B Physics on the Lattice: $\overline{\Lambda }$, ${\lambda }_1$, ${\overline{m}}_b({\overline{m}}_b)$, ${\lambda }_2$, $B^0-{\bar{B}}^0$ mixing, $\text{fb}$ and all that

Abstract

We present a short review of our most recent high statistics lattice determinations in the HQET of the following important parameters in B physics: the B--meson binding energy, $\overline{\Lambda }$ and the kinetic energy of the b quark in the B meson, ${\lambda }_1$, which due to the presence of power divergences require a non--perturbative renormalization to be defined; the $\overline{MS}$ running mass of the b quark, ${\overline{m}}_b({\overline{m}}_b)$; the $B^{\ast }$--$B$ mass splitting, whose value in the HQET is determined by the matrix element of the chromo--magnetic operator between B meson states, ${\lambda }_2$; the B parameter of the $B^0$--${\bar{B}}^0$ mixing, $B_B$, and the decay constant of the B meson, $f_B$. All these quantities have been computed using a sample of $600$ gauge field configurations on a $24^3\times 40$ lattice at $\beta =6.0$. For $\overline{\Lambda }$ and ${\overline{m}}_b({\overline{m}}_b)$, we obtain our estimates by combining results from three independent lattice simulations at $\beta =6.0$, $6.2$ and $6.4$ on the same volume.

Comments: 3 latex pages, uses espcrc2.sty (included). Talk presented at LATTICE96(heavy quarks)