Inclusive Hadronic Decay Rate of the tau Lepton from Lattice QCD: The us Flavor Channel and the Cabibbo Angle

We present a lattice determination of the inclusive decay rate of the process tau -> Xus vu_tau in which the tau lepton decays into a generic hadronic state Xus with us flavor quantum numbers. Our results have been obtained in Nf=2+1+1 isosymmetric QCD with full nonperturbative accuracy, without any operator product expansion 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 [M. Hansen et al., Phys. Rev. D 99, 094508 (2019)] that we have already successfully applied [A. Evangelista et al., Phys. Rev. D 108, 074513 (2023)] to compute the inclusive decay rate of the process tau -> Xud vu_tau in the ud flavor channel. By combining our first-principles theoretical results with the presently available experimental data, we extract the Cabibbo-Kobayashi-Maskawa matrix element |Vus|, the Cabibbo angle, with a 0.9% accuracy, dominated by the experimental error.