Low-lying doubly heavy baryons: Regge relation and mass scaling

Abstract In framework of heavy-diquark–light-quark endowed with heavy-pair binding, we explore excited baryons $$QQ^{\prime }q$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Q</mml:mi> <mml:msup> <mml:mi>Q</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:mi>q</mml:mi> </mml:mrow> </mml:math> containing two heavy quarks ( $$QQ^{\prime }=cc,bb,bc$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Q</mml:mi> <mml:msup> <mml:mi>Q</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:mo>=</mml:mo> <mml:mi>c</mml:mi> <mml:mi>c</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> <mml:mi>b</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> <mml:mi>c</mml:mi> </mml:mrow> </mml:math> ) by combining the method of Regge trajectory with the perturbative correction due to the heavy-pair interaction in baryons. Two Regge relations, one linear and the other nonlinear, are constructed semi-classically in the QCD string picture, and a mass scaling relation based on the heavy diquark–heavy antiquark symmetry are employed between the doubly heavy baryons and heavy mesons. We employ the ground-state mass estimates compatible with the observed doubly charmed baryon $$\Xi _{cc}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Ξ</mml:mi> <mml:mrow> <mml:mi>cc</mml:mi> </mml:mrow> </mml:msub> </mml:math> and spectra of the heavy quarkonia to determine the trajectory parameters and the binding energies of the heavy pair, and thereby compute the low-lying masses of the excited baryons $$\Xi _{QQ^{\prime }}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Ξ</mml:mi> <mml:mrow> <mml:mi>Q</mml:mi> <mml:msup> <mml:mi>Q</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:mrow> </mml:msub> </mml:math> and $$\Omega _{QQ^{\prime }}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Ω</mml:mi> <mml:mrow> <mml:mi>Q</mml:mi> <mml:msup> <mml:mi>Q</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:mrow> </mml:msub> </mml:math> up to 2S and 1P excitations of the light quark and heavy diquark. The level spacings of heavy diquark excitations are found to be smaller generally than that of the light-quark excitations, in according with the nature of adiabatic expansion between the heavy and light-quark dynamics.

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