Isospin Breaking in Lattice QCD Computations of Decay Amplitudes

The remarkable recent progress in the precision of Lattice QCD computations for a number of physical quantities relevant for flavour physics has motivated the introduction of isospin-breaking effects, including in particular electromagnetic corrections, to the computations. The isospin breaking corrections are necessary to fully exploit this improved precision for the determination of the fundamental parameters of the Standard Model, including the CKM matrix elements, and to look for deviations from experimental measurements which might signal the presence of new physics. Together with colleagues from Rome, we have developed and implemented a framework for including isospin-breaking corrections in leptonic decays $P\to\ell\bar\nu_\ell(\gamma)$, where $P$ is a pseudoscalar meson and $\ell$ a charged lepton, and the theoretical framework and numerical results are reviewed below. The status of our studies to extend this framework to semileptonic decays $P_1\to P_2\ell\bar\nu_\ell(\gamma)$, where $P_{1,2}$ are pseudoscalar mesons, is also presented.