Direct lattice calculation of inclusive hadronic decay rates of the $\tau$ lepton

TL;DR

This paper introduces a lattice QCD method to directly compute inclusive hadronic decay rates of the tau lepton, enabling precise determination of CKM matrix elements from first principles.

Contribution

It presents a novel approach using smeared spectral densities from Euclidean correlators for direct lattice calculation of tau decay rates.

Findings

Preliminary numerical results on two gauge ensembles

Method successfully applied to physical pion mass ensembles

Potential for improved CKM matrix element extraction

Abstract

The inclusive hadronic decay-rates of the $\tau$ lepton are particularly interesting from the phenomenological point of view since they give access to the CKM matrix elements $V_{ud}$ and $V_{us}$. In this talk, we discuss how a recent method for the extraction of smeared spectral densities from Euclidean lattice correlators can be used to obtain a direct lattice determination of inclusive hadronic $\tau$ decay rates. We also present preliminary numerical results obtained by applying this method to correlators measured on two gauge ensembles produced by the ETMC with $N_f=2+1+1$ dynamical flavours at physical pion masses, lattice spacing $a\simeq 0.08$ fm and volumes $L\simeq 5.1$ fm and $L\simeq 7.6$ fm.