The physics of hadronic tau decays

Abstract

Hadronic $\ensuremath{\tau}$ decays provide a clean laboratory for the precise study of quantum chromodynamics (QCD). Observables based on the spectral functions of hadronic $\ensuremath{\tau}$ decays can be related to QCD quark-level calculations to determine fundamental quantities like the strong-coupling constant, parameters of the chiral Lagrangian $\ensuremath{\mid}{V}_{us}\ensuremath{\mid}$, the mass of the strange quark, and to simultaneously test the concept of quark-hadron duality. Using the best available measurements and a revisited analysis of the theoretical framework, the value ${\ensuremath{\alpha}}_{s}({m}_{\ensuremath{\tau}}^{2})=0.345\ifmmode\pm\else\textpm\fi{}{0.004}_{\mathrm{exp}}\ifmmode\pm\else\textpm\fi{}{0.009}_{\mathrm{th}}$ is obtained. Taken together with the determination of ${\ensuremath{\alpha}}_{s}({M}_{Z}^{2})$ from the global electroweak fit, this result leads to the most accurate test of asymptotic freedom: the value of the logarithmic slope of ${\ensuremath{\alpha}}_{s}^{\ensuremath{-}1}(s)$ is found to agree with QCD at a precision of 4%. The $\ensuremath{\tau}$ spectral functions can also be used to determine hadronic quantities that, due to the nonperturbative nature of long-distance QCD, cannot be computed from first principles. An example for this is the contribution from hadronic vacuum polarization to loop-dominated processes like the anomalous magnetic moment of the muon. This article reviews the measurements of nonstrange and strange $\ensuremath{\tau}$ spectral functions and their phenomenological applications.