The properties of the $B_c$-meson family ($c\overline{b}$) are still not well determined experimentally because the specific mechanisms of formation and decay remain poorly understood. Unlike heavy quarkonia, i.e., the hidden heavy quark-antiquark sectors of charmonium ($c\overline{c}$) and bottomonium ($b\overline{b}$), the $B_c$ mesons cannot annihilate into gluons and they are, consequently, more stable. The excited $B_c$ states, lying below the lowest strong-decay $BD$ threshold, can only undergo radiative decays and hadronic transitions to the $B_c$ ground state, which then decays weakly. As a result of this, a rich spectrum of narrow excited states below the $BD$ threshold appear, whose total widths are 2 orders of magnitude smaller than those of the excited levels of charmonium and bottomonium. In a different article, we determined bottom-charmed meson masses using a nonrelativistic constituent quark model which has been applied to a wide range of hadron physical observables, and thus the model parameters are completely constrained. Herein, continuing to our study of the $B_c$ sector, we calculate the relevant radiative decay widths and hadronic transition rates between $c\overline{b}$ states which are below the $BD$ threshold. This shall provide the most promising signals for discovering excited $B_c$ states that are below the lowest strong-decay $BD$ threshold. Finally, our results are compared with other models to measure the reliability of the predictions and point out differences.

• Received 19 May 2022
• Accepted 25 August 2022

DOI:https://doi.org/10.1103/PhysRevD.106.054009

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Published by the American Physical Society