Precise ${\alpha }_s$ determination from charmonium sum rules

Abstract

The strong coupling, ${\alpha }_s$, governs perturbative Quantum Chromodynamics (QCD) and is one of the free parameters of the Standard Model. We introduce a new method that allows a precise extraction of ${\alpha }_s(m_Z)$ from dimensionless ratios of roots of moments of the charm-quark vector correlator. The ratios we use in our analysis have a rather weak logarithmic quark-mass dependence, starting at $\mathcal{O}({\alpha }_s^2)$, and can be obtained from experimental data with good precision, since they benefit from positive correlations among the individual experimentally determined moments. We perform a careful and conservative error analysis with special emphasis on uncertainties related to the truncation of perturbation theory, treating the renormalization scales such as to ensure order-by-order convergence. Our final result, with expressions at $\mathcal{O}({\alpha }_s^3)$, is ${\alpha }_s(m_Z)=0.1168\pm 0.0019$.

Comments: References added, enlarged discussion, results unchanged. Matches published version. 5 pages, 3 figures