Four-quark Bound States in Chiral SU(3) Quark Model

The possibility of $QQ\bar{q}\bar{q}$ heavy-light four-quark bound states has been analyzed by means of the chiral SU(3) quark model, where $Q$ is the heavy quark ($c$ or $b$) and $q$ is the light quark ($u$, $d$ or $s$). We obtain a bound state for the $bb\bar{n}\bar{n}$ configuration with quantum number $J^{P}=1^{+},I=0$ and for the $cc\bar{n}\bar{n}$ ($J^{P}=1^{+},I=0$) configuration which is not bound but slightly above the $D^{*}D^{*}$ threshold (n is $u$ or $d$ quark). Meanwhile, we also conclude that a weakly bound state in $bb\bar{n}\bar{n}$ system can also be found without considering the chiral quark interactions between the two light quarks, yet its binding energy is weaker than that with the chiral quark interactions.