Compatibility of $\alpha_s(M_\tau)$ with $\alpha_s(M_Z)$

Abstract

The current phenomenological determinations of $\alpha_s(M_\tau)$ and $\alpha_s(M_Z)$ are shown to be only marginally consistent with the QCD evolution of the strong coupling constant between $M_Z$ and $M_\tau$. This motivates a revised estimate of $\alpha_s(M_\tau)$ since the perturbative series used to extract $\alpha_s(M_\tau)$ from the $\tau$ hadronic width exhibits slow convergence. Pad\'e summation techniques provide an estimate of these unknown higher-order effects, leading to the revised determination $\alpha_s(M_\tau)=0.333\pm 0.030 $. This value is 10% smaller than current estimates, improving the compatibility of phenomenological estimates for $\alpha_s(M_\tau)$ and $\alpha_s(M_Z)$ with the QCD evolution of the strong coupling constant.