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Article
Report number	arXiv:2401.00216
Title	Heavy Wilson Quarks and O($a$) Improvement: Nonperturbative Results for $b_{\rm g}$
Related title	Heavy Wilson quarks and O(a) improvement: nonperturbative results for b$_{g}$
Author(s)	Dalla Brida, Mattia (CERN) ; Höllwieser, Roman (Wuppertal U.) ; Knechtli, Francesco (Wuppertal U.) ; Korzec, Tomasz (Wuppertal U.) ; Sint, Stefan (Hamilton Math. Inst., Dublin) ; Sommer, Rainer (Humboldt U., Berlin)
Collaboration	ALPHA Collaboration
Publication	2024-01-31
Imprint	2023-12-30
Number of pages	26
Note	26 pages, 5 figures. Included additional references and fixed some typos. Matches published version
In:	JHEP 2024 (2020) 188
DOI	10.1007/JHEP01(2024)188 (publication)
Subject category	hep-lat ; Particle Physics - Lattice
Accelerator/Facility, Experiment	ALPHA
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, $\tilde{g}_0^2 = g_0^2(1 + b_{\rm g} am_{\rm q})$, and the determination of $b_{\rm g}(g_0^2)$, 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 $\beta$-values and the line of constant physics are motivated by the ALPHA collaboration's decoupling strategy to determine $\alpha_s(m_Z)$. However, the improvement conditions and some insight into systematic effects may prove useful in other contexts, too.
Copyright/License	publication: © The Authors (License: CC-BY-4.0), sponsored by SCOAP³ preprint: (License: CC BY 4.0)

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