Can we trust small x resummation?

TL;DR

This paper reviews the status of small x resummation in parton distribution evolution, demonstrating its stability, robustness, and smooth matching with unresummed expansions, with minimal ambiguities when all relevant terms are included.

Contribution

It provides a comprehensive review showing that small x resummation is stable, robust, and well-matched to fixed-order calculations, clarifying ambiguities in the procedure.

Findings

Resummed perturbative expansion is stable and robust.

Resummation matches smoothly with unresummed expansions.

Ambiguities are small when all enhanced terms are included.

Abstract

We review the current status of small x resummation of evolution of parton distributions and of deep-inelastic coefficient functions. We show that the resummed perturbative expansion is stable, robust upon different treatments of subleading terms, and that it matches smoothly to the unresummed perturbative expansions, with corrections which are of the same order as the typical NNLO ones in the HERA kinematic region. We discuss different approaches to small x resummation: we show that the ambiguities in the resummation procedure are small, provided all parametrically enhanced terms are included in the resummation and properly matched.