X(3872) and Other Possible Heavy Molecular States

We perform a systematic study of the possible molecular states composed of a pair of heavy mesons such as $D\bar D$, $D^\ast\bar D$, $D^\ast \bar D^\ast$ in the framework of the meson exchange model. The exchanged mesons include the pseudoscalar, scalar and vector mesons. Through our investigation, we find that (1) the structure X(3764) is not a molecular state; (2) There exists strong attraction in the range $r < 1$ fm for the $D^*\bar D^*$ system with $J=0, 1$. If future experiments confirm $Z^+(4051)$ as a loosely bound molecular state, its quantum number is probably $J^{P}=0^+$. Its partner state $\Phi^{**0}$ may be searched for in the $\pi^0\chi_{c1}$ channel; (3) The vector meson exchange provides strong attraction in the $D^\ast \bar D$ channel together with the pion exchange. A bound state solution exists with a reasonable cutoff parameter $\Lambda\sim 1.4$ GeV. X(3872) may be accommodated as a molecular state dynamically although drawing a very definite conclusion needs further investigation; (4) The $B^\ast \bar B$ molecular state exists.