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

Abstract

We present a high-statistics lattice calculation of the kinetic energy $-{\lambda }_1/2m_b$ 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 $-{\lambda }_1=⟨B|\bar{h}(i\vec{D}{)}^{2}h|B⟩/(2M_B)=-(0.09\pm 0.14)$~GeV${}^2$, which is interesting for phenomenological applications. We also find ${\lambda }_2=0.07\pm 0.01$ GeV${}^2$, corresponding to $M_{B^{\ast }}^2-M_B^2=4{\lambda }_2=0.280\pm 0.060$ GeV${}^2$, which is about one half of the experimental value. The origin of the discrepancy with the experimental number needs to be clarified.

26 pages, latex, 5 figures

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