Mass spectra, wave functions and mixing effects of the ( bcq ) baryons

Mass spectra and wave functions of the J^P=1/2^+ ( bcq ) baryons are calculated by the relativistic Bethe–Salpeter equation (BSE) with considering the mixing effects between the 1^+ and 0^+ ( bc )-diquarks inside. Based on the diquark picture, the three-body problem of baryons is transformed into two two-body problems. The BSE and wave functions of the 0^+ diquark are given, and then solved numerically to obtain the effective mass spectra and form factors. Also we present the wave functions at zero point for the ( bc )-diquark. Considering the obtained diquark form factors, the ( bcq ) baryons are then described by the BSE as the bound state of a diquark and a light quark, where the interaction kernel includes the inner transitions between the 0^+ and 1^+ diquarks. The general wave function of the 1/2^+ ( bcq ) baryons is constructed and solved to obtain the corresponding mass spectra. Especially, by using the obtained wave functions, the mixing effects between Ξ _bc(Ω _bc) and Ξ _bc'(Ω '_bc) in ground states are computed and determined to be small ( ∼1% ). The numerical results indicate that it is a good choice to take Ξ _bc and Ξ '_bc as the baryon states with the inside ( bc )-diquarks occupying the definite spin.