A Hybrid Renormalization Scheme for Quasi Light-Front Correlations in Large-Momentum Effective Theory

TL;DR

This paper proposes a hybrid renormalization scheme for lattice QCD calculations of parton distributions in LaMET, effectively handling divergences and enabling accurate continuum matching without extra non-perturbative effects.

Contribution

It introduces a novel hybrid renormalization procedure for coordinate-space correlations in LaMET, improving the matching to the continuum scheme and addressing divergence issues.

Findings

The scheme effectively matches lattice correlations to the MSbar scheme.

It reduces non-perturbative effects at large z in the renormalization process.

Guidelines for extrapolating lattice data to obtain momentum-space distributions.

Abstract

In large-momentum effective theory (LaMET), calculating parton physics starts from calculating coordinate-space-$z$ correlation functions $\tilde h(z, a,P^z)$ in a hadron of momentum $P^z$ in lattice QCD. Such correlation functions involve both linear and logarithmic divergences in lattice spacing $a$, and thus need to be properly renormalized. We introduce a hybrid renormalization procedure to match these lattice correlations to those in the continuum $\overline{\rm MS}$ scheme, without introducing extra non-perturbative effects at large $z$. We analyze the effect of ${\cal O}(\Lambda_{\rm QCD})$ ambiguity in the Wilson line self-energy subtraction involved in this hybrid scheme. To obtain the momentum-space distributions, we recommend to extrapolate the lattice data to the asymptotic $z$-region using the generic properties of the coordinate space correlations at moderate and large $P^z$, respectively.