Self-Renormalization of Quasi-Light-Front Correlators on the Lattice

TL;DR

This paper presents a lattice QCD renormalization strategy for quasi-PDF operators that effectively disentangles divergences, demonstrating universality and independence from fermion formulations, with implications for improved non-perturbative renormalization methods.

Contribution

The authors develop a self-renormalization approach for quasi-light-front correlators on the lattice, addressing linear divergences and establishing universality across different fermion formulations.

Findings

Renormalization factors are universal across hadron states.

Physical matrix elements are independent of valence fermion formulations.

Hybrid renormalization scheme shows advantages over RI/MOM and ratio schemes.

Abstract

In applying large-momentum effective theory, renormalization of the Euclidean correlators in lattice regularization is a challenge due to linear divergences in the self-energy of Wilson lines. Based on lattice QCD matrix elements of the quasi-PDF operator at lattice spacing $a$= 0.03 fm $\sim$ 0.12 fm with clover and overlap valence quarks on staggered and domain-wall sea, we design a strategy to disentangle the divergent renormalization factors from finite physics matrix elements, which can be matched to a continuum scheme at short distance such as dimensional regularization and minimal subtraction. Our results indicate that the renormalization factors are universal in the hadron state matrix elements. Moreover, the physical matrix elements appear independent of the valence fermion formulations. These conclusions remain valid even with HYP smearing which reduces the statistical errors albeit reducing control of the renormalization procedure. Moreover, we find a large non-perturbative effect in the popular RI/MOM and ratio renormalization scheme, suggesting favor of the hybrid renormalization procedure proposed recently.