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 DD, D * D , D * D * 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 * 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 χc1 channel; (3) The vector meson exchange provides strong attraction in the D * D channel together with the pion exchange. A bound state solution exists 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 * B molecular state exists.

The hidden-charm pentaquark and tetraquark states

“…The proximity of their masses to the thresholds inspired molecular explanations of these structures [196,215,216,202,217,218,219,220,221,222,223,224,225,203,226,200,227,228,229,230,231,232,233,234,235,236,237,238,239]. With the refinement of the meson exchange model, many subtle aspects of this framework were investigated, such as the S-D wave mixing effect [185,197], coupled-channel effect [240,241,242], and recoil correction [243,244].…”

“…In the derivation of the OPE potential in the coordinate space, one generally keeps the principal value only when making the Fourier transformation to the scattering amplitude in the momentum space. The OPE potential of the DD * system not only oscillates but also decreases very slowly [220,226], which is an inherent uncertainty of the OBE model when the mass gap of the final and initial states in the crossed diagram is larger than the exchanged meson mass. The potential from the π meson exchange is…”

“…[226], which can be categorized into a flavor octet and a singlet. Through the OBE model, the effective potentials were obtained to check whether the corresponding bound state solution can be found.…”

“…[226]). They found that there does not exist the D * D * molecular bound state with a reasonable cutoff, so the Z + (4051) is probably not a molecular bound state [226]. However, the possibility of interpreting it as the D * D * molecular resonance was still not excluded.…”

Possible interpretation of theZb(10610) andZb(10650) in a chiral quark model

“…Hence, the coefficient C = ±1 represent C-even and -odd parity respectively, which are different from that of Ref. [4,3,24], since we use normal convention of PDG [25] i.e. B 0 = db andB 0 =db.…”