Inclusive Hadronic Decay Rate of the τ Lepton from Lattice QCD: The u¯s Flavor Channel and the Cabibbo Angle

Abstract

We present a lattice determination of the inclusive decay rate of the process τ↦Xusντ in which the τ lepton decays into a generic hadronic state Xus with u¯s 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 , ] that we have already successfully applied [A. Evangelista , ] to compute the inclusive decay rate of the process τ↦Xudντ in the u¯d 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. Published by the American Physical Society 2024