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

TL;DR

This paper applies Pade-approximant and Pade summation techniques to improve the extraction of the strong coupling constant from tau decay data, resulting in values that better align with QCD evolution predictions.

Contribution

It introduces Pade-based methods to estimate higher-order effects in the perturbative series for $ au$ decay, reducing the extracted $eta$ value by about 10%.

Findings

Reduced $eta$ value for $ au$ decay by ~10%.

Improved agreement with QCD evolution of $ ext{alpha}_s$.

Enhanced estimation of higher-order effects in perturbative series.

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 $\alpha_s(M_z)$.