Inclusive hadronic decay rate of the τ lepton from lattice QCD: the u̅ s flavour channel and the Cabibbo angle

We present a lattice determination of the inclusive decay rate of the process τ↦ X_usν_τ in which the τ lepton decays into a generic hadronic state X_us with u̅ s flavour quantum numbers. Our results have been obtained in n_f=2+1+1 iso-symmetric QCD with full non-perturbative accuracy, without any OPE approximation and, except for the presently missing long-distance isospin-breaking corrections, include a solid estimate of all sources of theoretical uncertainties. This has been possible by using the Hansen-Lupo-Tantalo method [1] that we have already successfully applied in [2] to compute the inclusive decay rate of the process τ↦ X_udν_τ in the u̅ d flavour channel. By combining our first-principles theoretical results with the presently-available experimental data we extract the CKM matrix element | V_us|, the Cabibbo angle, with a 0.9% accuracy, dominated by the experimental error.