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

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 α s Q ∗ 2 $$ {\alpha}_s\left({Q}_{\ast}^2\right) $$ 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 α s M Z 2 $$ {\alpha}_s\left({M}_Z^2\right) $$ = 0.1227 − 0.0132 + 0.0117 exp . ± 0.0016 the . $$ {0.1227}_{-0.0132}^{+0.0117}\left(\exp .\right)\pm 0.0016\left(\textrm{the}.\right) $$ , 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 α M Z 2 $$ \alpha \left({M}_Z^2\right) $$ within the tau-charm energy range