Decay constants ofBandDmesons from improved relativistic lattice QCD with two flavors of sea quarks

We present a calculation of the B and D meson decay constants in lattice QCD with two ${(N}_f=2)$ flavors of light dynamical quarks, using an O(a)-improved Wilson action for both light and heavy quarks and a renormalization-group improved gauge action. Simulations are made at three values of lattice spacing $a=0.22,0.16,0.11\mathrm{}$ fm and four values of sea quark mass in the range $m_{\mathrm{PS}}{/m}_V\approx 0.8-\mathrm{0.6.}$ Our provisional estimate for the continuum values of the decay constants are $f_{\mathrm{Bd}}=208\mathrm{}\left(10\right)\mathrm{}\left(29\right)\mathrm{}$ MeV, $f_{\mathrm{Bs}}{=250\mathrm{}\left(10\right)\mathrm{}\left(35\right)(}_{-0}^{+8\mathrm{}})$ MeV, $f_{\mathrm{Dd}}=225\mathrm{}\left(14\right)\mathrm{}\left(40\right)\mathrm{}$ MeV, $f_{\mathrm{Ds}}{=267\mathrm{}\left(13\right)\mathrm{}\left(48\right)(}_{-0}^{+10\mathrm{}})$ MeV for $N_f=2\mathrm{}$ where the statistical and systematic errors are separately listed, and the third error for $f_{\mathrm{Bs}}$ and $f_{\mathrm{Ds}}$ shows the uncertainty of the determination of the strange quark mass. We also carry out a set of quenched simulations using the same action to make a direct examination of sea quark effects. Taking the ratio of results for $N_f=2\mathrm{}$ and $N_f=0,$ we obtain $f_{\mathrm{Bd}}^{N_f=2\mathrm{}}{/f}_{\mathrm{Bd}}^{N_f=0\mathrm{}}{=1.11\mathrm{}\left(6\right),f}_{\mathrm{Bs}}^{N_f=2\mathrm{}}{/f}_{\mathrm{Bs}}^{N_f=0\mathrm{}}{=1.14\mathrm{}\left(5\right),f}_{\mathrm{Dd}}^{N_f=2\mathrm{}}{/f}_{\mathrm{Dd}}^{N_f=0\mathrm{}}{=1.03\mathrm{}\left(6\right),f}_{\mathrm{Ds}}^{N_f=2\mathrm{}}{/f}_{\mathrm{Ds}}^{N_f=0\mathrm{}}=1.07\mathrm{}\left(5\right).$ They show a 10–15 % increase in the $N_f=2\mathrm{}$ results over those of $N_f=0\mathrm{}$ for the B meson decay constants, while evidence for such a trend is statistically less...