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

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Abstract

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 $a=0.22,0.16,0.11$ fm and four values of sea quark mass in the range ${m}_{\mathrm{PS}}{/m}_{V}\ensuremath{\approx}0.8\ensuremath{-}0.6.$ Our provisional estimate for the continuum values of the decay constants are ${f}_{\mathrm{Bd}}=208(10)(29)$ MeV, ${f}_{\mathrm{Bs}}{=250(10)(35)(}_{\ensuremath{-}0}^{+8})$ MeV, ${f}_{\mathrm{Dd}}=225(14)(40)$ MeV, ${f}_{\mathrm{Ds}}{=267(13)(48)(}_{\ensuremath{-}0}^{+10})$ MeV for ${N}_{f}=2$ 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 ${N}_{f}=2$ and ${N}_{f}=0,$ we obtain ${f}_{\mathrm{Bd}}^{{N}_{f}=2}{/f}_{\mathrm{Bd}}^{{N}_{f}=0}{=1.11(6),f}_{\mathrm{Bs}}^{{N}_{f}=2}{/f}_{\mathrm{Bs}}^{{N}_{f}=0}{=1.14(5),f}_{\mathrm{Dd}}^{{N}_{f}=2}{/f}_{\mathrm{Dd}}^{{N}_{f}=0}{=1.03(6),f}_{\mathrm{Ds}}^{{N}_{f}=2}{/f}_{\mathrm{Ds}}^{{N}_{f}=0}=1.07(5).$ They show a 10--15 % increase in the ${N}_{f}=2$ results over those of ${N}_{f}=0$ for the B meson decay constants, while evidence for such a trend is statistically less clear for the D meson decay constants.

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