Systematical investigation on the stability of doubly heavy tetraquark states

Abstract

We systematically investigate the stability of the doubly heavy tetraquark states $[Q_1Q_2][\bar{q}_3\bar{q}_4]$ ($Q=c$ and b, $q=u$, d and s) within the framework of the alternative color flux-tube model involving a multi-body confinement potential, $\sigma$-exchange, one-gluon exchange and one-Goldstone-boson-exchange interactions. Our numerical analysis indicates that the states $[bb][\bar{u}\bar{d}]$ with $01^+$ and $[bb][\bar{u}\bar{s}]$ with $1^+$ are the most promising stable states against the strong interaction. The states $[cc][\bar{u}\bar{d}]$ with $01^+$, $[bc][\bar{u}\bar{d}]$ with $00^+$ and $01^+$, and $[bb][\bar{u}\bar{d}]$ 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 $[bb][\bar{u}\bar{d}]$ and $[bc][\bar{u}\bar{d}]$ with $IJ^P=12^+$ would not be stable although they are, respectively, below the $\bar{B}^*\bar{B}^*$ and $D^*\bar{B}^*$ thresholds because they can decay into D-wave $\bar{B}\bar{B}$ and $D\bar{B}$ through the strong interaction. The states should have narrow widths if they really exist as our model prediction.