Heavy Baryon Spectroscopy

A review of theoretical predictions for the mass spectra of heavy baryons, obtained within the relativistic quark model and the quark–diquark picture, is given. A detailed comparison is made with experimental data, including recent measurements of the LHCb Collaboration. Good agreement between the theoretical results and the experiment was found. Possible quantum numbers of excited states of heavy baryons are discussed.


INTRODUCTION
Nikolai Nikolaevich Bogolyubov has always conducted research at the forefront of theoretical and mathematical physics. The very next year after M. Gell-Mann and G. Zweig proposed the constituent quark model in 1964, he lectured on this model at Lomonosov Moscow State University. Following the contribution of Bogolyubov to the development of the composite picture of hadrons, we developed a relativistic quark model [1][2][3][4]. This model is based on a quasi-potential approach in quantum field theory with a quasi-potential motivated by quantum chromodynamics. Hadrons are considered as bound states of constituent quarks and are described by a single-time wave function satisfying a three-dimensional relativistically invariant Schrödinger-type equation. The quasi-potential of the interaction consists of the perturbative part: the one-gluon exchange potential, and the nonperturbative confining part, which linearly increases with distance. The Lorentz structure of the confining interaction is chosen as a mixture of scalar and vector interactions. The vertex of the long-range vector interaction contains an additional Pauli term (anomalous chromomagnetic quark moment), which leads to the vanishing of the spin-dependent chromomagnetic interaction at large distances.
In the past few years, significant experimental progress has been made in the study of spectroscopy of heavy baryons. Many new excited states of heavy baryons have been discovered. A significant contribution was made by the LHCb Collaboration [5][6][7][8][9][10]. This is due to the fact that heavy baryons are abundantly produced at the Large Hadron Collider (LHC). In this paper, these new experimental data are compared with the predictions of the relativistic quark-diquark model of baryons [2][3][4].

RELATIVISTIC QUARK-DIQUARK MODEL
OF BARYONS A heavy baryon is described as a relativistic bound state of a heavy quark and a light diquark. Thus, a very complex relativistic three-body problem is reduced to solving two substantially simpler two-body problems. First, the properties of the diquark are calculated. A diquark is a bound two-quark system; therefore, it is not a point object. As a result, its interaction with gluons is smeared by a form factor, which can be calculated as the overlap integral of the diquark wave functions. This form factor enters into the vertex of the interaction of the diquark with the gluon, which effectively describes its internal structure [2,4]. It should be noted that the ground state of a diquark composed of quarks of different flavors can be in both the scalar and the axial-vector state, while a diquark consisting of quarks of the same flavor can only be in the axial-vector state, according to the Pauli principle. Using a numerical solution of the quasi-potential equation [1], we calculated the masses and wave functions and, based on them, the diquark form factors. For heavylight baryons, only the ground states of light diquarks were considered, while, for doubly heavy baryons, the orbital and radial excitations of heavy diquarks, were taken into account. Then, the masses of heavy baryons were calculated considering them as relativistic bound states of a heavy quark and a light diquark [2,4]. It is assumed that all excitations occur only between these constituents. On the other hand, a doubly heavy baryon was considered as a bound state of a light quark and a heavy diquark. In this case, the excitations between the quark and diquark as well as inside the diquark were taken into consideration. It should be noted that, within this approach, significantly fewer excited states than in the ( ') qq ', QQ three-quark picture of baryons are predicted. This difference increases with increasing excitation. It should be emphasized that the calculations did not use nonrelativistic expansions in and in i.e., quarks and diquarks were considered fully relativistically.

HEAVY BARYONS
The calculated masses of baryons [4] are given in Tables 1-5. The first column gives the total isospin I, spin J, and parity of the baryon; the second column gives the state of the quark-diquark system; the next three columns give the predicted mass, the experimental status and the mass [11] for charmed baryons and, the next three columns, for bottom baryons. New states of baryons [5][6][7][8][9][10] are marked "New".
It can be seen from Tables 1 and 2 that (or ), if it is a genuine state Λ c , can be explained as the first radial ( ) excitation with If it is a state Σ c , then it can be associated with the first orbital excitation ( ) with (see Table 2). The baryon corresponds to the second orbital excitation ( ) with in accordance with the experimental analysis [5]. Another baryon, probably has isospin since it was detected in the The new state [9] can be the first orbital excitation (1P) with and and can be states with and Predictions for baryons are given in Tables 3  and 4. Baryons and correspond to . .

2D
( ) ( )   Table 5. The masses of the ground (1S) states were predicted [3] before their experimental detection. Recently, five new excited, narrow states that are also consistent with our predictions were observed [6]. Three lighter states and are described well as the first radial excitations (1P) with and and a theoretical analysis shows that they should be narrow states.
The remaining states with should be wide; therefore, their experimental observation is difficult. The small peak with smaller masses in the distribution (see Fig. 1) may correspond to the state with a predicted mass of 2966 MeV (see Table 5).
The two heavier states and can naturally be described as the first radial excitations

DOUBLY HEAVY BARYONS
The masses of doubly heavy baryons were calculated in the light quark-heavy diquark picture in [2]. The light quark was considered fully relativistic; the expansion only in the inverse masses of the heavy diquark was used. The calculation results for the masses of are given in Table 6. The states are denoted as where is the radial quantum number; is the orbital angular momentum of the diquark; is the radial quantum number; is the orbital angular momentum of the light quark; and and are the total angular momentum and parity of the baryon. Table 7 gives a comparison of the predicted masses of the ground states of doubly heavy baryons. Our pre-      In the sector of doubly heavy baryons, the mass of the recently discovered baryon is consistent with our prediction [2], made 15 years before its discovery. The masses of the ground states of doubly charmed baryons are predicted in the range (3.5-3.9) GeV. The masses of the ground states of doubly-bottom baryons are (10.1-10.5) GeV, and the masses of bottomcharmed baryons are (6.8-7.2) GeV. A rich spectroscopy of narrow excited states under the thresholds of strong decays is expected. The experimental search for new excited states of heavy baryons and, in particular, doubly heavy baryons is an extremely important task.