A High Statistics Lattice Calculation of $f_B^{static}$ at $\beta =6.2$ Using the Clover Action

We present a calculation of $f_B$ in the static limit, obtained by numerical simulation of quenched QCD, at $\beta =6.2$ on a ${18}^3\times 64$ lattice, using the SW-Clover quark action. The decay constant has been extracted by studying heavy(static)-light correlation functions of different smeared operators, on a sample of 220 gauge field configurations. We have obtained $f_B^{static}=(290 \pm 15 \pm 45)$ MeV, where the first error comes from the uncertainty in the determination of the matrix element and the second comes from the uncertainty in the lattice spacing. We also obtain $M_{B_s}-M_{B_d}=(70\pm 10)$ MeV and $f_{B_s}^{stat}\mathrm{/}{f}_{B_d}^{stat}=1.11(3)$. A comparison of our results with other calculations of the same quantity is made.