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

Abstract

Mass spectra and wave functions of the $$J^P=\frac{1}{2}^+$$ J P = 1 2 + (bcq) baryons are calculated by the relativistic Bethe–Salpeter equation (BSE) with considering the mixing effects between the $$1^+$$ 1 + and $$0^+$$ 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 $$0^+$$ 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 $$0^+$$ 0 + and $$1^+$$ 1 + diquarks. The general wave function of the $$\frac{1}{2}^+$$ 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 $$\Xi _{bc}(\Omega _{bc})$$ Ξ bc ( Ω bc ) and $$\Xi _{bc}'(\Omega '_{bc})$$ Ξ bc ′ ( Ω bc ′ ) in ground states are computed and determined to be small ($$\sim \!1\%$$ ∼ 1 % ). The numerical results indicate that it is a good choice to take $$\Xi _{bc}$$ Ξ bc and $$\Xi '_{bc}$$ Ξ bc ′ as the baryon states with the inside (bc)-diquarks occupying the definite spin.

Strong decays of $P_ψ^N(4312)^+\to J/ψ(η_c) p$ within the Bethe-Salpeter framework

“…(2.20) into the Salpeter equation (2.7), eliminating the spinor, calculating the trace, we can obtain two coupled eigenvalue equations with the pentaquark mass M as the eigenvalue and f 1(2) as the eigen wave functions (see Ref. [26,43,44] for details). Solving the eigenvalue equations numerically, we can obtain the corresponding mass spectra and numerical wave functions, which are also graphically displayed in Fig.…”

“…Another advantage is that the constructed BS wave functions only depend on the good quantum number spinparity and Lorentz covariance. The BS methods have already been successfully used to cope with mass spectra of the doubly heavy baryons [43,44], producing the recently observed molecular pentaquarks [26] and the fully heavy tetraquark T QQ Q Q states [45], and also the hadronic transitions and decays [46][47][48][49][50][51][52]. The theoretical calculations from BS methods achieve satisfactory consistences with the experimental measurements.…”

Models and potentials in hadron spectroscopy

“…Li et al studied fully heavy tetraquark states using BSE formalism [36]. Using instantaneous approximation, the tetraquark state was taken as a bound state of diquark and an antidiquark.…”

Search for the doubly heavy baryon decaying to *

“…1.9 < η < 4.9 p T To date, no search has been performed for the baryon, a bound state with quark content . This baryon is expected to have a mass in the range of 6700 -7029 MeV/ [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35], while its lifetime is predicted to be between and [21,31,[36][37][38]. The production cross-section at a centre-of-mass energy of =13 TeV is predicted to be about 16 nb [39] in the fiducial region and , where is the momentum component transverse to the beam direction and η is the pseudorapidity.…”