Inclusive hadronic decay rate of the $\tau$ lepton from lattice QCD: the $\bar u s$ flavour channel and the Cabibbo angle

• Main Authors: Alexandrou, C, Bacchio, S, De Santis, A, Evangelista, A, Finkenrath, J, Frezzotti, R, Gagliardi, G, Garofalo, M, Kostrzewa, B, Lubicz, V, Romiti, S, Sanfilippo, F, Simula, S, Tantalo, N, Urbach, C, Wenger, U
• Format: Journal Article
• Language: English
• Published: 08-03-2024
• Subjects: Physics - High Energy Physics - Lattice; Physics - High Energy Physics - Phenomenology
• DOI: 10.48550/arxiv.2403.05404

We present a lattice determination of the inclusive decay rate of the process
$\tau\mapsto X_{us} \nu_\tau$ in which the $\tau$ lepton decays into a generic
hadronic state $X_{us}$ with $\bar u s$ flavour quantum numbers. Our results
have been obtained in $n_f=2+1+1$ 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 $\tau\mapsto X_{ud}
\nu_\tau$ in the $\bar u d$ flavour channel. By combining our first-principles
theoretical results with the presently-available experimental data we extract
the CKM matrix element $\vert V_{us}\vert$, the Cabibbo angle, with a $0.9$\%
accuracy, dominated by the experimental error.