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 Collaboration with $N_f=2+1+1$ 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 $K_{\mu 2}\mathrm{/}{\pi }_{\mu 2}$ decay ratio is $-1.22(16)\mathrm{\%}$ to be compared to the estimate $-1.12(21)\mathrm{\%}$ based on Chiral Perturbation Theory and adopted by the Particle Data Group.