First lattice calculation of the QED corrections to leptonic decay rates

The leading-order electromagnetic and strong isospin-breaking corrections to the ratio of $K_{\mu 2}$ and $\pi_{\mu 2}$ decay rates are evaluated for the first time on the lattice, following a method recently proposed. The lattice results are obtained using the gauge ensembles produced by the European Twisted Mass Collaborationwith $N_f = 2 + 1 + 1$ dynamical quarks. Systematics effects are evaluated and the impact of the quenched QED approximation is estimated. Our result for the correction to the tree-level $K_{\mu 2} / \pi_{\mu 2}$ decay ratio is $-1.22\,(16) \%$ to be compared to the estimate $-1.12\,(21) \%$ based on Chiral Perturbation Theoryand adopted by the Particle Data Group.