First-principle evaluation of inclusive hadronic $\ddot{I}„$ decays in QCD+QED

Abstract

We present a strategy to extend lattice calculations of inclusive hadronic $\ddot{I}„$ 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 $\ddot{I}„$ decay rates with direct implications for the extraction of the CKM matrix element $|V_{us}|$.

10 pages, 2 figures, contribution to 42nd International Symposium on Lattice Field Theory (Lattice 2025), TIFR Mumbai, India, 2025