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

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. Following a method recently proposed in Ref. [1] the emission of virtual photons at leading order in the electromagnetic coupling is evaluated on the lattice and the infrared divergence computed for a point-like meson at finite lattice volume is subtracted. The physical decay rate is then obtained by adding the emission of real and virtual photons regularised with a photon mass. Using the gauge 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 pions and kaons are presented.