Isospin-breaking corrections to weak decays: the current status and a new infrared improvement

Abstract

We provide an overview of the current state of lattice calculations concerning isospin-breaking corrections in weak decays, focusing in particular on leptonic decays of light pseudoscalar mesons. We examine the two currently existing calculations, placing a particular emphasis on the role of electromagnetic finite-volume corrections. Given the large systematic uncertainty associated with such corrections, we propose a novel method to improve the finite-volume scaling of leptonic decay rates and other hadronic observables, like hadron masses and the hadronic vacuum polarization contribution to the muon $g-2$. We introduce a new prescription for the QED action, referred to as QED${}_{\mathrm{r}}$, which effectively removes finite-volume corrections at $\mathcal{O}(1/L^3)$ and consequently shifts the systematic uncertainty to a higher order. The specifics of this action, the practical implementation of the infrared improvement, and the ongoing numerical tests are also discussed.

Comments: 18 pages, 4 figures, Plenary talk at the 40th International Symposium on Lattice Field Theory (Lattice 2023)