Mass spectra of doubly heavyΩQQ′baryons

Abstract

We evaluate the masses of baryons composed of two heavy quarks and a strange quark, taking into account spin-dependent splittings in the framework of the potential model with the ${\mathrm{K}}^{2}\mathrm{O}$ potential [V. V. Kiselev, A. E. Kovalsky, and A. I. Onishchenko, Phys. Rev. D 64, 054009 (2001)] motivated by QCD with a three-loop $\ensuremath{\beta}$ function for the effective charge consistent with both the perturbative limit at short distances and a linear confinement term at long distances between the quarks. The factorization of dynamics is assumed and explored in the nonrelativistic Schr\"odinger equation for motion in a system of two heavy quarks constituting the doubly heavy diquark and the strange quark interaction with the diquark. The limits of the approach, its justification, and uncertainties are discussed. Excited quasistable states are classified by the quantum numbers of a heavy diquark composed of heavy quarks of the same flavor.