Bottom-charmed meson spectrum from a QCD approach based on the Tamm-Dancoff approximation

The bottom-charmed meson spectrum is studied 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 the theoretical predictions of other models.

Figure 1

Bogoliubov angles ${\varphi }_k^b$ and ${\varphi }_k^c$, obtained from the solutions of the gap equation [Eq. (9)], as a function of the modulus of the momentum ($k$). We have used the current quark masses $m_b=4000\mathrm{MeV}$, $m_c=950\mathrm{MeV}$, and the set III for the parameters $(m_g,C_h)$, in conformity with Table 1.

Figure 2

$B_c$ spectrum generated for set of parameters III.

Figure 3

Top panel: parent and Regge trajectories in the $(J,M^2)$ plane for $B_c$ states with unnatural parity $P=(-1{)}^J$ for $n=1,\dots ,5$ (from bottom to top). Middle panel: Regge trajectories in $(n,M^2)$ plane for $S$-wave vector, $P$-wave vector, and $D$-wave tensor $B_c$ states. Bottom panel: nonlinear trajectories in the $(J,M^2)$ plane starting from vector, pseudoscalar, and scalar $B_c$ states (from bottom to top), with lines indicating the regions of the $1S$, $1P$, and $1D$ states. Circles represent the predicted masses shown in Table 2, taking the values of set of parameters III.