Progress on double-logarithmic large-x and small-x resummations for (semi-)inclusive hard processes

TL;DR

This paper reviews recent advances in resumming double-logarithmic contributions at large-x and small-x in QCD, highlighting methods to derive higher-order coefficients and discussing current limitations.

Contribution

It provides an overview of methods to derive the highest three logarithm coefficients at all orders in QCD from NNLO results, advancing resummation techniques for hard processes.

Findings

Derived coefficients of the top three logarithms at all orders in many cases.

Presented analytical and numerical results illustrating resummation progress.

Discussed limitations and future directions of current resummation methods.

Abstract

Over the past few years considerable progress has been made on the resummation of double-logarithmically enhanced threshold (large-x) and high-energy (small-x) higher-order contributions to the splitting functions for parton and fragmentation distributions and to the coefficient functions for inclusive deep-inelastic scattering and semi-inclusive e^+e^- annihilation. We present an overview of the methods which allow, in many cases, to derive the coefficients of the highest three logarithms at all orders in the strong coupling from next-to-next-to-leading order results in massless perturbative QCD. Some representative analytical and numerical results are shown, and the present limitations of these resummations are discussed.