Abstract
The bottom-charmed meson spectrum is studied in this work via an effective version of the Coulomb gauge QCD Hamiltonian. The Tamm-Dancoff approximation is employed to estimate the energies of the low-lying and radial-excited $B_c$ states with quantum numbers $J^P = 0^{-}, 0^{+}, 1^{-}, 1^{+}, 2^{+}, 2^{-}$. In particular, we analyze the effects of incorporating an effective transverse hyperfine interaction and spin mixing. The Regge trajectories and hyperfine splitting of both $S$- and $P$-wave states are also examined. The numerical results are compared with available experimental data and theoretical predictions of other models.
Highlights
Despite the enormous experimental developments in heavy-hadron physics in recent decades, bottom-charmed ðBcÞ spectroscopy remains much less known than the charmonium and bottomonium sectors
These aspects suggest that Bc states are more stable than their analogs in charmonium and bottomonium families, and it is fairly important to study heavy-quark dynamics to understand the dynamics of the strong interaction in a deeper level
In the Coulomb gauge quantum chromodynamics (QCD) model, the input parameters to be fitted to the experimental data are the dynamical mass of the constituent gluon mg, the current quark masses of the b and c quarks, mb and mc, and the magnitude of the transverse potential Ch
Summary
Despite the enormous experimental developments in heavy-hadron physics in recent decades, bottom-charmed ðBcÞ spectroscopy remains much less known than the charmonium and bottomonium sectors. The vacuum is represented as a coherent BCS ground state with quark and gluon Cooper pairs (condensates), and the hadrons interpreted as quasiparticle excitations This approach has been successfully applied to the description of properties of some types of light and heavy mesons, glueballs, gluelumps, hybrids, and tetraquarks [30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47]. In the Appendixes, we explicitly present the Bc-meson spin-orbital wave functions and kernels of the Tamm-Dancoff approximation (TDA) equation of motion used
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