Hadron Bound States With J^PC=3^-+

Mesons with exotic internal structure or quantum numbers always play a signifi-cant role in studying the properties of nonperturbative quantum chromodynamics(QCD) theory, which can also deepen our understanding of mechanism of low-energy strong interaction. The newly discovered XYZ states by various experimental groups, espe-cially the charged ones, whose structures can not be explained by conventional quark model, are generally regarded as candidates of exotic states. However, the exotic spin-parity quantum numbers can equally become an excellent indication for the experimen-tal search of exotic states. In order to provide information for experiments, the existence of state with exotic JPC=3-+is studied. Since the new XYZ states can be well un-derstood in the hadron-hadron molecule picture, we discuss JPC=3-+states in the molecule model.After analyzing the mass thresholds and partial waves of various combinations of possible charmed mesons, we find the lowest3-+state is in the S-wave D*D*2system and we investigate its properties such as binding energy and root-mean-square radius in the frame of molecule model. The first step in obtaining these physical quantities is to find the one-pion-exchange potential(OPEP) and one-sigma-exchange potential(OSEP) of D*D*2, with OPEP and OSEP determining the long-range interaction and interme-diate interaction, respectively. From the Lagrangian describing the interaction between charmed mesons and light exchanged mesons, the corresponding Feynman rules and scattering amplitudes are derived. One finally obtains the interactional potentials with Breit approximation. Since charmed meson is made up of a charm quark and a light quark, the lagrangian then at the first approximation has both SU(3)L×SU(3)R chi-ral symmetry and heavy quark spin-flavor symmetry. After inserting the potentials into Schrodinger equation and performing the numerical calculation, we get the binding en-ergy and root-mean-square radius. The results indicate that the isospin scalar X(4472) with JPC=3-+composed of D*and D*2might exist if a phenomenological cutoff parameter around2.3GeV is reasonable in the one-pion-exchange model. The cutoff for binding solutions may be reduced to a smaller value once the exchange contribution is included.Due to the contribution of higher partial waves to the formation of D*D*2molecule bound state, coupled-channel effect is further considered. To simplify the calculation process, the potential (matrix) here is expressed in terms of newly defined transition spin operators. Meanwhile, the S-wave part of the potential is examined and its expression is consistent with the former result. Finally, the binding energy and the related wave func-tion are derived by solving coupled-channel Schrodinger equation. The results show that the JPC=3-+exotic state might exist if the cutoff parameter is reasonable. Be-sides, the possible decay channels of the X(4472) are also analyzed and it is clear that X(4472) can be most likely to be found in J/ψω channel in the experiments if this state really exists.