Speaker
Description
The increasing accuracy in the experimental measurements of several hadronic observables related to weak processes, which in many cases is smaller than $\mathcal{O}(1\%)$, requires the inclusion in theoretical calculations of subleading corrections that were neglected so far. Over the past decade isospin breaking effects due to electromagnetic interactions and to the up-down quark mass splitting have been included by different collaborations in lattice QCD calculations of the hadron spectrum and of weak decays of mesons. In this talk we present the first RBC-UKQCD lattice calculation of the leading isospin-breaking corrections to the ratio of leptonic decay rates of kaons and pions into muon and neutrino, $\Gamma(K_{\ell 2})/\Gamma(\pi_{\ell 2})$. This computation is performed using domain wall fermions with close-to-physical (light and strange) quark masses. The QED effects are implemented using a perturbative approach and infrared divergences are regulated according to the QED$_\mathrm{L}$ prescription. We describe the strategy to extract the relevant hadronic matrix elements from Euclidean correlation functions and we discuss the important role of finite volume effects in this calculation.
