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

• Published in: Physical review letters Vol. 132; no. 26; p. 261901
• Main Authors: Alexandrou, Constantia, Bacchio, Simone, De Santis, Alessandro, Evangelista, Antonio, Finkenrath, Jacob, Frezzotti, Roberto, Gagliardi, Giuseppe, Garofalo, Marco, Kostrzewa, Bartosz, Lubicz, Vittorio, Romiti, Simone, Sanfilippo, Francesco, Simula, Silvano, Tantalo, Nazario, Urbach, Carsten, Wenger, Urs
• Format: Journal Article
• Language: English
• Published: United States 28.06.2024
• ISSN: 1079-7114
• DOI: 10.1103/PhysRevLett.132.261901

We present a lattice determination of the inclusive decay rate of the process τ↦X_{us}ν_{τ} in which the τ lepton decays into a generic hadronic state X_{us} with u[over ¯]s flavor quantum numbers. Our results have been obtained in n_{f}=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)PRVDAQ2470-001010.1103/PhysRevD.99.094508] that we have already successfully applied [A. Evangelista et al., Phys. Rev. D 108, 074513 (2023)PRVDAQ2470-001010.1103/PhysRevD.108.074513] to compute the inclusive decay rate of the process τ↦X_{ud}ν_{τ} in the u[over ¯]d flavor channel. By combining our first-principles theoretical results with the presently available experimental data, we extract the Cabibbo-Kobayashi-Maskawa matrix element |V_{us}|, the Cabibbo angle, with a 0.9% accuracy, dominated by the experimental error.