The physics of hadronic tau decays

Hadronic tau decays provide a clean laboratory for the precise study of quantum chromodynamics (QCD). Observables based on the spectral functions of hadronic tau decays can be related to QCD quark-level calculations to determine fundamental quantities like the strong-coupling constant, parameters of the chiral Lagrangian \V-us\, 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 alpha(s)(m(tau)(2))=0.345 +/- 0.004(exp)+/- 0.009(th) is obtained. Taken together with the determination of 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 alpha(-1)(s)(s) is found to agree with QCD at a precision of 4%. The 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 tau spectral functions and their phenomenological applications.