Heavy Wilson quarks and O(a) improvement: nonperturbative results for b$_{g}$

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

Preprint

PUBDB-2023-07490

Heavy Wilson quarks and O(a) improvement: nonperturbative results for b$_{g}$

Dalla Brida, M.DESY* ; Höllwieser, R.Extern* ; Knechtli, F.Extern* ; Korzec, T.Extern* ; Sint, S. ; Sommer, R.DESY* ; ALPHA Collaboration (Collaboration Author)

2024

[10.3204/PUBDB-2023-07490]

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Please use a persistent id in citations: doi:10.3204/PUBDB-2023-07490

Report No.: DESY-24-001; arXiv:2401.00216

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 α$_{s}$(m$_{Z}$) [1]. However, the improvement conditions and some insight into systematic effects may prove useful in other contexts, too.

Keyword(s): quark: Wilson ; dimension: 5 ; flow: gradient ; mass: operator ; quantum chromodynamics ; lattice field theory: action ; space-time ; symmetry: chiral ; decoupling ; nonperturbative ; mass dependence ; rescaling ; perturbation theory ; beta function ; coupling constant ; Algorithms and Theoretical Developments ; Lattice QCD ; Non-Perturbative Renormalization ; Standard Model Parameters

Classification:

ddc:530

Note: J. High Energ. Phys. 2024, 188 (2024). 26 pages, 5 figures. Included additional references and fixed some typos. Matches published version The work is supported by the German Research Foundation (DFG) research unit FOR5269 “Futuremethods for studying confined gluons in QCD”.

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