A High-Statistics Lattice Calculation of ${\lambda }_1$ and ${\lambda }_2$ in the $B$ meson

We present a high-statistics lattice calculation of the kinetic energy $-{\lambda }_1\mathrm{/}2m_b$ of the heavy quark inside the $B$-meson and of the chromo-magnetic term ${\lambda }_2$, related to the $B^{\ast }$–$B$ mass splitting, performed in the HQET. Our results have been obtained from a numerical simulation based on 600 gauge field configurations generated at $\beta =6.0$, on a lattice volume ${24}^3\times 40$ and using, for the meson correlators, the results obtained with the SW-Clover $O(a)$ improved lattice action for the light quarks. For the kinetic energy we found $-\lambda_1=\langle B \vert \bar h (i\vec{D})^{2} h \vert B \rangle /(2 M_B )=-(0.09 \pm 0.14)$GeV$^2$, which is interesting for phenomenological applications. We also find $\lambda_2= 0.07 \pm 0.01$GeV$^2$,correspondingto$M^2_{B^*}-M^2_B= 4 \lambda_2= 0.280 \pm 0.060 $GeV$^2$, which is about one half of the experimental value. The origin of the discrepancy with the experimental number needs to be clarified.