Pade-Improved Extraction of $\alpha_s(M_\tau)$ from $R_\tau$

Abstract

The perturbative series used to extract $\alpha_s(M_\tau)$ from the $\tau$ hadronic width exhibits slow convergence. Asymptotic Pade-approximant and Pade summation techniques provide an estimate of these unknown higher-order effects, leading to values for $\alpha_s(M_\tau)$ that are about 10% smaller than current estimates. Such a reduction improves the agreement of $\alpha_s(M_\tau)$ with the QCD evolution of the strong coupling constant from $\alpha_s(M_z)$.