Is J^PC=3^-＋ molecule possible

The confirmation of charged charmonium-like states indicates that heavy quark molecules should exist. Here we discuss the possibility of a molecule state with ^PC=3^-＋. In a one-boson-exchange model investigation for the S wave C=＋ D^＊D2^＊ states, one finds that the strongest attraction is in the case J= 3 and I=0 for both π and σ exchanges. Numerical analysis indicates that this hadronic bound state might exist if a phenomenological cutoff parameter around 2.3 GeV （1.5 GeV） is reasonable with a dipole （monopole） type form factor in the one-pion- exchange model. The cutoff for binding solutions may be reduced to a smaller value once the σ exchange contribution is included. If a state around the D^＊D2^＊ threshold （≈4472 MeV） in the channel J/ψω （P wave） is observed, the heavy quark spin symmetry implies that it is not ace meson and the jPC are likely to be 3^-＋.