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Description
The strong coupling $\alpha_s$ is the most important parameter of Quantum Chromodynamics (QCD) therefore it is essential to determine it with high precision. This work presents an improved approach for extracting $\alpha_s$ comparing the numerical results of lattice QCD simulations to the perturbative expansion of the QCD static energy. We apply R-improvement to its 3-loop fixed-order prediction, enabling the subtraction of the $u=1/2$ renormalon and the corresponding summation of large logarithms. We also perform resummation of large ultra-soft logs to N$^3$LL accuracy using renormalization group equations. A new and more flexible parametrization of the renormalization scale has been implemented, allowing us to extend perturbation theory to distances of the order of 1 fm. Perturbative uncertities are estimated randomly varying the parameters that specify the renormalization scale. Performing R-evolution in the MSR mass scheme, we show that the extracted value of $\alpha_s$ is strongly correlated to the prediction for the leading renormalon normalization.