The analytical forms of the interaction potentials between one S-wave and one P-wave heavy mesons as well as the potentials between two P-wave heavy mesons are deduced based on a chiral quark model. Our results explicitly show the attractive property between two heavy mesons. Consequently, a series of possible molecular states are obtained. It is expected that our study might shed some light on the popular discussions of the newly observed XYZ states. 12.40.Yx, 13.75.Lb
I. INTRODUCTIONThe newly discovered XYZ states, such as new charmonium-like states of X(3872) [1-4], X(3940) [5-7], X(4050) ± [8,9], X(4140) [10,11], X(4160) [12], X(4250) ± [8,9], X(4260) [13][14][15], X(4350) [10], X(4360) [16,17], X(4430) ± [18-20], X(4660) [16,17], and botomnium-like states of, are of great interests, since they cannot be simply considered as normal quarkonium of cc or bb, especially for the charged ones. For these XYZ states, many different explanations have been taken into account, including tetraquark, molecular states, hybrid charmonia, cusps, and threshold effects.In our previous works [22,23], the possible two S-wave heavy meson molecular explanations for the new resonances of X(3872), X(3940), Z b (10610) ± and Z b (10650) ± are obtained. In this paper we extend our study of the S-wave heavy meson interactions to the P-wave heavy meson interactions, and we try to explain the structures of the other XYZ states, particularly for X(4250) ± , X(4350), X(4360), X(4260), X(4430) ± . As far as X(4250) ± is concerned, it was explained as a I G (J P C ) = 0 + (1 − ) D * D 1 molecule by Close [24], however Nielsen et al. [25][26][27] considered it as a 1 + (1 − ) DD 1 molecule with QCD sum rules, while Ding [28] found that the DD 1 and D * 0D * molecules couldn't be the explanation for X(4250) ± , but for X(4260). For the latter resonance, Close [24] and Nielsen et al. [25][26][27] both agreed with Ding's conclusion. Moreover, concluded that X(4430) ± could be regarded as a tetraquark or a D * D 1 molecule. Close [24] and Ding et al. [29] confirmed this molecular explanation, however, the calculation of Liu et al. [30] disfavored the D * D 1 molecular explanation using the resonating group method in our chiral quark model.In this paper, our chiral quark model will be employed to study the heavy meson interactions. The model has been explained, in detail,. In this chiral SU(3) quark model, one-gluon-exchange (OGE), confinement potential, scalar meson exchange as well as pseudoscalar meson exchange are taken into account. Moreover, this chiral SU(3) quark model was developed into the extended chiral SU(3) quark model by introducing the vector meson exchanges. It has been proved that both models are quite successful in reproducing the spectra of the baryon ground states, the binding energy of deuteron, the nucleon-nucleon (N N ), kaon-nucleon (KN ) scattering phase shifts, and the hyperon-nucleon (Y N ) cross sections [31][32][33][34][35]. During the past years, by using the Resonating Group Method (RGM), Liu [30,36,37] and Wan...