$Z_S/Z_P$ from three-flavour lattice QCD

TL;DR

This paper presents a non-perturbative calculation of the ratio of scalar to pseudoscalar renormalization constants in three-flavour lattice QCD, aiding precise quark mass determinations.

Contribution

It introduces a Ward identity-based method using Schrödinger functional boundary conditions to compute $Z_S/Z_P$ across various couplings and lattice spacings.

Findings

Results cover a range of couplings relevant for phenomenology.

Provides $Z_S/Z_P$ ratios at lattice spacings around 0.09 fm and below.

Supports accurate renormalized quark mass calculations.

Abstract

We report on advances in the non-perturbative determination of the ratio $Z_S/Z_P$ of the pseudoscalar to the scalar renormalization constants in three-flavour lattice QCD with Wilson-clover quarks and tree-level Symanzik improved gluons. The computations are based on the Ward identity approach, using Schr\"odinger functional boundary conditions. Our results for $Z_S/Z_P$ cover a range of couplings along a line of constant physics with lattice spacings of about 0.09 fm and below, relevant for phenomenological applications such as the calculation of renormalized quark masses.