Abstract
In this work, we study the BK¯ molecule in the Bethe-Salpeter (BS) equation approach. With the kernel containing one-particle-exchange diagrams and introducing two different form factors (monopole form factor and dipole form factor) in the vertex, we solve the BS equation numerically in the covariant instantaneous approximation. We investigate the isoscalar and isovector BK¯ systems, and we find that X5568 cannot be a BK¯ molecule.
Highlights
The physics of exotic multiquark states has been a subject of intense interest in recent years
In order to manipulate the off shell effect of the exchanged mesons ρ and ω and finite size effect of the interacting hadrons, we introduce a form factor F(k2) at each vertex
We shall treat the cutoff Λ in the form factors as a parameter varying in a much wider range 0.8-4.8 GeV, in which we will try to search for all the possible solutions of the BK bound states
Summary
The physics of exotic multiquark states has been a subject of intense interest in recent years. Many theoretical groups have studied possible ways to explain X(5568) as a tetraquark state, a molecular state, etc., within various models, and they obtained different results. X(5568) is disfavored as a P-wave coupled-channel scattering molecule involving the states B푠π, B∗푠 π, BK, and B∗K in Ref. [25] using QCD two-point and light-cone sum rules, and their results strengthen the diquark-antidiquark picture for the X(5568) state rather than a meson molecule structure. Based on the quark model, X(5568) could exist as a mixture of a tetraquark and hadronic molecule [28]. By this chance, we will systematically study the BK molecular state in the BS equation approach. We give a summary and some discussions
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