Speaker
Description
Hadronic decays of the $\tau$ lepton provide an independent avenue for determining the CKM matrix elements $V_{us}$ and $V_{ud}$. This is particularly relevant given the persistent tensions with CKM unitarity observed when these elements are extracted from leptonic and semileptonic decays of light mesons, as well as from nuclear beta decays. A recent lattice QCD calculation by the ETM Collaboration of the inclusive hadronic $\tau$ decay rate, performed in the isospin-symmetric limit using the HLT method to reconstruct the underlying spectral density, yields $|V_{us}| = 0.2189(7)_\text{th}(18)_\text{exp}$. This result is consistent with a determination based on the operator product expansion but reveals a $3\sigma$ tension with CKM unitarity. To properly assess this discrepancy, it is essential to include electromagnetic and strong isospin-breaking corrections, which are currently neglected in the isospin-symmetric calculation. In this talk, I will present ongoing efforts and future prospects for computing these corrections using both the perturbative RM123 approach and fully dynamical QCD+QED simulations. I will also discuss how such corrections to the decay rate can be extracted from Euclidean lattice correlators through spectral reconstruction techniques, with proper treatment of the correlator renormalisation. The application of the HLT method to these isospin-breaking effects paves the way for future studies of radiative corrections in a broader class of weak decay processes.
| Parallel Session (for talks only) | Quark and lepton flavor physics |
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