Smeared quasidistributions in perturbation theory

TL;DR

This paper calculates the flavor nonsinglet unpolarized quasi distribution at one loop in perturbation theory, demonstrating the use of gradient flow to handle divergences and matching to the MS scheme for lattice QCD to experimental PDF comparisons.

Contribution

It introduces a perturbative calculation of quasi distributions with gradient flow, enabling better connection between lattice QCD results and phenomenological PDFs.

Findings

Gradient flow does not alter the infrared structure at one loop.

Derived matching formulas to relate smeared matrix elements to MS scheme PDFs.

Validated the approach for nonperturbative lattice QCD applications.

Abstract

Quasi and pseudo distributions provide a new approach to determining parton distribution functions (PDFs) from first principles' calculations of quantum chromodynamics (QCD). Here I calculate the flavor nonsinglet unpolarized quasi distribution at one loop in perturbation theory, using the gradient flow to remove ultraviolet divergences. I demonstrate that, as expected, the gradient flow does not change the infrared structure of the quasi distribution at one loop and use the results to match the smeared matrix elements to those in the $\ms$ scheme. This matching calculation is required to relate numerical results obtained from nonperturbative lattice QCD computations to light-front PDFs extracted from global analyses of experimental data.