First-principle evaluation of inclusive hadronic $\tau$ decays in QCD+QED

TL;DR

This paper proposes a lattice QCD+QED approach to compute inclusive hadronic tau decay rates from first principles, accounting for electromagnetic and isospin-breaking effects, with implications for CKM matrix element extraction.

Contribution

It introduces a novel strategy to extend lattice calculations from QCD to QCD+QED for tau decays, including a decomposition of radiative corrections within the RM123 framework.

Findings

Preliminary results for leptonic and factorizable corrections in electro-quenched approximation.

A detailed plan for completing the first-principles calculation of tau decay rates.

Discussion of implications for determining the CKM matrix element |V_{us}|.

Abstract

We present a strategy to extend lattice calculations of inclusive hadronic $\tau$ decays from isosymmetric QCD to QCD+QED. The inclusive decay rate can be related to suitable Euclidean correlation functions, allowing for a first-principles evaluation of electromagnetic and isospin-breaking effects. Within the RM123 framework, radiative corrections are decomposed into leptonic, factorizable and non-factorizable contributions. We report preliminary results for the leptonic and factorizable terms in the electro-quenched approximation and discuss the remaining steps towards a complete calculation. This programme aims at a first-principles determination of inclusive $\tau$ decay rates with direct implications for the extraction of the CKM matrix element $|V_{us}|$.