Hadrons with Charm and Beauty

Abstract

By combining potential models and QCD spectral sum rules (QSSR), we discuss the spectroscopy of the $(b\bar{c})$ mesons and of the $(bcq)$, $(ccq)$ and $(bbq)$ baryons ($q\equiv d$ or $s$), the decay constant and the (semi)leptonic decay modes of the $B_c$ meson. For the masses, the best predictions come from potential models and read: $M_{B_c}=(6255\pm 20)$~MeV, $M_{B_c^{\ast }}=(6330\pm 20)$~MeV, $M_{\Lambda (bcu)}=(6.93\pm 0.05)$~GeV, $M_{\Omega (bcs)}=(7.00\pm 0.05)$~GeV, $M_{{\Xi }^{\ast }(ccu)}=(3.63\pm 0.05)$~GeV and $M_{{\Xi }^{\ast }(bbu)}=(10.21\pm 0.05)$~GeV. The decay constant $f_{B_c}=(2.94\pm 0.21)f_{\pi }$ is well determined from QSSR and leads to: $\Gamma (B_c\to {\nu }_{\tau }\tau )=(3.0\pm 0.4)(V_{cb}/0.037{)}^2$ $\times 10^{10}$ s${}^{-1}$.The uses of the vertex sum rules for the semileptonic decays of the $B_c$ show that the $t$-dependence of the form factors is much stronger than predicted by vector meson dominance. It also predicts the almost equal strength of about 0.30 $\times 10^{10}$ sec${}^{-1}$ for the semileptonic rates $B_c$ into $B_s,B_s^{\ast },{\eta }_c$ and J/$\psi$. Besides these phenomenological results, we also show explicitly how the Wilson coefficients of the $⟨{\alpha }_s{G}^2⟩$ and $⟨G^3⟩$ gluon condensates already contain the full heavy quark- ($⟨\bar{Q}Q⟩$) and mixed- ($⟨\bar{Q}GQ⟩$) condensate contributions in the OPE.}

Comments: 32 pages, LaTeX, no changes in the 1994 paper, latex errors corrected in 2014