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. Padé 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.

Latex2e, 12 pages, 4 figures