Speaker
Description
The inclusive hadronic decays of the $\tau$ lepton are of great interest as they provide an alternative method for determining the CKM matrix elements $V_{\rm ud}$ and $V_{\rm us}$. In this talk, I will present the results of the ETM Collaboration on the inclusive hadronic decay rate of the $\tau$. Our results have been obtained in $N_{f}=2+1+1$ QCD using the novel HLT method, which circumvents the well-known inverse Laplace transform problem that hinders this calculation, i.e. for the first time without relying on the operator-product expansion or on perturbative QCD.
Except for isospin-breaking effects, all sources of systematic errors are under control. We obtain a value for the Cabibbo angle of $\vert V_{us}\vert_{\tau\mathrm{-latt-incl}}=0.2189(7)\mathrm{th}(18)\mathrm{exp}$, which shows a $3\sigma$ tension with purely hadronic determinations of $\vert V_{us}\vert$. We believe that this tension, which can no longer be attributed to the OPE approximation, deserves further scrutiny of the experimental uncertainties and calls for a first-principles determination of the isospin-breaking corrections, which we are currently investigating.
