We calculate deep inelastic scattering (DIS) scheme splitting and coefficient functions for electromagnetic DIS with small $x$ resummations, as given by the next-to-leading-logarithmic Balitsky-Fadin-Kuraev-Lipatov (NLL BFKL) equation with running coupling and approximate NLL resummed impact factors. The resummations are combined with a next-to-leading order (NLO) fixed-order expansion, and the improved quantities thus obtained are stable at small $x$ and significantly suppressed with respect to leading logarithmic (LL) results. These results are implemented in a global fit to DIS and related data, and the results compared to a NLO fixed-order DIS scheme fit and with a previous LL resummed fit. The NLL resummed fit quality is excellent and constitutes a marked improvement over the purely fixed-order approach. The input gluon, at $Q_0^2=1{\mathrm{GeV}}^2$, obtained from the resummed fit is positive and slightly increasing as $x\to 0$, in contrast to the result obtained at fixed order. A resummed prediction for the longitudinal structure function $F_L$ is presented. It is positive definite and growing with energy at low $x$ and $Q^2$, where the fixed-order results show a significant perturbative instability.

• Received 16 November 2006

DOI:https://doi.org/10.1103/PhysRevD.75.034005