Possible $D^{(\ast )}{\bar{D}}^{(\ast )}$ and $B^{(\ast )}{\bar{B}}^{(\ast )}$ molecular states in the extended constituent quark models

Abstract

The possible neutral $D^{(\ast )}{\bar{D}}^{(\ast )}$ and $B^{(\ast )}{\bar{B}}^{(\ast )}$ molecular states are studied in the framework of the constituent quark models, which is extended by including the $s$-channel one gluon exchange. Using different types of quark-quark potentials, we solve the four-body Schrödinger equation by means of the Gaussian expansion method. The bound states of $D^{(\ast )}{\bar{D}}^{(\ast )}$ with $J^{PC}=1^{++},2^{++}$ and $B^{(\ast )}{\bar{B}}^{(\ast )}$ with $J^{PC}=0^{++},1^{+-},1^{++},2^{++}$ are obtained. The molecular states $D^{\ast }\bar{D}$ with $J^{PC}=1^{++}$ and $B^{\ast }\bar{B}$ with $J^{PC}=1^{+-}$ are good candidates for the $X(3872)$ and $Z_b^0(10610)$, respectively.

Comments: 8 pages, 2 figures