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Static force from generalized Wilson loops on the lattice using the gradient flow
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abstract
The static QCD force from the lattice can be used to extract $\Lambda_{\overline{\textrm{MS}}}$, 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 $\Lambda_{\overline{\textrm{MS}}}^{n_f=0}$ from the data by exploring different methods to perform the zero-flow-time limit. We obtain the value $\sqrt{8t_0} \Lambda_{\overline{\textrm{MS}}}^{n_f=0} =0.629^{+22}_{-26}$, 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
Forward citations
Cited by 4 Pith papers
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Lattice study of correlators of chromoelectric fields for heavy quarkonium dynamics in the quark-gluon plasma
Adjoint chromoelectric correlators relevant for quarkonium dynamics are calculated in quenched lattice QCD and found to equal the fundamental correlator times Casimir factors, confirming leading-order relations nonper...
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Strong coupling in (2+1+1)-flavor QCD
A first, preliminary extraction of the QCD strong coupling from static quark-antiquark energy in (2+1+1)-flavor lattice QCD, consistent with previous determinations but not yet final.
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Computing $1/m_Q$ and $1/m_Q^2$ corrections to the static potential with lattice gauge theory using gradient flow
Tree-level improvement of flowed Wilson loops reduces lattice and flow-time errors, giving preliminary 1/m_Q and 1/m_Q^2 corrections to the static quark-antiquark potential.
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Adjoint chromoelectric correlators for heavy quarkonium diffusion
First lattice measurement of adjoint chromoelectric correlators shows they scale with the fundamental heavy-quark diffusion correlator by the perturbative factors 5/4 and 9/4.
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