Study on $Z_{cs}$ and excited $B_s^0$ states in the chiral quark model

Abstract: Stimulated by the newly observed charged hidden-charm state $Z_{cs}(3985)^-$ by BESIII Collaboration, $Z_{cs}(4000)^+$, $Z_{cs}(4220)^+$ and the excited $B_s^0$ states by LHCb Collaboration, a full calculation including masses and decay widths is emerged in the chiral quark model. For $Z_{cs}$ states, we assign quantum numbers $I(J^P)=\frac{1}{2}(1^+)$ and quark composition $c\bar{c}s\bar{u}$ according to the experiment. For $B_s^0$ states, systematically investigations are performed with $I(J^P)=0(0^+), 0(1^+), 0(2^+)$ both in 2-body $b\bar{s}$ and 4-body $b\bar{s}q\bar{q}~(q=u~\rm{or}~d)$ systems. Each tetraquark calculation takes all structures including meson-meson, diquark-antidiquark and all possible color configurations into account. Among the numerical techniques to solve the 2-body and 4-body Schr{\"o}dinger equation, the spatial wave functions are expanded in series of Gaussian basis functions for high precision, which is the way Gaussian expansion method so called. Our results indicate that the low-lying states of 4-quark system are all higher than the corresponding thresholds either for $c\bar{c}s\bar{u}$ or for $b\bar{s}q\bar{q}$ systems. With the help of the real scaling method, we found two resonance states with masses of 4023 MeV and 4042 MeV for $c\bar{c}s\bar{u}$ system. The state $c\bar{c}s\bar{u}(4042)$ has a consistent mass and decay width with the recent observed state $Z_{cs}(3985)^-$. For $b\bar{s}q\bar{q}$ system with $J=0$, some resonance states are also found. The newly observed excited $B_s^0$ states can be accommodated in the chiral quark model as $2S$ or $1D$ states, and the mixing with four-quark states are also needed to be considered.