Heavy Wilson Quarks and O($a$) Improvement: Nonperturbative Results for $b_{\rm g}$

Mattia Dalla Brida; Roman Höllwieser; Francesco Knechtli; Tomasz Korzec; Stefan Sint; Rainer Sommer

doi:10.1007/JHEP01(2024)188

paper

Heavy Wilson Quarks and O( $a$ ) Improvement: Nonperturbative Results for $b_{g}$

arXiv:2401.00216 · doi:10.1007/JHEP01(2024)188

Abstract

With Wilson quarks, on-shell O( $a$ ) improvement of the lattice QCD action is achieved by including the Sheikholeslami-Wohlert term and two further operators of mass dimension 5, which amount to a mass-dependent rescaling of the bare parameters. We here focus on the rescaled bare coupling, $g ~_{0}^{2} = g_{0}^{2} (1 + b_{g} a m_{q})$ , and the determination of $b_{g} (g_{0}^{2})$ , which is currently only known to 1-loop order of perturbation theory. We derive suitable improvement conditions in the chiral limit and in a finite space-time volume and evaluate these for different gluonic observables, both with and without the gradient flow. The choice of $β$ -values and the line of constant physics are motivated by the ALPHA collaboration's decoupling strategy to determine $α_{s} (m_{Z})$ . However, the improvement conditions and some insight into systematic effects may prove useful in other contexts, too.

arXiv comment26 pages, 5 figures. Included additional references and fixed some typos. Matches published version

Heavy Wilson Quarks and O( $a$ ) Improvement: Nonperturbative Results for $b_{g}$

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Heavy Wilson Quarks and O(a) Improvement: Nonperturbative Results for bg​

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Heavy Wilson Quarks and O( $a$ ) Improvement: Nonperturbative Results for $b_{g}$