Determination of alpha_s from tau decays

TL;DR

This paper discusses methods to accurately determine the strong coupling constant alpha_s from tau decay data, emphasizing the importance of controlling perturbative and non-perturbative QCD corrections and duality violations.

Contribution

It provides a detailed analysis of the theoretical and methodological issues involved in extracting alpha_s from tau decays, including the treatment of perturbative series resummation and operator product expansion parameters.

Findings

Comparison of contour-improved and fixed-order resummation methods.

Importance of self-consistent fits including all theory parameters.

Strategies for controlling higher-dimensional operator corrections.

Abstract

Hadronic tau decays offer the possibility of determining the strong coupling alpha_s at relatively low energy. Precisely for this reason, however, good control over the perturbative QCD corrections, the non-perturbative condensate contributions in the framework of the operator product expansion (OPE), as well as the corrections going beyond the OPE, the duality violations (DVs), is required. On the perturbative QCD side, the contour-improved versus fixed-order resummation of the series is still an issue, and will be discussed. Regarding the analysis, self-consistent fits to the data including all theory parameters have to be performed, and this is also explained in some detail. The fit quantities are moment integrals of the tau spectral function data in a certain energy window and care should be taken to have acceptable perturbative behaviour of those moments as well as control over higher-dimensional operator corrections in the OPE.