Novel method to reliably determine the QCD coupling from Ruds measurements and its effects to muon g − 2 and $$ \alpha \left({M}_Z^2\right) $$ within the tau-charm energy region

Novel method to reliably determine the QCD coupling from R_uds measurements and its effects to muon g − 2 and $ \alpha \left({M}_Z^2\right) $ within the tau-charm energy region

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Abstract

We present a novel method for precisely determining the QCD running coupling from R_uds measurements in electron-positron annihilation. When calculating the fixed-order perturbative QCD (pQCD) approximant of R_uds, its effective coupling constant $ {\alpha}_s\left({Q}_{\ast}^2\right) $ is determined by using the principle of maximum conformality, a systematic scale-setting method for gauge theories, whose resultant pQCD series satisfies all the requirements of renormalization group. Contribution due to the uncalculated higher-order (UHO) terms is estimated by using the Bayesian analysis. Using R_uds data measured by the KEDR detector at 22 centre-of-mass energies between 1.84 GeV and 3.72 GeV, we obtain $ {\alpha}_s\left({M}_Z^2\right) $ = $ {0.1227}_{-0.0132}^{+0.0117}\left(\exp .\right)\pm 0.0016\left(\textrm{the}.\right) $, where the theoretical uncertainty (the.) is negligible compared to the experimental one (exp.). Numerical analyses confirm that the new method for calculating R_uds removes conventional renormalization scale ambiguity, and the residual scale dependence due to the UHO-terms will also be highly suppressed due to a more convergent pQCD series. This leads to a significant stabilization of the perturbative series, and a significant reduction of theoretical uncertainty. It thus provides a reliable theoretical basis for precise determination of the QCD running coupling from R_uds measurements at future Tau-Charm Facility. It can also be applied for the precise determination of the hadronic contributions to muon g − 2 and QED coupling $ \alpha \left({M}_Z^2\right) $ within the tau-charm energy range.

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Acknowledgments

We are grateful to Prof. Guang-Shun Huang, Hai-Ming Hu, Shu-Lei Zhang, Andrei Kataev, and Sergey Mikhailov for helpful discussions. This work was supported in part by the Natural Science Foundation of China under Grant No.11905056, No.12147102, No.12175025 and No.12265011.

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School of Physics and Electronics, Hunan Provincial Key Laboratory of High-Energy Scale Physics and Applications, Hunan University, Changsha, 410082, People’s Republic of China
Jian-Ming Shen & Bing-Hai Qin
Department of Physics, Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University, Chongqing, 401331, People’s Republic of China
Jiang Yan & Xing-Gang Wu
Department of Physics, Guizhou Minzu University, Guiyang, 550025, People’s Republic of China
Sheng-Quan Wang

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Jian-Ming Shen
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Shen, JM., Qin, BH., Yan, J. et al. Novel method to reliably determine the QCD coupling from R_uds measurements and its effects to muon g − 2 and $ \alpha \left({M}_Z^2\right) $ within the tau-charm energy region. J. High Energ. Phys. 2023, 109 (2023). https://doi.org/10.1007/JHEP07(2023)109

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Received: 03 April 2023
Revised: 19 May 2023
Accepted: 05 July 2023
Published: 12 July 2023
DOI: https://doi.org/10.1007/JHEP07(2023)109

Novel method to reliably determine the QCD coupling from R_uds measurements and its effects to muon g − 2 and \( \alpha \left({M}_Z^2\right) \) within the tau-charm energy region

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Novel method to reliably determine the QCD coupling from Ruds measurements and its effects to muon g − 2 and \( \alpha \left({M}_Z^2\right) \) within the tau-charm energy region

Abstract

Article PDF

Similar content being viewed by others

Determination of the muonic branching ratio of the W boson and its total width via cross-section measurements at the Tevatron and LHC

\( t\overline{t}b\overline{b} \) at the LHC: on the size of corrections and b-jet definitions

High-precision limits on W–\(W'\) and Z–\(Z'\) mixing from diboson production using the full LHC Run 2 ATLAS data set

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Novel method to reliably determine the QCD coupling from R_uds measurements and its effects to muon g − 2 and \( \alpha \left({M}_Z^2\right) \) within the tau-charm energy region