Systematical investigation on the stability of doubly heavy tetraquark states

We systematically investigate the stability of the doubly heavy tetraquark states [Q${}_1$Q${}_2$][${\overline{q}}_3{\overline{q}}_4$] (Q=c and b, q=u, d and s) within the framework of the alternative color flux-tube model involving a multi-body confinement potential, σ-exchange, one-gluon exchange and one-Goldstone-boson-exchange interactions. Our numerical analysis indicates that the states [bb][$\overline{u}\overline{d}$] with 01${}^{+}$ and [bb][$\overline{u}\overline{s}$] with 1${}^{+}$ are the most promising stable states against the strong interaction. The states [cc][$\overline{u}\overline{d}$] with 01${}^{+}$, [bc][$\overline{u}\overline{d}$] with 00${}^{+}$ and 01${}^{+}$, and [bb][$\overline{u}\overline{d}$] with 01${}^{-}$ as stable states are also predicted in the model. The dynamical mechanism producing those stable states with tetrahedral structure are discussed in the model. The states [bb][$\overline{u}\overline{d}$] and [bc][$\overline{u}\overline{d}$] with IJ${}^P$=12${}^{+}$ would not be stable although they are, respectively, below the $\overline{B}$*$\overline{B}$* and D*$\overline{B}$* thresholds because they can decay into D-wave $\overline{B}\overline{B}$ and D$\overline{B}$* through the strong interaction. The states should have narrow widths if they really exist as our model prediction.