Heavy Meson Decay Constants from Quenched Lattice QCD

A quenched lattice QCD calculation of the $B$ and $D$ meson decay constants is presented. To investigate scaling violation associated with the heavy quarks, parallel simulations are carried out employing both Wilson and the $O\left(a\right)$-improved clover quark actions. The discretization errors due to the large $b$ quark mass are estimated with the aid of the nonrelativistic interpretation approach of El-Khadra, Kronfeld, and Mackenzie [Phys. Rev. D 55, 3933 (1997)]. As the best values from our simulations at $\beta =5.9\mathrm{}$, 6.1, and 6.3 we obtain $f_B=173\mathrm{}\left(4\right)\mathrm{MeV}$, $f_{B_s}=199\mathrm{}\left(3\right)\mathrm{MeV}$ for $B$ mesons and $f_D=197\mathrm{}\left(2\right)\mathrm{MeV}$, $f_{D_s}=224\mathrm{}\left(2\right)\mathrm{MeV}$ for $D$ mesons where the errors are statistical. In addition we expect a $5\%$ ( $7\%$ for $D$ mesons) systematic error and a $5\%$ error in the uncertainty to determine the lattice scale, besides the quenching error, which is not estimated in this Letter.