Determination of $\alpha_s(M_\tau^2)$: a conformal mapping approach

TL;DR

This paper introduces a conformal mapping technique in perturbative QCD to more accurately determine the strong coupling constant _s from  decays, achieving a precise prediction with reduced uncertainties.

Contribution

It presents a novel conformal mapping approach for perturbative QCD expansions, improving the extraction of _s from  decay data.

Findings

Predicted _s(M_ au^2)= 0.320 b1 0.011.

The method extends to fifth order in the ar MS scheme.

Provides a new framework for  determination with reduced theoretical uncertainties.

Abstract

We discuss a new class of expansions in perturbative QCD, based on the technique of conformal mappings of the Borel plane, and apply them for the determination of $\alpha_s$ from the hadronic decays of the $\tau$ lepton. Using the expansion up to fifth order in the $\bar{\rm MS}$ scheme, the method leads to the prediction $\alpha_s(M_\tau^2)= 0.320\pm 0.011$.