevier Science B.V.