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 ∼m _s/10) and at three lattice spacings (a≈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 _D=1.188(25) , where the numbers in parentheses are the total statistical and systematic uncertainties added in quadrature.