Isospin and flavor SU(3) symmetry breaking in doubly heavy baryons

Abstract

The recent observations of the $Ξ_{cc}^{+}$ and the $Ω_{cc}^{+}$ by the LHCb Collaboration complete the ground-state triplet of doubly charmed baryons, so that its internal mass pattern can be used to test symmetry breaking in the light-quark sector. We study the doubly heavy baryons within the pion mean-field approach, regarding them as bound states of the $N_c-2$ valence light quarks that generate the pion mean field in the presence of a compact heavy diquark. All dynamical parameters for flavor SU(3) and isospin symmetry breaking were determined in the light and singly heavy baryon sectors, and the hyperfine coupling is fixed by the singly heavy spectrum. With the heavy-quark masses taken from the PDG values, the measured $Ξ_{cc}^{++}$ mass is used only to determine the collective rotational energy of the light subsystem, so that the mass splittings within the triplet are predictions. We obtain $M_{Ξ_{cc}^{+}}=(3620.17\pm13.08)$ MeV and $M_{Ω_{cc}^{+}}=(3746.62\pm13.22)$ MeV. The predicted isospin splitting, $M_{Ξ_{cc}^{++}}-M_{Ξ_{cc}^{+}}=(1.43\pm0.38)$ MeV, is consistent with the LHCb observation of the $Ξ_{cc}^{+}$. We also present the masses of the spin-3/2 doubly charmed states and the doubly bottom spectrum.