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

We present a lattice determination of the inclusive decay rate of the process τ↦ Xᵤₛ ν_τ in which the τ lepton decays into a generic hadronic state Xᵤₛ with u s flavour quantum numbers. Our results have been obtained in nf=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↦ Xud ν_τ in the u d flavour channel. By combining our first-principles theoretical results with the presently-available experimental data we extract the CKM matrix element Vᵤₛ, the Cabibbo angle, with a $0.9$% accuracy, dominated by the experimental error.