Bound States of the Heavy Flavor Vector Mesons and Y(4008) and $Z_1^{+}(4050)$

Abstract

The $D^{\ast }{\bar{D}}^{\ast }$ and $B^{\ast }{\bar{B}}^{\ast }$ systems are studied dynamically in the one boson exchange model, where $\pi$, $\eta$, $\sigma$, $\rho$ and $\omega$ exchanges are taken into account. Ten allowed states with low spin parity are considered. We suggest that the $1^{--}$, $2^{++}$, $0^{++}$ and $0^{-+}$ $B^{\ast }{\bar{B}}^{\ast }$ molecules should exist, and the $D^{\ast }{\bar{D}}^{\ast }$ bound states with the same quantum numbers very likely exist as well. However, the CP exotic ($1^{-+}$, $2^{+-}$) $B^{\ast }{\bar{B}}^{\ast }$ and $D^{\ast }{\bar{D}}^{\ast }$ states may not be bound by the one boson exchange potential. We find that the I=0 configuration is more deeply bound than the I=1 configuration, hence $Z_1^{+}(4050)$ may not be a $D^{\ast }{\bar{D}}^{\ast }$ molecule. Although Y(4008) is close to the $D^{\ast }{\bar{D}}^{\ast }$ threshold, the interpretation of Y(4008) as a $D^{\ast }{\bar{D}}^{\ast }$ molecule is not favored by its huge width. $1^{--}$ $D^{\ast }{\bar{D}}^{\ast }$ and $B^{\ast }{\bar{B}}^{\ast }$ states can be produced copiously in $e^{+}{e}^{-}$ annihilation, detailed scanning of the $e^{+}{e}^{-}$ annihilation data near the $D^{\ast }{\bar{D}}^{\ast }$ and $B^{\ast }{\bar{B}}^{\ast }$ threshold is an important check to our predictions.

Comments: 17 pages,6 figure