Inclusive hadronic decay rate of the tau lepton from lattice QCD

Title:

Inclusive hadronic decay rate of the tau lepton from lattice QCD

Abstract:

The inclusive hadronic decays of the $\tau$ are of great interest, as they provide an alternative way of determining the CKM matrix elements
$V_{\rm ud}$ and $V_{\rm us}$. However, a direct lattice QCD calculation of the corresponding inclusive hadronic decay rates is hindered by the
need of performing a numerical inverse Laplace transform of an Euclidean correlation function, a notoriously ill-posed problem. In this seminar, I will discuss a novel approach that effectively bypasses the inverse Laplace transform problem, and that allows  to evaluate the inclusive decay rates in given flavour channels without relying on the operator-product expansion or perturbative QCD. The method is applied to the inclusive decay $\tau \to X_{\rm ud} \nu_{\tau}$, where $X_{\rm ud}$ represents any hadronic state with $\bar{u}d$ flavour quantum numbers. With all sources of systematic errors under control, except for isospin-breaking effects, we obtain a value for $|V_{ud}|$ with an accuracy of $0.4\%$, which is in agreement with the determination from superallowed nuclear beta decays. Finally, I will discuss the prospects for determining $|V_{\rm us}|$ from $\tau \to X_{\rm us} \nu_{\tau}$.