Phenomenological predictions of the properties of theBcsystem

Abstract

We present a comprehensive calculation of the energies, splittings and electromagnetic decays of the low-lying levels of the bottom charmed meson system. In order to incorporate running coupling constant effects, we choose Richardson's potential for the central potential and take the spin-dependent potentials from the radiative one-loop calculation of Pantaleone, Tye and Ng. The effects of a nonperturbative spin-orbit potential are also included. Our parameters are determined from the low-lying levels of charmonium (average deviation of 19.9 MeV) and of the upsilon system (average deviation of 4.3 MeV). We carry out a detailed comparison with the calculations of Eichten and Quigg and the lattice calculations of the NRQCD Collaboration. Our predicted result for the ground state energy is ${6286}_{\ensuremath{-}6}^{+15}\mathrm{MeV}.$ Our results are generally in agreement with earlier calculations. However, we find the two lowest ${1}^{+}$ states to be very close to the $j\ensuremath{-}j$ limit, in contrast with some of the earlier calculations. The implications of this finding for the photon spectra of the $1P$ and $2S$ states are discussed in detail. Some strategies for the observation of these states are discussed, and a table of their cascades to the ground state is presented. Our calculated value for the ground state lifetime is $0.38\ifmmode\pm\else\textpm\fi{}0.03\mathrm{ps},$ in good agreement with the recent CDF measurement.