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_{µ2} and π_{µ2} 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. Systematic effects are evaluated and the impact of the quenched QED approximation is estimated. Our result for the correction to the tree-level K_{µ2}/π_{µ2} decay ratio is -1.22(16)%, to be compared to the estimate of -1.12(21)% based on chiral perturbation theory and adopted by the Particle Data Group.