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

Abstract

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 ($\alpha \approx$ 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, $f_{B_{s}}$=242.0(10.0) MeV, $f_{D^{+}}$=218.9(11.3) MeV, $f_{D_{s}}$=260.1(10.8) MeV, and the SU(3) flavor-breaking ratios $f_{B_{s}}$/$f_{B}$=1.229(26) and $f_{D_{s}}$/$f_{D}$=1.188(25), where the numbers in parentheses are the total statistical and systematic uncertainties added in quadrature.