A High Statistics Lattice Calculation of The B-meson Binding Energy

Abstract

We present a high statistics lattice calculation of the B--meson binding energy $\overline{\Lambda}$ of the heavy--quark inside the pseudoscalar B--meson. Our numerical results have been obtained from several independent numerical simulations at $\beta=6.0$, $6.2$ and $6.4$, and using, for the meson correlators, the results obtained by the APE group at the same values of $\beta$. Our best estimate, obtained by combining results at different values of $\beta$, is $\overline{\Lambda}=180^{+30}_{-20}$ MeV. For the $\overline{MS}$ running mass, we obtain $\overline{m}_{b}(\overline{m}_{b})=4.15 \pm 0.05 \pm 0.20$ GeV, in reasonable agreement with previous determinations. The systematic error is the truncation of the perturbative series in the matching condition of the relevant operator of the Heavy Quark Effective Theory.