A High-Statistics Lattice Calculation of $λ_1$ and $λ_2$ in the $B$ meson

Details A High-Statistics Lattice Calculation of $λ_1$ and $λ_2$ in the $B$ meson A High-Statistics Lattice Calculation of $λ_1$ and $λ_2$ in the $B$ meson

1996-07-24

arxiv.org/abs/hep-lat/9607055v1

Nucl.Phys.B486:227-244,1997

Physics

High Energy Physics

High Energy Physics - Lattice

26 pages, latex, 5 figures

Scientific paper

10.1016/S0550-3213(96)00696-7

We present a high-statistics lattice calculation of the kinetic energy $-\lambda_1/2 m_b$ of the heavy quark inside the $B$-meson and of the chromo-magnetic term $\lambda_2$, related to the $B^*$--$B$ 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$^2$, corresponding to $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.

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