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

Abstract We present a novel method for precisely determining the QCD running coupling from Ruds measurements in electron-positron annihilation. When calculating the fixed-order perturbative QCD (pQCD) approximant of Ruds, its effective coupling constant $$ {\alpha}_s\left({Q}_{\ast}^2\right) $$ 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 Ruds data measured by the KEDR detector at 22 centre-of-mass energies between 1.84 GeV and 3.72 GeV, we obtain $$ {\alpha}_s\left({M}_Z^2\right) $$ α s M Z 2 = $$ {0.1227}_{-0.0132}^{+0.0117}\left(\exp .\right)\pm 0.0016\left(\textrm{the}.\right) $$ 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 Ruds 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 Ruds 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 $$ \alpha \left({M}_Z^2\right) $$ α M Z 2 within the tau-charm energy range.