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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.00216 |
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| _version_ | 1866929230627995648 |
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| author | Brida, Mattia Dalla Höllwieser, Roman Knechtli, Francesco Korzec, Tomasz Sint, Stefan Sommer, Rainer |
| author_facet | Brida, Mattia Dalla Höllwieser, Roman Knechtli, Francesco Korzec, Tomasz Sint, Stefan Sommer, Rainer |
| contents | 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 $β$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00216 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Heavy Wilson Quarks and O($a$) Improvement: Nonperturbative Results for $b_{\rm g}$ Brida, Mattia Dalla Höllwieser, Roman Knechtli, Francesco Korzec, Tomasz Sint, Stefan Sommer, Rainer High Energy Physics - Lattice 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 $β$-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. |
| title | Heavy Wilson Quarks and O($a$) Improvement: Nonperturbative Results for $b_{\rm g}$ |
| topic | High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2401.00216 |