Non-perturbative renormalization of the quark condensate in Ginsparg-Wilson regularizations

TL;DR

This paper introduces a non-perturbative method for calculating the renormalization constant of the scalar density in Ginsparg-Wilson fermions, leveraging chiral symmetry and matching RG invariant masses, applicable to various lattice regularizations.

Contribution

It presents a general approach for non-perturbative renormalization of scalar and pseudoscalar densities using chiral symmetry, applicable across different lattice regularizations.

Findings

Computed the non-perturbative factor relating the quark condensate to its bare value.

Applied the method to overlap fermions at beta=5.85 in quenched approximation.

Demonstrated the approach's generality for chiral-symmetric lattice regularizations.

Abstract

We present a method to compute non-perturbatively the renormalization constant of the scalar density for Ginsparg-Wilson fermions. It relies on chiral symmetry and is based on a matching of renormalization group invariant masses at fixed pseudoscalar meson mass, making use of results previously obtained by the ALPHA Collaboration for O(a)-improved Wilson fermions. Our approach is quite general and enables the renormalization of scalar and pseudoscalar densities in lattice regularizations that preserve chiral symmetry and of fermion masses in any regularization. As an application we compute the non-perturbative factor which relates the renormalization group invariant quark condensate to its bare counterpart, obtained with overlap fermions at beta=5.85 in the quenched approximation.