The mass spectra and electromagnetic decay rates of charmonium, bottomonium, and $B_c$ mesons are comprehensively investigated in the relativistic quark model. The presence of only heavy quarks allows the expansion in powers of their velocities. All relativistic corrections of order $v^2{/c}^2,$ including retardation effects and one-loop radiative corrections, are systematically taken into account in the computations of the mass spectra. The obtained wave functions are used for the calculation of radiative magnetic dipole $\mathrm{}\left(M1\mathrm{}\right)\mathrm{}$ and electric dipole $\mathrm{}\left(E1\mathrm{}\right)\mathrm{}$ transitions. It is found that relativistic effects play a substantial role. Their account and the proper choice of the Lorentz structure of the quark-antiquark interaction in a meson is crucial for bringing theoretical predictions in accord with experimental data. A detailed comparison of the calculated decay rates and branching fractions with available experimental data for radiative decays of charmonium and bottomonium is presented. The possibilities to observe the currently missing spin-singlet S and P states as well as D states in bottomonium are discussed. The results for $B_c$ masses and decays are compared with other quark model predictions.

Mass spectra of heavy baryons are calculated in the heavy-quark–light-diquark picture in the framework of the QCD-motivated relativistic quark model. The dynamics of light quarks in the diquark as well as the dynamics of the heavy quark and light diquark in the baryon are treated completely relativistically without application of nonrelativistic $v/c$ and heavy quark $1/m_Q$ expansions. Such an approach allows us to get predictions for the heavy baryon masses for rather high orbital and radial excitations. On this basis the Regge trajectories of heavy baryons for orbital and radial excitations are constructed, and their linearity, parallelism, and equidistance are verified. The relations between the slopes and intercepts of heavy baryons are considered and a comparison of the slopes of Regge trajectories for heavy baryons and heavy-light mesons is performed. All available experimental data on heavy baryons fit nicely to the constructed Regge trajectories. The possible assignment of the quantum numbers to the observed excited charmed baryons is discussed.

Mass spectra of baryons consisting of two heavy $(b$ or $c)$ and one light quark 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.

Masses of the ground state and the orbitally and radially excited states of quark-antiquark mesons composed of light $(u,d,s)$ quarks are calculated within the framework of the relativistic quark model based on the quasipotential approach. The relativistic treatment of the light quark dynamics results in mass spectra which agree well with available experimental data for the masses of the most well-established states. The Regge trajectories for angular and radial excitations are constructed, and their linearity, parallelism, and equidistance are verified. The assignment of experimentally observed light mesons to particular Regge trajectories is based on their masses and quantum numbers.

The mass spectra of the excited heavy baryons consisting of two light (u,d,s) and one heavy (c,b) quarks are calculated in the heavy-quark–light-diquark approximation within the constituent quark model. The light quarks, forming the diquark, and the light diquark in the baryon are treated completely relativistically. The expansion in v/c up to the second order is used only for the heavy (b and c) quarks. The internal structure of the diquark is taken into account by inserting the diquark–gluon interaction form factor. An overall good agreement of the obtained predictions with available experimental data is found