B- and D-meson decay constants from three-flavor lattice QCD

We calculate the leptonic decay constants of B-(S) and D-(S) mesons in lattice QCD using staggered light quarks and Fermilab bottom and charm quarks. We compute the heavy-light-meson correlation functions on the MILC Asqtad-improved staggered gauge configurations, which include the effects of three light dynamical sea quarks. We simulate with several values of the light valence-and sea-quark masses (down to similar to m(S)/10) and at three lattice spacings (a approximate to 0.15, 0.12, and 0.09 fm) and extrapolate to the physical up and down quark masses and the continuum using expressions derived in heavy-light-meson staggered chiral perturbation theory. We renormalize the heavy-light axial current using a mostly nonperturbative method such that only a small correction to unity must be computed in lattice perturbation theory, and higher-order terms are expected to be small. We use the two finer lattice spacings for our central analysis, and we use the third to help estimate discretization errors. We obtain f(B)+ = 196.9(9.1) MeV, f(BS) = 242.0(10.0) MeV, f(D)+ = 218.9(11.3) MeV, f(DS) = 260.1(10.8) MeV, and the SU(3) flavor-breaking ratios f(BS)/f(B) = 1.229(26) and f(DS)/f(DS) = 1.188(25), where the numbers in parentheses are the total statistical and systematic uncertainties added in quadrature.