Global fit to scattering data with next-to-leading logarithmic BFKL resummations

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 Q₀²=1 GeV², obtained from the resummed fit is positive and slightly increasing as x→0, in contrast to the result obtained at fixed order. A resummed prediction for the longitudinal structure function FL is presented. It is positive definite and growing with energy at low x and Q², where the fixed-order results show a significant perturbative instability.