Lattice computation of the electromagnetic contributions to kaon and pion masses

We present a lattice calculation of the electromagnetic (EM) effects on the masses of light pseudoscalar mesons. The simulations employ 2 + 1 dynamical flavors of asqtad QCD quarks and quenched photons. Lattice spacings vary from approximate to 0.12 fm to approximate to 0.045 fm. We compute the quantity epsilon, which parametrizes the corrections to Dashen's theorem for the K+-K-0 EM mass splitting, as well as epsilon(K0), which parametrizes the EM contribution to the mass of the K-0 itself. An extension of the nonperturbative EM renormalization scheme introduced by the BMW group is used in separating EM effects from isospin-violating quark mass effects. We correct for leading finite-volume effects in our realization of lattice electrodynamics in chiral perturbation theory, and remaining finite-volume errors are relatively small. While electroquenched effects are under control for epsilon, they are estimated only qualitatively for epsilon(K0) and constitute one of the largest sources of uncertainty for that quantity. We find epsilon = 0.78(1)(stat)((+8)(-11))(syst) and epsilon(K0) = 0.035(3)(stat)(20)(syst). We then use these results on 2 + 1 + 1 flavor pure QCD highly improved staggered quark (HISQ) ensembles and find m(u)/m(d) = 0.4529(48)(stat)((+150)(-67))(syst).