A novel approach to nonperturbative renormalization of singlet and nonsinglet lattice operators

TL;DR

This paper introduces a new nonperturbative method for renormalizing lattice operators using the Feynman-Hellmann relation, enabling calculation of renormalization factors for both singlet and nonsinglet operators.

Contribution

The paper presents a novel Feynman-Hellmann based approach for nonperturbative renormalization applicable to singlet and nonsinglet lattice operators, demonstrated with axial and scalar operators.

Findings

Excellent agreement with existing methods for nonsinglet operators.

Successfully computed renormalization factors for singlet operators.

Method proves effective for Nf=3 SLiNC fermions.

Abstract

A novel method for nonperturbative renormalization of lattice operators is introduced, which lends itself to the calculation of renormalization factors for nonsinglet as well as singlet operators. The method is based on the Feynman-Hellmann relation, and involves computing two-point correlators in the presence of generalized background fields arising from introducing additional operators into the action. As a first application, and test of the method, we compute the renormalization factors of the axial vector current $A_\mu$ and the scalar density $S$ for both nonsinglet and singlet operators for $N_f=3$ flavors of SLiNC fermions. For nonsinglet operators, where a meaningful comparison is possible, perfect agreement with recent calculations using standard three-point function techniques is found.