Novel method to reliably determine the QCD coupling from R uds measurements and its effects to muon g − 2 and α(M_Z^2) within the tau-charm energy region

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 α_s(Q_∗^2) 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 α_s(M_Z^2) = 0.1227_-0.0132^+0.0117(exp .)± 0.0016(the.) , 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 α(M_Z^2) within the tau-charm energy range.