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, \( {\tilde{g}}_0^2={g}_0^2\left(1+{b}_{\textrm{g}}a{m}_{\textrm{q}}\right) \), and the determination of \( {b}_{\textrm{g}}\left({g}_0^2\right) \) 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 αs(mZ) [1]. However, the improvement conditions and some insight into systematic effects may prove useful in other contexts, too.
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Acknowledgments
The work is supported by the German Research Foundation (DFG) research unit FOR5269 “Future methods for studying confined gluons in QCD”. RH was supported by the programme “Netzwerke 2021”, an initiative of the Ministry of Culture and Science of the State of Northrhine Westphalia, in the NRW-FAIR network, funding code NW21-024-A. SS and RS acknowledge funding by the H2020 program in the Europlex training network, grant agreement No. 813942. Generous computing resources were supplied by the North-German Supercomputing Alliance (HLRN, project bep00072) and by the John von Neumann Institute for Computing (NIC) at DESY, Zeuthen. The authors are grateful for the hospitality extended to them at CERN during the initial stage of this project. MDB would like to thank the members of the Lattice QCD group at Instituto de Física Teórica of Madrid for their kind hospitality and support during the final stages of this work. We thank our colleagues in the ALPHA-collaboration, and especially Alberto Ramos, for valuable discussions. The sole responsibility for the content of this publication lies with the authors.
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Dalla Brida, M., Höllwieser, R., Knechtli, F. et al. Heavy Wilson quarks and O(a) improvement: nonperturbative results for bg. J. High Energ. Phys. 2024, 188 (2024). https://doi.org/10.1007/JHEP01(2024)188
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DOI: https://doi.org/10.1007/JHEP01(2024)188