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We present a determination of the parton distribution functions of the protonin which NLO and NNLO fixed-order calculations are supplemented by NLLx small-xresummation. Deep inelastic structure functions are computed consistently atNLO+NLLx or NNLO+NLLx, while for hadronic processes small-x resummation isincluded only in the PDF evolution, with kinematic cuts introduced to ensurethe fitted data lie in a region where the fixed-order calculation of the hardcross-sections is reliable. In all other respects, the fits use the samemethodology and are based on the same global dataset as the recent NNPDF3.1analysis. We demonstrate that the inclusion of small-x resummation leads to aquantitative improvement in the perturbative description of the HERA inclusiveand charm-production reduced cross-sections in the small x region. The impactof the resummation in our fits is greater at NNLO than at NLO, becausefixed-order calculations have a perturbative instability at small x due tolarge logarithms that can be cured by resummation. We explore thephenomenological implications of PDF sets with small-x resummation for thelongitudinal structure function $F_L$ at HERA, for parton luminosities and LHCbenchmark cross-sections, for ultra-high energy neutrino-nucleuscross-sections, and for future high-energy lepton-proton colliders such as theLHeC.

Parton distributions with small-x resummation: evidence for BFKL dynamics in HERA data