RI/MOM renormalization of the quasi-PDF in lattice regularization

TL;DR

This paper investigates the lattice spacing dependence of quasi-PDF matrix elements in lattice QCD, revealing challenges in divergence cancellation and the impact of fermion actions on linear divergences.

Contribution

It provides a detailed analysis of the lattice spacing effects and divergence issues in RI/MOM renormalization of quasi-PDFs across multiple fermion actions and lattice spacings.

Findings

RI/MOM leaves a linearly divergent residue for quasi-PDFs.

Divergence cancellation deteriorates at smaller lattice spacings.

Interaction between Wilson link and external state causes linear divergence depending on fermion action.

Abstract

We analyze the lattice spacing dependence for the pion unpolarized matrix element of a quark bilinear operator with Wilson link (quasi-PDF operator) in the rest frame, using 13 lattice spacings ranging from 0.032 fm 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 an $1/a$ divergence, the cancelation of which in many ratios can be numerically tricky. Indeed, our results show that this cancelation 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.