Mass spectra of baryons consisting of two heavy (b or c) and one light quarks are calculated in the framework of the relativistic quark model. The light quark-heavy diquark structure of the baryon is assumed. Under this assumption the ground and excited states of both the diquark and quark-diquark bound system are considered.The quark-diquark potential is constructed. The light quark is treated completely relativistically, while the expansion in the inverse heavy quark mass is used revealing the close similarity with the mass spectra of B and D mesons. We find that the relativistic treatment of the light quark plays an important role. The level inversion of the p-wave excitations of the light quark in doubly heavy baryons is discussed.

Mass spectra of the ground-state baryons consisting of three or two heavy (b or c) and one light (u, d, s) quarks are calculated in the framework of the relativistic quark model and the hyperspherical expansion. The predictions of masses of the triply and doubly heavy baryons are obtained by employing the perturbation theory for the spin-independent and spin-dependent parts of the three-quark Hamiltonian. The transition from two-quark bound states to three-quark bound states opens new problems which refer both to the form of the quark interaction in the baryon and the structure of three-quark relativistic wave equation describing this system. In general form they were studied and solved already by many authors [1,2,3,4,5,6,7,8] (see other references in Ref.[6]). In practice it is important to have an approach which can allow to obtain simple and reliable estimates for the different experimental quantities regarding to the baryon spectroscopy, the production and decay rates. Whereas heavy baryons with one or two heavy quarks were investigated both theoretically and experimentally, the triply heavy baryons Ω Q 1 Q 2 Q 3 containing b− and c− quarks have not studied so much. The estimate of masses of the lowest-lying (ccc), (ccb), (bbc) and (bbb) states is presented in Refs. [9,10,11]. Their production in a c− or b− quark fragmentation is calculated in Refs. [12,13]. The doubly heavy baryons (Q 1 Q 2 q) represent a unique part of three-quark systems. Two heavy quarks compose a localized quark nucleus while the light quark moves around this color source at a distance of order (1/m q ). This picture leads to the quark-diquark model for doubly heavy baryons which was used in Refs. [14,15,16] for the description of the mass spectrum and decay widths. Moreover, relativistic and bound state corrections to the mass spectra of mesons and baryons (in the quark-diquark approximation) and their different decay rates were also considered in the relativistic quark model [14,15,16,17,18]. Estimates for the masses of baryons containing two heavy quarks have been presented by many authors [4,19,20,21,22,23] using different QCD inspired models for the quark interactions. The aim of the present paper is a twofold one. First, we go beyond the scope of the quark-diquark approximation in Refs. [14,15] treating the total baryon Hamiltonian as a sum of two-quark interactions and using the hyperradial approximation for the ground state triply and doubly heavy baryons. Secondly, we take into account relativistic and bound state corrections of order v 2 /c 2 by the perturbation theory. So, the purpose of our new investigation consists in the elaboration of an alternative calculational scheme of the baryon mass spectrum as compared with the earlier performed investigations in Refs. [14,15] through the use of *

The correct account for the identity of heavy quarks composing the bb and cc diquarks requires that expressions for the diquark transition matrix elements (bb ! bc and bc ! cc) should be divided by ffiffiffi 2 p. The resulting semileptonic decay rates of doubly heavy baryons should be divided by two. The corrected values of the decay rates (previously contained in Tables II and III) are presented in Table I.We are grateful to Dr. E. Hernández for bringing our attention to this problem. The agreement of our results and those from C. Albertus, E. Hernandez, J. Nieves, and J. M. Verde-Velasco, Eur. Phys. J. A 32, 183 (2007) is preserved after mutual correction. TABLE I. Semileptonic decay rates of doubly heavy baryons Ä bb , Ä bc and bb , bc (in Â10 À14 Gev). Decay À Decay À Decay À Decay À Ä bb ! Ä 0 bc 0.82 Ä 0 bc ! Ä cc 0.88 bb ! 0 bc 0.83 0 bc ! cc 0.95 Ä bb ! Ä bc 1.63 Ä 0 bc ! Ä Ã cc

On the basis of the perturbative QCD and the relativistic quark model we investigate the relativistic and bound state effects in the production processes of a pair of S-wave doubly heavy mesons with opposite charge conjugation consisting of b and c quarks. All possible relativistic corrections in the production amplitude including the terms connected with the transformation law of the bound state wave function to the reference frame of the moving pseudoscalar P− and vector V− mesons are taken into account. We obtain a growth of the cross section for the reaction e + + e − → J/Ψ + η c due to considered effects by a factor 2 ÷ 2.5 in the range of the center-of-mass energy √ s = 6 ÷ 12 GeV.