Static force from generalized Wilson loops on the lattice using the gradient flow
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929488835641344 |
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| author | Brambilla, Nora Leino, Viljami Mayer-Steudte, Julian Vairo, Antonio |
| author_facet | Brambilla, Nora Leino, Viljami Mayer-Steudte, Julian Vairo, Antonio |
| contents | The static QCD force from the lattice can be used to extract $Λ_{\overline{\textrm{MS}}}$, which determines the running of the strong coupling. Usually, this is done with a numerical derivative of the static potential. However, this introduces additional systematic uncertainties; thus, we use another observable to measure the static force directly. This observable consists of a Wilson loop with a chromoelectric field insertion. We work in the pure SU(3) gauge theory. We use gradient flow to improve the signal-to-noise ratio and to address the field insertion. We extract $Λ_{\overline{\textrm{MS}}}^{n_f=0}$ from the data by exploring different methods to perform the zero-flow-time limit. We obtain the value $\sqrt{8t_0} Λ_{\overline{\textrm{MS}}}^{n_f=0} =0.629^{+22}_{-26}$, where $t_0$ is a flow-time reference scale. We also obtain precise determinations of several scales: $r_0/r_1$, $\sqrt{8 t_0}/r_0$, $\sqrt{8 t_0}/r_1$ and we compare these to the literature. The gradient flow appears to be a promising method for calculations of Wilson loops with chromoelectric and chromomagnetic insertions in quenched and unquenched configurations |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_17231 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Static force from generalized Wilson loops on the lattice using the gradient flow Brambilla, Nora Leino, Viljami Mayer-Steudte, Julian Vairo, Antonio High Energy Physics - Lattice High Energy Physics - Phenomenology High Energy Physics - Theory Nuclear Theory The static QCD force from the lattice can be used to extract $Λ_{\overline{\textrm{MS}}}$, which determines the running of the strong coupling. Usually, this is done with a numerical derivative of the static potential. However, this introduces additional systematic uncertainties; thus, we use another observable to measure the static force directly. This observable consists of a Wilson loop with a chromoelectric field insertion. We work in the pure SU(3) gauge theory. We use gradient flow to improve the signal-to-noise ratio and to address the field insertion. We extract $Λ_{\overline{\textrm{MS}}}^{n_f=0}$ from the data by exploring different methods to perform the zero-flow-time limit. We obtain the value $\sqrt{8t_0} Λ_{\overline{\textrm{MS}}}^{n_f=0} =0.629^{+22}_{-26}$, where $t_0$ is a flow-time reference scale. We also obtain precise determinations of several scales: $r_0/r_1$, $\sqrt{8 t_0}/r_0$, $\sqrt{8 t_0}/r_1$ and we compare these to the literature. The gradient flow appears to be a promising method for calculations of Wilson loops with chromoelectric and chromomagnetic insertions in quenched and unquenched configurations |
| title | Static force from generalized Wilson loops on the lattice using the gradient flow |
| topic | High Energy Physics - Lattice High Energy Physics - Phenomenology High Energy Physics - Theory Nuclear Theory |
| url | https://arxiv.org/abs/2312.17231 |