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

Abstract

Mass spectra and wave functions of the $J^P={\frac{1}{2}}^{+}$ $(bcq)$ 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 ${\frac{1}{2}}^{+}$ $(bcq)$ baryons is constructed and solved to obtain the corresponding mass spectra. Especially, by using the obtained wave functions, the mixing effects between ${\Xi }_{bc}({\Omega }_{bc})$ and ${\Xi }_{bc}^{\prime }({\Omega }_{bc}^{\prime })$ in ground states are computed and determined to be small ($\sim 1\%$). The numerical results indicate that it is a good choice to take ${\Xi }_{bc}$ and ${\Xi }_{bc}^{\prime }$ as the baryon states with the inside $(bc)$-diquarks occupying the definite spin.

arXiv comment26 pages, 15 figures

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