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 K 2 O potential ͓V. V. Kiselev, A. E. Kovalsky, and A. I. Onishchenko, Phys. Rev. D 64, 054009 ͑2001͔͒ motivated by QCD with a three-loop ␤ 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 Schrödinger 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.

Heavy hadron spectroscopy and the bag model

“…Predictions of Refs. [25,26] are also very close to ours. The largest masses in this case (about 240-280 MeV higher then ours) are given by [19].…”

“…[25,26], our values lie higher by about 70-80 MeV, and all other approaches predict even larger masses of these baryons. As regards the mass splittings of doubly-heavy baryons Ξ * cc −Ξ cc and Ω * cc −Ω cc , the predictions vary from about 70 MeV [60] to 130 MeV [26], our estimate (approximately 100 MeV) together with the predictions given by Ref. [29] being somewhere in the middle.…”

“…We compare our predictions obtained in the modified bag model for baryons from the charm sector (Table 7) and for baryons from the bottom sector (Tables 8 and 9) with some other estimates and experimental data. The works we want to compare our results with are: the baryon mass estimates in relativistic [29,30] and nonrelativistic [25,26] potential models with assumed quark-diquark ansatz, usual nonrelativistic potential model [19], variational calculations [23,24], and estimates obtained using various sum rules [60]. All but the one experimental masses for bottom baryons are from the Particle Data Tables [42].…”

“…Even the early treatments [15][16][17] predict the masses of many hadrons with good accuracy. Among the recent treatments there are extensive developments of the traditional approach [18,19], calculations using the method of hyperspherical harmonics [20], solving the Faddeev equations [21], variational calculations [22][23][24], nonrelativistic calculations using quarkdiquark approximation [25,26], etc. Relativistic effects are taken into account by building up the relativistic quark models based on approximate solution of the Bethe-Salpeter equation [27], or using quark-diquark approximation to simplify relativistic dynamics [28][29][30].…”

Doubly heavy baryon spectra guided by lattice QCD

“…Once charmonium and bottomonium spectra were understood within a constituent quark model framework by means of simple Cornell-like potentials [13,14], the question of predicting and trying to understand the structure of open-flavor mesons with a heavy-quark was soon posed [15]. Compared to the heavy meson case we have the great advantage of the guidance of nonperturbative lattice QCD results and the static potentials derived within SU(3) lattice QCD, which combined with the exact method to solve the threebody problem, makes the difference between our work and other studies of doubly heavy baryons [16][17][18][19][20][21][22][23][24][25][26][27][28][29]. Our results may also serve for a future analysis of the validity of the socalled superflavor symmetry, relating the spectra and properties of singly heavy mesons and doubly heavy baryons [30,31], broken by the smallness of the heavy quark masses, which makes the size of the heavy diquark not small enough compared to 1/Λ QCD .…”