Evolution of Parton Distribution Functions in the Short-Distance Factorization Scheme

TL;DR

This paper investigates the evolution of non-singlet parton distribution functions within the short-distance factorization scheme, derived from lattice QCD data, and compares it with perturbative expectations to improve lattice calculations.

Contribution

It introduces a method for non-perturbative evolution of PDFs in the short-distance scheme from lattice data, aiding in data fluctuation reduction and proposing a new lattice calculation strategy.

Findings

Non-perturbative evolution can reduce lattice data fluctuations.

Comparison shows partial agreement with perturbative matching.

Current limitations suggest using small-volume lattice calculations.

Abstract

Lattice QCD offers the possibility of computing parton distributions from first principles, although not in the usual $\overline{MS}$ factorization scheme. We study in this paper the evolution of non-singlet parton distribution functions (PDFs) in the short-distance factorization scheme which notably arises in lattice calculations in the pseudo-distribution approach. We provide an assessment of non-perturbative evolution of PDFs from already published lattice matrix elements, and show how this evolution can be used to reduce the fluctuation of the lattice data. We compare our result with expectations obtained thanks to a perturbative matching to $\overline{MS}$. By highlighting the limitations of the current computations, we advocate for a new strategy using lattice calculations in small volume.