Speaker
Description
Inclusive hadronic $\tau$ decays are particularly interesting from the phenomenological since they give access to $V_{ud}$ and $V_{us}$. A long-standing issue is the tension between the $V_{us}$ determinations coming from leptonic and semileptonic kaon decays and the ones obtained from inclusive hadronic $\tau$ decays. To date (as far as we know) the problem has been addressed indirectly by using sum-rule techniques and non-perturbative lattice inputs complemented with perturbative calculations. In this talk we discuss how a recent method for the extraction of smeared spectral densities from euclidean lattice correlators can profitably be used to obtain a direct lattice calculation of inclusive hadronic $\tau$ decay rates. No perturbative inputs are used in our approach as the decay rate is extracted directly from euclidean correlators with two insertions of the relevant hadronic weak current. We also present preliminary numerical results obtained by applying our method to the correlators produced by ETMC with $N_f=2+1+1$ dynamical flavours at $a=0.08\,\mathrm{fm}$ and physical pion masses.
