Non-perturbative renormalization of bilinear operators with M\"obius domain-wall fermions in the coordinate space

TL;DR

This paper presents a non-perturbative method to determine renormalization constants of quark bilinear operators using coordinate space correlation functions with Mobius domain-wall fermions, converting results to the $ mar{MS}$ scheme at 2 GeV.

Contribution

It introduces a coordinate space approach for non-perturbative renormalization of bilinear operators with Mobius domain-wall fermions on the lattice.

Findings

Renormalization constants determined at two lattice spacings.

Results converted to $ mar{MS}$ scheme at 2 GeV.

Method applied to flavor non-singlet quark bilinear operators.

Abstract

We study the non-perturbative determination of the renormalization constants of flavor non-singlet quark bilinear operators on the lattice. The renormalization condition is imposed on correlation functions of bilinear operators in the coordinate space. The results are converted to the value at 2 GeV in the $\rm\overline{MS}$ scheme by a perturbative matching. The calculation is carried out on gauge configurations generated with the Mobius domain-wall fermions at two lattice spacings $a^{-1} = 2.4$ GeV and $a^{-1} = 3.6$ GeV.