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

We present a high statistics lattice calculation of the B–meson binding energy $\bar{\mathrm{\Lambda }}$ 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 $\bar{\mathrm{\Lambda }}=180_{-20}^{+30}$ MeV. For the $\overline{MS}$ running mass, we obtain ${\bar{m}}_b({\bar{m}}_b)=4.15\pm 0.05\pm 0.20$ 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.