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Spectroscopy of $\mathbf{B_c}$ mesons and the possibility of finding exotic $\mathbf{B_c}$-like structures

The bottom-charmed ($B_c$) mesons are more stable than their charmonium ($c\bar c$) and bottomium ($b\bar b$) partners because they cannot annihilate into gluons. However, the low production cross-sections and signal-to-background ratios avoided until now their clear identification. The recent experimental results reported by CMS and LHCb at CERN open the possibility of having a $B_c$ spectrum as complete as the ones of charmonium and bottomonium. Motivated by this expectation, we compute bottom-charmed meson masses in the region energies in which decay meson-meson thresholds are opened, looking for the analogs to the $X(3872)$ in the $B_c$ spectroscopy. We use a constituent quark model in which quark-antiquark degrees of freedom are complemented by four-body Fock states configurations. The model has been applied to a wide range of hadronic observables, in particular to the $X(3872)$, and thus the model parameters are completely constrained. No extra states are found in the $J^P=0^+$ and $J^P=1^+$ sectors. However, in the $J^P=2^+$ sector we found an additional state very close to the $D^*B^*$ threshold which could be experimentally detected.