Dynamical Study of S-Wave $\bar{Q}Q\bar{q}q$ System

Abstract

The spectrum of the S-wave $\bar{Q}Q\bar{q}q$ (where $Q=c,b$ and $q=u,d,s$) system are studied within two constituent quark models. The bound states of $B^*\bar{B}^*$ with $I(J^{PC})=1(0^{++}),~1(1^{+-}),~0(2^{++})$ and $B\bar{B}^*$ with isospin $I=1$, or 0 are obtained in color-singlet-singlet channel. If considering the coupling of color channels, apart from the deep bound states appear in $[b\bar{q}]^{(*)}[q\bar{b}]^{(*)}$ scenario, a bound state $[c\bar{q}]^*[q\bar{c}]^*$ with $I(J^{PC})=1(0^{++})$ is also formed. The $B\bar{B}^*$ and the $B^*\bar{B}^*$ with quantum number $1(1^{+-})$ are good candidates for $Z_b^{\pm }(10{,}610)$ and $Z_b^{\pm }(10{,}650)$ reported by Belle Collaboration respectively, while the $B\bar{B}^*$ with isospin 0 can be interpret as a candidate for $Z_b^{0}(10{,}610)$. A bound state $[c\bar{q}]^*[q\bar{c}]^*$ with $I(J^{PC})=1(0^{++})$ may be found in the $e^+e^-\rightarrow D^*\bar{D}^*\pi \pi$ channel in the future by BES and other experimental collaborations.