Inclusive Hadronic Decay Rate of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi></mml:math> Lepton from Lattice QCD: The <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mover accent="true"><mml:mi>u</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mi>s</mml:mi></mml:math> Flavor Channel and the Cabibbo Angle
Constantia Alexandrou, Simone Bacchio, Alessandro De Santis, Antonio Evangelista, Jacob Finkenrath, R. Frezzotti, G. Gagliardi, Marco Garofalo, Bartosz Kostrzewa, V. Lubicz, Simone Romiti, Francesco Sanfilippo, Silvano Simula, Nazario Tantalo, Carsten Urbach, Urs Wenger
Abstract
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.