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arXiv · 2403.05404

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

C. Alexandrou·S. Bacchio·A. De Santis·A. Evangelista·J. Finkenrath·R. Frezzotti·G. Gagliardi·M. Garofalo·B. Kostrzewa·V. Lubicz·S. Romiti·F. Sanfilippo·S. Simula·N. Tantalo·C. Urbach·U. Wenger
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Abstract

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.

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C. Alexandrou, S. Bacchio, A. De Santis, A. Evangelista, J. Finkenrath, R. Frezzotti, G. Gagliardi, M. Garofalo, B. Kostrzewa, V. Lubicz, S. Romiti, F. Sanfilippo, S. Simula, N. Tantalo, C. Urbach, U. Wenger. 2024-03-08. Inclusive hadronic decay rate of the $\tau$ lepton from lattice QCD: the $\bar u s$ flavour channel and the Cabibbo angle. https://arxiv.org/abs/2403.05404

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