Compatibility of $α_s(M_τ)$ with $α_s(M_Z)$

Abstract

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