Eur. Phys. J. C (2018) 78: 321
https://doi.org/10.1140/epjc/s10052-018-5774-4

Regular Article - Theoretical Physics

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

¹ The Higgs Centre for Theoretical Physics, University of Edinburgh, JCMB, KB, Mayfield Rd, Edinburgh, EH9 3JZ, Scotland, UK
² Department of Physics and Astronomy, VU University, 1081 HV, Amsterdam, The Netherlands
³ Nikhef Theory Group, Science Park 105, 1098 XG, Amsterdam, The Netherlands
⁴ Dipartimento di Fisica, Sapienza Università di Roma and INFN, Sezione di Roma, Piazzale Aldo Moro 5, 00185, Rome, Italy
⁵ Dipartimento di Fisica, Università di Genova and INFN, Sezione di Genova, Via Dodecaneso 33, 16146, Genoa, Italy
⁶ Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford, OX1 3NP, UK

^* e-mail: luca.rottoli@physics.ox.ac.uk

Received: 18 October 2017
Accepted: 23 March 2018
Published online: 20 April 2018

Abstract

We present a determination of the parton distribution functions of the proton in which NLO and NNLO fixed-order calculations are supplemented by NLLx small-x resummation. Deep-inelastic structure functions are computed consistently at or , while for hadronic processes small-x resummation is included only in the PDF evolution, with kinematic cuts introduced to ensure the fitted data lie in a region where the fixed-order calculation of the hard cross-sections is reliable. In all other respects, the fits use the same methodology and are based on the same global dataset as the recent NNPDF3.1 analysis. We demonstrate that the inclusion of small-x resummation leads to a quantitative improvement in the perturbative description of the HERA inclusive and charm-production reduced cross-sections in the small x region. The impact of the resummation in our fits is greater at NNLO than at NLO, because fixed-order calculations have a perturbative instability at small x due to large logarithms that can be cured by resummation. We explore the phenomenological implications of PDF sets with small-x resummation for the longitudinal structure function at HERA, for parton luminosities and LHC benchmark cross-sections, for ultra-high-energy neutrino–nucleus cross-sections, and for future high-energy lepton–proton colliders such as the LHeC.