Determination of the strong coupling from hadronic tau decays using renormalization group summed perturbation theory

TL;DR

This paper extracts the strong coupling constant lpha_s from tau hadronic decays using a novel renormalization group summed perturbation theory, showing improved series behavior and consistent results with existing methods.

Contribution

The paper introduces a renormalization group summed (RGS) expansion for the Adler function, providing a new approach with good RG improvement and comparable results to CIPT.

Findings

lpha_s(M_ au^2)= 0.338  0.010

RGS expansion exhibits similar behavior to CIPT

Series convergence can be improved via Borel transformation

Abstract

We determine the strong coupling constant \alpha_s from the \tau hadroni width using a renormalization group summed (RGS) expansion of the QCD Adler function. The main theoretical uncertainty in the extraction of \alpha_s is due to the manner in which renormalization group invariance is implemented, and the as yet uncalculated higher order terms in the QCD perturbative series. We show that new expansion exhibits good renormalization group improvement and the behaviour of the series is similar to that of the standard CIPT expansion. The value of the strong coupling in {\bar{\rm MS}} scheme obtained with the RGS expansion is \alpha_s(M_\tau^2)= 0.338 \pm 0.010. The convergence properties of the new expansion can be improved by Borel transformation and analytic continuation in the Borel plane. This is discussed elsewhere in these proceedings.