Progress in computing parton distribution functions from the quasi-PDF approach

TL;DR

This paper reviews recent progress in calculating parton distribution functions using the quasi-PDF approach, focusing on non-perturbative renormalization techniques and their systematic effects.

Contribution

It introduces a non-perturbative RI' scheme renormalization method for quasi-PDFs and analyzes associated systematic uncertainties.

Findings

Renormalization functions computed and converted to MSbar scheme

Renormalized matrix elements presented

Discussion of systematic effects in Z-factors

Abstract

We discuss the current developments by the European Twisted Mass Collaboration in extracting parton distribution functions from the quasi-PDF approach. We concentrate on the non-perturbative renormalization prescription recently developed by us, using the RI$'$ scheme. We show results for the renormalization functions of matrix elements needed for the computation of quasi-PDFs, including the conversion to the $\overline{\rm MS}$ scheme, and for renormalized matrix elements. We discuss the systematic effects present in the $Z$-factors and the possible ways of addressing them in the future.