Constituent-quark-model based coupled-channels calculation of the $\mathbf{bb}\bar{\mathbf{c}}\bar{\mathbf{c}}$ and $\mathbf{bc}\bar{\mathbf{b}}\bar{\mathbf{c}}$ tetraquark systems

Abstract

We perform a coupled-channels study of the $bb\bar{c}\bar{c}$ and $bc\bar{b}\bar{c}$ tetraquark systems in a molecular approach using a constituent quark model which has been widely used to satisfactorily describe a broad range of properties of heavy quark hadron systems, either conventional or exotic. Within a molecular framework, the interaction in the heavy quark sector is governed by gluon exchange or confinement forces that are inherently color-dependent. While the $B_c{B}_c$ system contains two identical quarks, enabling stronger interactions via exchange diagrams, the forces in the $B_c{\bar{B}}_c$ and $(c\bar{c})-(b\bar{b})$ systems are expected to be significantly weaker. Consequently, the theoretical and experimental analysis of $B_c^{(\ast )}{B}_c^{(\ast )}$, $B_c^{(\ast )}{\bar{B}}_c^{(\ast )}$, and charmonium-bottomonium bound structures could play a crucial role in clarifying the dominant mechanisms responsible for the formation of fully-heavy tetraquarks. For the $bb\bar{c}\bar{c}$ tetraquark sector, we find several resonance states with different spin-parity quantum numbers. These resonances are characterized by their proximity, but not too close, to the $B_c^{(\ast )}{B}_c^{(\ast )}$ thresholds and their large total decay widths, indicating strong decay channels. In contrast, our analysis of the $bc\bar{b}\bar{c}$ tetraquark sector reveals no bound states, virtual states, or resonances; suggesting that tetraquark states of the $(c\bar{c})-(b\bar{b})$ or $B_c^{(\ast )}{\bar{B}}_c^{(\ast )}$ molecular type are unlikely to be formed, within our model assumptions.

9 pages, 4 tables