Leptonic decays of pseudoscalar mesons from lattice QCD+QED calculations

A high precision determination of the elements of the Cabibbo-Kobayashi-Maskawa (CKM) matrix allows for stringent tests of the Standard Model. These can be extracted from weak leptonic and semi-leptonic decays of hadrons, combining the experimental values of the decay rates and the theoretical prediction of the relevant hadronic matrix elements. The current level of precision reached in the evaluation of the latter from lattice QCD calculations, makes the inclusion of QED and strong isospin-breaking corrections necessary. In this talk we present the results of the two existing lattice calculations of isospin breaking corrections to pion and kaon leptonic decays from the RM123+Soton (2019) and the RBC-UKQCD (2023) collaborations, respectively. We also discuss the important role of finite volume effects and the ongoing effort to tame such source of systematic uncertainty. Finally, we discuss the prospects for extending these calculations to the case of heavier mesons and to semi-leptonic decays.