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⏛₂ and π⏛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 N₅=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⏛₂/π⏛₂ 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.