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We present a novel method for precisely determining the QCD running couplingfrom $R_{\rm uds}$ measurements in electron-positron annihilation. Whencalculating the fixed-order perturbative QCD (pQCD) approximant of $R_{\rmuds}$, its effective coupling constant $\alpha_s(Q_*^2)$ is determined by usingthe principle of maximum conformality, a systematic scale-setting method forgauge theories, whose resultant pQCD series satisfies all the requirements ofrenormalization group. Contribution due to the uncalculated higher-order (UHO)terms is estimated by using the Bayesian analysis. Using $R_{\rm uds}$ datameasured by the KEDR detector at $22$ centre-of-mass energies between $1.84$GeV and $3.72$ GeV, we obtain $\alpha_s(M_Z^2)=0.1227^{+0.0117}_{-0.0132}({\rmexp.})\pm0.0016({\rm the.})$, where the theoretical uncertainty (the.) isnegligible compared to the experimental one (exp.). Numerical analyses confirmthat the new method for calculating $R_{\rm uds}$ removes conventionalrenormalization scale ambiguity, and the residual scale dependence due to theUHO-terms will also be highly suppressed due to a more convergent pQCD series.This leads to a significant stabilization of the perturbative series, and asignificant reduction of theoretical uncertainty. It thus provides a reliabletheoretical basis for precise determination of the QCD running coupling from$R_{\rm uds}$ measurements at future Tau-Charm Facility. It can also be appliedfor the precise determination of the hadronic contributions to muon $g-2$ andQED coupling $\alpha(M_Z^2)$ within the tau-charm energy range.

the journal of high energy physics/the journal of high energy physics

Novel Method to Reliably Determine the QCD Coupling from $R_{\rm uds}$  Measurements and its effects to Muon $g-2$ and $\alpha(M_Z^2)$ within the  Tau-Charm Energy Region