The physics of hadronic tau decays

Hadronic τ decays provide a clean laboratory for the precise study of quantum chromodynamics (QCD). Observables based on the spectral functions of hadronic τ decays can be related to QCD quark-level calculations to determine fundamental quantities like the strong-coupling constant, parameters of the chiral Lagrangian Vᵤₛ, 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 αₛ(m_τ²)=0.345±0.004ₑₓₚ±0.009ₜₕ is obtained. Taken together with the determination of αₛ(MZ²) from the global electroweak fit, this result leads to the most accurate test of asymptotic freedom: the value of the logarithmic slope of αₛ^-1(s) is found to agree with QCD at a precision of 4%. The τ 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 τ spectral functions and their phenomenological applications.