<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi></mml:math>meson decay constants from two-flavor lattice QCD with nonrelativistic heavy quarks

Abstract

We present a study of leptonic B meson decay constants in lattice QCD with two flavors ${(N}_{f}=2)$ of light dynamical quarks using nonrelativistic QCD for the heavy quark. Gauge configurations are generated with a renormalization-group improved gauge action and a mean-field-improved clover light quark action. Measurements are carried out at two values of $\ensuremath{\beta}{=6/g}^{2},$ each for four sea quark masses, corresponding to inverse lattice spacings ${a}^{\ensuremath{-}1}\ensuremath{\approx}1.3$ and 1.8 GeV in the chiral limit of the sea quark. The continuum values of the decay constants are derived by evaluating the discretization errors at each finite lattice spacing. We find ${f}_{B}^{{N}_{f}=2}=204(8)(29)(+44)$ MeV, ${f}_{{B}_{s}}^{{N}_{f}=2}=242(9)(34)(+38)$ MeV, and ${f}_{{B}_{s}}^{{N}_{f}=2}{/f}_{B}^{{N}_{f}=2}=1.179(18)(23),$ where the errors listed are statistical, systematic and uncertainty due to choice of the physical quantity used to fix the scale. Comparison is made to quenched results ${(N}_{f}=0)$ obtained with the same action combination and matching lattice spacings. We find ${f}_{B}^{{N}_{f}=2}{/f}_{B}^{{N}_{f}=0}=1.07(5),$ ${f}_{{B}_{s}}^{{N}_{f}=2}{/f}_{{B}_{s}}^{{N}_{f}=0}=1.10(5)$ and ${(f}_{{B}_{s}}{/f}_{B}{)}^{{N}_{f}=2}{/(f}_{{B}_{s}}{/f}_{B}{)}^{{N}_{f}=0}=1.03(2),$ which indicate a 5--10 % increase in the values of the decay constants, but no appreciable change in the ratio ${f}_{{B}_{s}}{/f}_{B},$ due to sea quarks.