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<p>The strong coupling <i>α</i><sub><i>s</i></sub> is determined with high precision from fits to lattice QCD simulations on the static energy. Our theoretical setup relies on R-improving the three-loop fixed-order prediction for the static energy by removing its <i>u</i> = 1/2 renormalon and summing up the associated large (infrared) logarithms which, in combination with radius-dependent renormalization scales (called profile functions) extends the validity of perturbation theory to distances up to ~ 0.5 fm. Furthermore, we resum large ultrasoft logarithms to N<sup>3</sup>LL accuracy using renormalization group evolution. We have checked that the standard four-loop R-evolution treats N<sup>4</sup>LL and higher remnants in a non-symmetric way, hence we also account for this potential bias. Our estimate of the perturbative uncertainty is based on a random scan over the parameters specifying the profile functions and the treatment of R-evolution. We also devise a method to statistically combine into a single dataset results from independent simulations which use different lattice spacing and cover various ranges, which can be used to carry out fits in a much faster way. We explore the dependence of the extracted <i>α</i><sub><i>s</i></sub> value on the smallest and largest distances included in the dataset, on how R-evolution is treated, on how the fit is performed, and on the accuracy of ultrasoft resummation. From our final analysis, after evolving to the <i>Z</i>-pole we obtain <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi>α</mi> <mi>s</mi> <mfenced close=")" open="("> <mrow> <msub> <mi>n</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>5</mn> </mrow> </mfenced> </msubsup> <mfenced close=")" open="("> <msub> <mi>m</mi> <mi>Z</mi> </msub> </mfenced> <mo>=</mo> <mn>0.1170</mn> <mo>±</mo> <mn>0.0009</mn> </math></EquationSource> <EquationSource Format="TEX">\( {\alpha}_s^{\left({n}_f=5\right)}\left({m}_Z\right)=0.1170\pm 0.0009 \)</EquationSource> </InlineEquation>, compatible with the world average with the same incertitude.</p>

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A precise αs determination from the R-improved QCD static energy

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  • 发表日期：

    2026年6月1日

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  • Jose M. Mena-Valle,
  • Vicent Mateu,
  • Pablo G. Ortega

摘要

The strong coupling αs is determined with high precision from fits to lattice QCD simulations on the static energy. Our theoretical setup relies on R-improving the three-loop fixed-order prediction for the static energy by removing its u = 1/2 renormalon and summing up the associated large (infrared) logarithms which, in combination with radius-dependent renormalization scales (called profile functions) extends the validity of perturbation theory to distances up to ~ 0.5 fm. Furthermore, we resum large ultrasoft logarithms to N3LL accuracy using renormalization group evolution. We have checked that the standard four-loop R-evolution treats N4LL and higher remnants in a non-symmetric way, hence we also account for this potential bias. Our estimate of the perturbative uncertainty is based on a random scan over the parameters specifying the profile functions and the treatment of R-evolution. We also devise a method to statistically combine into a single dataset results from independent simulations which use different lattice spacing and cover various ranges, which can be used to carry out fits in a much faster way. We explore the dependence of the extracted αs value on the smallest and largest distances included in the dataset, on how R-evolution is treated, on how the fit is performed, and on the accuracy of ultrasoft resummation. From our final analysis, after evolving to the Z-pole we obtain α s n f = 5 m Z = 0.1170 ± 0.0009 \( {\alpha}_s^{\left({n}_f=5\right)}\left({m}_Z\right)=0.1170\pm 0.0009 \) , compatible with the world average with the same incertitude.