$\mathrm{O}(a)$ improvement of the flavour singlet scalar density in a setup with Wilson fermions

TL;DR

This paper determines the $ ext{O}(a)$ improvement coefficient for the flavour singlet scalar density in three-flavour lattice QCD with Wilson-clover fermions, aiding more accurate simulations of hadronic properties.

Contribution

It provides a non-perturbative determination of the $ ext{O}(a)$ improvement coefficient $g_S$ and relates it to the gauge coupling improvement parameter $b_g$ in Wilson fermion lattice QCD.

Findings

Determined $g_S$ for five couplings covering CLS simulation range.

Established a relation between $g_S$ and $b_g$ for $ ext{O}(a)$ improvement.

Outlined a procedure for extracting $b_g$ non-perturbatively.

Abstract

We report on our Ward identity determination of the $\mathrm{O}(a)$ improvement coefficient for the flavour singlet scalar density, namely $g_\mathrm{S}$, from three-flavour lattice QCD with Wilson-clover fermions and the tree-level Symanzik improved gauge action. We employ five couplings, $g_0^2 \in [1.5,1.77]$, that cover the range used in large-volume CLS simulations. While $g_\mathrm{S}$ itself is for instance relevant for the $\mathrm{O}(a)$ improvement of meson and baryon sigma terms, a relation to $b_\mathrm{g}$, the $\mathrm{O}(a)$ improvement parameter of the gauge coupling, can also be established, allowing for its non-perturbative extraction as well. With Wilson fermions, $b_\mathrm{g}$ is in principle required for full $\mathrm{O}(a)$ improvement at non-vanishing sea quark masses. We outline our procedure for extracting $b_\mathrm{g}$.