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arXiv · 2512.09888

A Precise $\alpha_s$ Determination from the R-improved QCD Static Energy

Jose M. Mena-Valle
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Abstract

The strong coupling $\alpha_s$ is extracted with high precision through fits to lattice-QCD data for the static energy. Our theoretical framework is based on R-improving the three-loop fixed-order prediction for the static energy: we remove the $u=1/2$ renormalon and resum the associated large infrared logarithms. Combined with radius-dependent renormalization scales (the so-called profile functions), this procedure extends the range of validity of perturbation theory to distances as large as $\sim 0.5\,$fm. In addition, we resum large ultrasoft logarithms to N$^3$LL accuracy using renormalization-group evolution. Since the standard four-loop R-evolution treats N$^4$LL and higher-order contributions asymmetrically, we also incorporate this potential source of bias in our analysis. Our estimate of the perturbative uncertainty is obtained through a random scan over the parameters controlling the profile functions and the implementation of R-evolution. We analyze how the extracted value of $\alpha_s$ depends on the shortest and longest distances included in the fit, on the details of the R-evolution procedure, on the fitting strategy itself, and on the accuracy of ultrasoft resummation. From our final analysis, and after evolution to the $Z$ pole, we obtain $\alpha^{(n_f=5)}_s(m_Z)=0.1170\pm 0.0009$, a result fully compatible with the world average and with a comparable uncertainty.

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Jose M. Mena-Valle. 2025-12-10. A Precise $\alpha_s$ Determination from the R-improved QCD Static Energy. https://doi.org/10.22323/1.485.0238

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