Renormalization of domain-wall bilinear operators with short-distance current correlators

TL;DR

This paper non-perturbatively determines renormalization constants for domain-wall fermion operators using short-distance correlators, achieving high precision with perturbative coefficients up to four loops.

Contribution

It introduces a coordinate-space renormalization scheme for fermion bilinear operators with M"obius domain-wall fermions, utilizing high-order perturbative expansions and multiple lattice spacings.

Findings

Renormalization constants are accurately computed for various lattice spacings.

The method reproduces perturbative results at short distances.

High-precision non-perturbative renormalization achieved.

Abstract

We determine the renormalization constants for flavor non-singlet fermion bilinear operators of M\"obius domain-wall fermions. The renormalization condition is imposed on the correlation functions in the coordinate space, such that the non-perturbative lattice calculation reproduces the perturbatively calculated counterpart at short distances. The perturbative expansion is precise as the coefficients are available up to $O(\alpha_s^4)$. We employ $2+1$-flavor lattice ensembles at three lattice spacings in the range 0.044--0.080~fm.