X(3872) and other possible heavy molecular states

Abstract

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 the following results. (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 Φ ^**0 may be searched for in the π ⁰ χ _c1 channel. (3) Vector meson exchange provides strong attraction in the $D^{\ast}\bar{D}$ channel together with pion exchange. A bound state solution may exist with a reasonable cutoff parameter Λ∼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 may exist.