Resummation of small-x double logarithms in QCD: inclusive deep-inelastic scattering

TL;DR

This paper develops a comprehensive resummation of small-x double logarithms in inclusive deep-inelastic scattering, improving theoretical predictions in QCD by summing dominant high-energy corrections to all orders.

Contribution

It introduces a novel resummation method for small-x double logarithms in inclusive DIS, achieving NNLL accuracy in full QCD and extending to N^3LL in the large-n_c limit.

Findings

Resummed double logarithms using modified Bessel functions.

Provided fixed-order expansions up to five loops.

Clarified the small-x structure of inclusive DIS in perturbation theory.

Abstract

We present a comprehensive study of high-energy double logarithms in inclusive DIS. They appear parametrically as alpha_s^n ln^{2n-k} x at the n-th order in perturbation theory in the splitting functions for the parton evolution and the coefficient functions for the hard scattering process, and represent the leading corrections at small $x$ in the flavour non-singlet case. We perform their resummation, in terms of modified Bessel functions, to all orders in full QCD up to NNLL accuracy, and partly to N^3LL and beyond in the large-n_c limit, and provide fixed-order expansions up to five loops. In the flavour-singlet sector, where these double logarithms are sub-dominant at small x compared to single-logarithmic alpha_s^n x^{-1} ln^{n-k} x BFKL contributions, we construct fixed-order expansions up to five loops at NNLL accuracy in full QCD. The results elucidate the analytic small-x structure underlying inclusive DIS results in fixed-order perturbation theory and provide important information for present and future numerical and analytic calculations of these quantities.