Light-meson leptonic decay rates in lattice QCD plus QED

The leading electromagnetic (e.m.) and strong isospin-breaking corrections to the pi(+ )-> mu(+) nu[gamma] and K+ -> mu(+)nu[gamma] leptonic decay rates are evaluated for the first time on the lattice. The results are obtained using gauge ensembles produced by the European Twisted Mass Collaboration with N-f = 2 + 1 + 1 dynamical quarks. The relative leading-order e.m. and strong isospin-breaking corrections to the decay rates are 1.53(19)% for pi(mu 2) decays and 0.24(10)% for K-mu 2 decays. Using the experimental values of the pi(mu 2) and K-mu 2 decay rates and updated lattice QCD results for the pion and kaon decay constants in isosymmetric QCD, we find that the Cabibbo-Kobayashi-Maskawa matrix element vertical bar V-us vertical bar = 0.22538(46), reducing by a factor of about 1.8 the corresponding uncertainty in the particle data group review. Our calculation of vertical bar V-us vertical bar allows also an accurate determination of the first-row Cabibbo-Kobayashi-Maskawa unitarity relation vertical bar V-ud vertical bar(2) + vertical bar V-us vertical bar(2) + vertical bar V-ub vertical bar(2) = 0.99988(46). Theoretical developments in this paper include a detailed discussion of how QCD can be defined in the full QCD + QED theory and an improved renormalization procedure in which the bare lattice operators are renommlized nonperturbatively into the regularization independent momentum subtraction (RI'-MOM) scheme and subsequently matched perturbatively at O(alpha(em)alpha(s) (M-W)) into the W-regularization scheme appropriate for these calculations.