ar X iv : 1 60 3 . 01 13 1 v 1 [ he p - ph ] 3 M ar 2 01 6 X ( 5568 ) and and its partner states

Very recently, the DØ Collaboration observed a narrow structure by analyzing the Bsπ ± invariant mass spectrum, which was named as the X(5568) [1]. The X(5568) has a mass m = 5567.8 ± 2.9(stat)+0.9 −1.9(syst) MeV and width Γ = 21.9 ± 6.4(stat)+5.0 −2.5(syst) MeV [1]. Its discovery mode indicates that the valence quark component of the X(5568) should be lsl̄b̄ (l = u or d). Thus, the X(5568) is a good candidate of the exotic tetraquark state. In the past decades, experimental search for the exotic states and the corresponding theoretical investigations have been an important research topic of hadron physic (see recent review on the study of the exotic states in Ref. [2]). Under the general tetraquark scheme, there exist two possible configurations for the X(5568), i.e., the B̄K molecular state and a compact tetraquark composed of a diquark and anti-diquark. In Ref. [3], Liu et al. studied the B̄K interaction in the framework of chiral perturbative theory. The authors found that the Weinberg-Tomozawa term for the B̄K interaction in the isovector sector is zero [3], which shows that the attraction between B̄ and K is not strong. If assigning the X(5568) as the B̄K molecular state, the binding energy of the B̄K system should be around 200 MeV. In other words, this B̄K molecular state is a deeply bound state. It is obvious that the study from Ref. [3] does not support such a deeply bound B̄K molecular state scenario. We also notice a dynamical study of the interaction between B̄ and K by exchanging the ρ and ω mesons [4]. They did not find a bound state solution for the S-wave B̄K system [4]. The observation of X(5568) has inspired extensive discus-