RI/MOM renormalization of the parton quasidistribution functions in lattice regularization

Kuan Zhang,Yuan-Yuan Li,Peng Sun,Andreas Schäfer,Yi-Kai Huo,Yi-Bo Yang

doi:10.1103/physrevd.104.074501

Abstract

We analyze the lattice spacing dependence for the pion unpolarized matrix element of a quark bilinear operator with a Wilson link (parton quasidistribution functions operator, quasi-PDFs) in the rest frame, using 13 lattice spacings ranging from 0.032 to 0.121 fm. We compare results for three different fermion actions with or without good chiral symmetry on dynamical gauge ensembles from three collaborations. This investigation is motivated by the fact that the gauge link generates a $1/a$ divergence, the cancellation of which in many ratios can be numerically tricky. Indeed, our results show that this cancellation deteriorates with decreasing lattice spacing, and that the RI/MOM method leaves a linearly divergent residue for quasi-PDFs. We also show that in the Landau gauge the interaction between the Wilson link and the external state results in a linear divergence which depends on the discretized fermion action.

Highlights

Parton distribution functions (PDFs) play a key role for most processes in high energy and hadron physics, ranging, e.g., from the search for new physics to the detailed analysis of nucleon properties
Our results show that this cancellation deteriorates with decreasing lattice spacing, and that the RI/MOM method leaves a linearly divergent residue for quasi-PDFs
We show that in the Landau gauge the interaction between the Wilson link and the external state results in a linear divergence which depends on the discretized fermion action

Summary

INTRODUCTION

Parton distribution functions (PDFs) play a key role for most processes in high energy and hadron physics, ranging, e.g., from the search for new physics to the detailed analysis of nucleon properties It is one of the most important tasks of lattice QCD to determine PDFs by first principle theory calculations. An accurate nonperturbative examination of this cancellation in lattice regularization is still missing To close this gap, we study the RI/MOM renormalized pion quasi-PDF matrix element in the rest frame, for 13 lattice spacings ranging from 0.032 to 0.121 fm using different quark and gluon actions. Our results show that the cancellation deteriorates with decreasing lattice spacing and that the RI/MOM method leaves a linearly divergent residue for quasi-PDFs. We show that in the Landau gauge the interaction between the Wilson link and the external state results in a linear divergence which depends on the discretized fermion action

NUMERICAL SETUP

RESULTS

POSSIBLE ORIGIN OF THE RESIDUAL LINEAR DIVERGENCE

SUMMARY