Speaker
Description
Current discrepancies between inclusive and exclusive determinations of the CKM matrix-element $V_{us}$ necessitate the inclusion of isospin-breaking effects to reach sub-percent precision. Here we present some results of an exploratory study of the determination of the inclusive hadronic decay-rate of the tau lepton without neglecting isospin-breaking effects. To allow charged states to propagate in a finite volume, we use $\mathrm{QCD}+\mathrm{QED}$ ensembles with $C^*$ boundary conditions. Our non-perturbative approach will be complemented with a RM123 study by our collaborators at the ETMC. We use a single $\mathrm{RC}^*$ ensemble at a lattice spacing of $a=0.0539(2)\,\mathrm{fm}$ on a $64\times 32^3$ lattice with $m_\pi\approx380\,\mathrm{MeV}$. We calculate the necessary $2$- and $4$-point functions that enter the spectral reconstruction in a partially-quenched set-up and describe how this data can be used in the HLT-method to determine the decay-rate.