Lattice computation of the electromagnetic contributions to kaon and pion masses

Abstract

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 $\approx 0.12$ fm to $\approx 0.045$ fm. We compute the quantity $\hat{I}\mu$, which parameterizes the corrections to Dashen's theorem for the $K^{+}$-$K^0$ EM mass splitting, as well as $\hat{I}{\mu }_{K^0}$, which parameterizes 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 $\hat{I}\mu$, they are estimated only qualitatively for $\hat{I}{\mu }_{K^0}$, and constitute one of the largest sources of uncertainty for that quantity. We find $\hat{I}\mu =0.78(1{)}_{\mathrm{stat}}({}_{-11}^{+8}{)}_{\mathrm{syst}}$ and $\hat{I}{\mu }_{K^0}=0.035(3{)}_{\mathrm{stat}}(20{)}_{\mathrm{syst}}$. We then use these results on 2+1+1 flavor pure QCD HISQ ensembles and find $m_u/m_d=0.4529(48{)}_{\mathrm{stat}}({}_{-67}^{+150}{)}_{\mathrm{syst}}$.

Version published in Phys. Rev. D. Compared to v1, more discussion of nonperturbative EM renormalization scheme, of statistical errors (with 3 added figures), and of choice QED_{TL} in finite volume. 87 pages, 35 figures