https://doi.org/10.1140/epjc/s10052-022-10006-8
Regular Article - Theoretical Physics
Mass spectra, wave functions and mixing effects of the (bcq) baryons
1
School of Physical Science and Technology, Northwestern Polytechnical University, 710072, Xi’an, China
2
Institute of Theoretical Physics, Chinese Academy of Sciences, 100190, Beijing, China
3
School of Physical Sciences, University of Chinese Academy of Sciences, 19A Yuquan Road, 100049, Beijing, China
4
CCAST (World Laboratory), P.O. Box 8730, 100190, Beijing, China
5
Department of Physics, Chongqing University, 401331, Chongqing, China
6
Department of Physics, Hebei University, 071002, Baoding, China
a
liruo@nwpu.edu.cn
b
zhangzx@itp.ac.cn
Received:
20
December
2021
Accepted:
6
January
2022
Published online:
21
January
2022
Mass spectra and wave functions of the 
(bcq) baryons are calculated by the relativistic Bethe–Salpeter equation (BSE) with considering the mixing effects between the 
and 
(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 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 and diquarks. The general wave function of the 
(bcq) baryons is constructed and solved to obtain the corresponding mass spectra. Especially, by using the obtained wave functions, the mixing effects between 
and 
in ground states are computed and determined to be small (
). The numerical results indicate that it is a good choice to take 
and 
as the baryon states with the inside (bc)-diquarks occupying the definite spin.
© The Author(s) 2022
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