$B$-Meson Decay Constant from Unquenched Lattice QCD

We present determinations of the $B$-meson decay constant $f_B$ and of the ratio $f_{B_s}/f_B$ using the MILC Collaboration unquenched gauge configurations, which include three flavors of light sea quarks. The mass of one of the sea quarks is kept around the strange quark mass, and we explore a range in masses for the two lighter sea quarks down to $m_s/8$. The heavy $b$ quark is simulated using nonrelativistic QCD, and both the valence and sea light quarks are represented by the highly improved (AsqTad) staggered quark action. The good chiral properties of the latter action allow for a more accurate chiral extrapolation to physical up and down quarks than has been possible in the past. We find $f_B=216(9)(19)(4)(6)\mathrm{MeV}$ and $f_{B_s}/f_B=1.20(3)(1)$.

Figure 1

The ratio ${\xi }_{\Phi }={\Phi }_s/{\Phi }_q$ versus $m_q/m_s$. The full line through the data shows a fit to full QCD staggered $\chi \mathrm{PT}$ (see text). Errors are statistical errors only. The fine lattice points were not included in the fit. The vertical line at $m_q/m_s=1/27.4$ denotes the physical chiral limit.

Figure 2

${\Phi }_q$ versus $m_q/m_s$. Errors include both statistical and scale uncertainty errors. The fine lattice points were not included in the fit.