# A complete non-perturbative renormalization prescription for quasi-PDFs

## TL;DR

This paper introduces a comprehensive non-perturbative renormalization method for quasi-PDFs in an RI' scheme, addressing divergences and operator mixing, with practical application to lattice QCD data.

## Contribution

It presents the first non-perturbative renormalization prescription for various quasi-PDFs, including treatment of divergences and operator mixing, and provides a procedure to convert to the MS scheme.

## Key findings

- Successful non-perturbative renormalization of quasi-PDFs
- Elimination of operator mixing in unpolarized quasi-PDFs
- Application to lattice data with improved artifact control

## Abstract

In this work we present, for the first time, the non-perturbative renormalization for the unpolarized, helicity and transversity quasi-PDFs, in an RI' scheme. The proposed prescription addresses simultaneously all aspects of renormalization: logarithmic divergences, finite renormalization as well as the linear divergence which is present in the matrix elements of fermion operators with Wilson lines. Furthermore, for the case of the unpolarized quasi-PDFs, we describe how to eliminate the unwanted mixing with the twist-3 scalar operator. We utilize perturbation theory for the one-loop conversion factor that brings the renormalization functions to the MS-scheme at a scale of 2 GeV. We also explain how to improve the estimates on the renormalization functions by eliminating lattice artifacts. The latter can be computed in one-loop perturbation theory and to all orders in the lattice spacing. We apply the methodology for the renormalization to an ensemble of twisted mass fermions with Nf=2+1+1 dynamical light quarks, and a pion mass of around 375 MeV.