In the framework of the chiral quark model, we investigate the $Qq\bar{ q}\bar{ q}$ ($Q= c, b$ and $q= u, d$) tetraquark system with two structures: $Q\bar{ q}$-$q\bar{ q}$ and $Qq$-$\bar{ q}\bar{ q}$. The bound-state calculation shows that for the single channel, there is no evidence for any bound state below the minimum threshold in both $cq\bar{ q}\bar{ q}$ and $bq\bar{ q}\bar{ q}$ systems. However, after coupling all channels of two structures, we obtain a bound state below the minimum threshold in the $cq\bar{ q}\bar{ q}$ system with the energy of $1998$ MeV, and the quantum number is $IJ^{ P}=\frac{ 1}{ 2}0^{ +}$. Meanwhile, in the $bq\bar{ q}\bar{ q}$ system, two bound states with energies of $5414$ MeV and $5456$ MeV are obtained, and the quantum numbers are $IJ^{ P}=\frac{ 1}{ 2}0^{ +}$ and $IJ^{ P}=\frac{ 1}{ 2}1^{ +}$, respectively. Besides, we also employe the real-scaling method to search for resonance states in the $cq\bar{ q}\bar{ q}$ and $bq\bar{ q}\bar{ q}$ systems. Unfortunately, no genuine resonance states were obtained in both systems. We suggest future experiments to search for these three possible bound states.
Categories: hep-ph