X(3872) and the bound state problem of $D^0{\bar{D}}^{\ast 0}$ (${\bar{D}}^0{D}^{\ast 0}$) in a chiral quark model

Abstract

The bound state problem of $D^0{\bar{D}}^{\ast 0}$ (${\bar{D}}^0{D}^{\ast 0}$) is relevant to the molecular interpretation of the X(3872). We investigated this problem in a chiral quark model by solving the resonating group method equation. We found the system is unbound through S-wave $\pi$ and $\sigma$ interactions. The inclusion of $\rho$ and $\omega$ meson exchanges is helpful to the formation of a molecule. Because the binding energy relies on the coupling constants, we cannot draw a definite conclusion whether a molecular state exists in $D^0{\bar{D}}^{\ast 0}$ (${\bar{D}}^0{D}^{\ast 0}$) system. When moving on to the bottom counterpart, we obtained an S-wave $B{\bar{B}}^{\ast }$ state.

Comments: 8 pages, 2 figures, 7 tables, published in Phys. Rev. C