Looking for a $ud\overline{s}\overline{b}$ bound state in the chiral quark model

Inspired by the report of D0 Collaboration on the state $X(5568)$ with four different flavors, a similar state, $ud\overline{s}\overline{b,}$ is investigated in the present work. The advantage of looking for this state over the state $X(5568)$ with quark contents, $bu\overline{d}\overline{s}$ or $bd\overline{u}\overline{s}$, is that the $BK$ threshold is 270 MeV higher than that of $B_s\pi$, and it allows a large mass region for $ud\overline{s}\overline{b}$, which cannot decay to $B_s\pi$, to be stable. The chiral quark model and Gaussian expansion method are employed to do the calculations of four-quark states, $ud\overline{s}\overline{b}$, with quantum numbers $I{J}^P$ ($I=0,1;J=0,1,2;P=+$). Two structures, diquark-antidiquark and meson-meson, with all possible color configurations are considered. The results indicate that energies of the tetraquark with diquark-antiquark configuration are all higher than the threshold of $BK$, but the resonances are still possible because of their structures. For the state of $I{J}^P=00^{+}$ in the meson-meson structure, the energies are just below the corresponding thresholds, where the color channel coupling plays an important role. The bound state is possible. The distances between two objects (quark/antiquark) show that the state is a molecular one.

Figure 1

The eigenenergy of the $00^{+}$ state as a function of the distance between the diquark and antidiquark.