Spectroscopic parameters of $B_c$ meson

Abstract

We investigate the spectroscopic and decay properties of the $B_c$ meson within a nonrelativistic quark model. We calculate the mass spectrum of radially and orbitally excited states in the $S$-, $P$-, and $D$-wave sectors, the pseudoscalar and vector decay constants with one-loop QCD corrections, the E1 and M1 radiative widths, and radial Regge trajectories. The ground state and its first radial excitation agree well with experiment. The predicted decay constants are in line with relativistic model estimates and yield a corresponding prediction for the leptonic decay $B_c\to \tau {\nu }_{\tau }$. The E1 transition pattern is governed primarily by radial-wave-function overlaps, and the dominant transitions of the lowest $D$-wave multiplet suggest the $D\to P\to S$ radiative cascade as a promising pathway to the unobserved $D$-wave states. The model predicts an inverted fine-structure ordering in the $P$- and $D$-wave multiplets, reflecting the competition between the one-gluon-exchange (OGE) and confinement contributions to the spin--orbit interaction. The allowed M1 widths are strongly suppressed by the small predicted hyperfine splittings, highlighting the importance of a direct $B_c^{\ast }$ mass measurement. The radial Regge trajectories are nearly linear across all considered families, with slopes decreasing as the orbital angular momentum increases. These results identify the $B_c^{\ast }$ mass and the fine-structure ordering of the lowest $P$-wave multiplet as the key measurements for testing the spin-dependent dynamics of the $B_c$ system.

Comments: 19, 10 figures, 10 tables