Soft-Gluon Resummation and PDF Theory Uncertainties

TL;DR

The paper investigates how soft-gluon resummation and higher-order corrections affect parton distribution functions (PDFs) and their determinations. It formalizes factorization and scheme/scale choices, then develops resummation in DIS and hadronic processes (e.g., Drell–Yan), showing that threshold resummation can modify high-$x$ PDFs and reduce scale sensitivity, while remaining largely compatible with existing NLO PDFs for moderate kinematics. It advocates incorporating resummed coefficient functions into global PDF fits to better capture higher-order effects, especially near partonic threshold, and discusses power-suppressed (higher-twist) corrections as additional scheme-like extensions. Overall, resummation offers a path to more accurate PDF determinations and more stable predictions in regions where large logarithms are important.

Abstract

Parton distribution functions are determined by the comparison of finite-order calculations with data. We briefly discuss the interplay of higher order corrections and PDF determinations, and the use of soft-gluon resummation in global fits.

Figures (2)

• Figure 1: Ratio of Mellin-$N$ moments of resummed and NLO $\overline{\rm MS}$-scheme quark coefficient functions for $F_2$. The numbers denote the value of $Q^2$ in GeV$^2$. We have chosen $\mu=Q$.
• Figure 2: Ratio of the valence parts of the resummed and NLO proton structure function $F_2 (x,Q^2)$, as a function of $Q^2$ for various values of Bjorken-$x$. For $F_2^{\rm res}$, the 'resummed' parton densities have been determined through Eq. (\ref{['fresdef']}).