Mass spectra of doubly heavy baryons in the relativized quark model with heavy-quark dominance

Abstract In the framework of the relativized quark model, the mass spectra of the doubly heavy baryons are rigorously calculated in the three-quark system under the heavy-quark dominance mechanism, by using the Gaussian expansion method and the infinitesimally-shifted Gaussian basis functions. With the obtained mass spectra of all doubly heavy baryon families, the contribution of each Hamiltonian term to the energy levels is analyzed. It is found that the spin splitting is mainly determined by the spin-dependent interactions associated with the light quark. Moreover, it is shown that the spin splitting evolves regularly with the mass of heavy quarks by the evolution of the spectral structure, which is consistent with the heavy quark symmetry. Meanwhile, the orbital excitation is dominated by the $$\rho $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ρ</mml:mi> </mml:math> -mode, which is different from that of the singly heavy baryons. At last, our analysis indicates that the $$\Xi _{cc}^{+}(3520)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>Ξ</mml:mi> <mml:mrow> <mml:mi>cc</mml:mi> </mml:mrow> <mml:mo>+</mml:mo> </mml:msubsup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>3520</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> state should not exist truly and the $$\Xi _{cc}^{++}(3621)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>Ξ</mml:mi> <mml:mrow> <mml:mi>cc</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mo>+</mml:mo> </mml:mrow> </mml:msubsup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>3621</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> should be the true ground state with $$J^{P}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>J</mml:mi> <mml:mi>P</mml:mi> </mml:msup> </mml:math> = $$\frac{1}{2}^{+}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> <mml:mo>+</mml:mo> </mml:msup> </mml:math> . It is recommended to design the corresponding experiments to search for the $$\Xi _{cc}^{*}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mi>Ξ</mml:mi> <mml:mrow> <mml:mi>cc</mml:mi> </mml:mrow> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mrow> </mml:mmultiscripts> </mml:math> in the energy range from 3694 to 3714 MeV.