Nonperturbative renormalization of composite operators with overlap fermions

TL;DR

This paper non-perturbatively computes renormalization constants for composite operators using overlap fermions on a quenched lattice, validating key relations and matching to the MS-bar scheme with minimal lattice artifacts.

Contribution

It provides the first non-perturbative renormalization constants for overlap fermions on a coarse lattice and tests fundamental relations like Z_A=Z_V and Z_S=Z_P.

Findings

Z_A and Z_V agree within 1% above 1.6 GeV

Renormalization constants match MS-bar scheme after RG analysis

Small lattice artifacts and weak quark mass dependence observed

Abstract

We compute non-perturbatively the renormalization constants of composite operators on a quenched $16^3 \times 28 $ lattice with lattice spacing $a$ = 0.20 fm for the overlap fermion by using the regularization independent (RI) scheme. The quenched gauge configurations were generated with the Iwasaki action. We test the relations $Z_A = Z_V$ and $ Z_S=Z_P$ and find that they agree well {(less than 1%)} above $\mu$ = 1.6 GeV. %even for our lattice with a coarse lattice spacing. We also perform a Renormalization Group (RG) analysis at the next-to-next-to-leading order and match the renormalization constants to the $\bar{\rm MS}$ scheme. The wave-function renormalization $Z_{\psi}$ is determined from the vertex function of the axial current and $Z_A$ from the chiral Ward identity. Finally, we examine the finite quark mass behavior for the renormalization factors of the quark bilinear operators. We find that the $(pa)^2$ errors of the vertex functions are small and the quark mass dependence of the renormalization factors to be quite weak.