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Electromagnetic effects in the leptonic decay rates $\pi^+ \to \mu^+ \nu$ and$K^+ \to \mu^+ \nu$ are evaluated for the first time on the lattice. Followinga method recently proposed in Ref. [1] the emission of virtual photons atleading order in the electromagnetic coupling is evaluated on the lattice andthe infrared divergence computed for a point-like meson at finite latticevolume is subtracted. The physical decay rate is then obtained by adding theemission of real and virtual photons regularised with a photon mass. Using thegauge ensembles produced by the European Twisted Mass Collaboration with $N_f =2 + 1 + 1$ dynamical quarks the feasibility of our approach is demonstrated.Preliminary results for the electromagnetic corrections to charged (neutral)pion and kaon masses as well as to the leptonic decay rates of charged pionsand kaons are presented.

Electromagnetic corrections to the leptonic decay rates of charged pseudoscalar mesons: lattice results