Abstract

Purpose. Calculation of the spectrum of masses of system b¯c consisting of two heavy b and c quarks (B_c mesons family) within the potential models of heavy quarkonium. In particular, to calculate the spin-dependent splitting of the energy S and P levels of a given of heavy mesons family. Investigate the dependence of the energy splitting magnitude on the parameters of the interaction potential between the quarks.
Methods. The spin-dependent splittings of the S and P energy levels caused by spin-spin, spin-orbital and tensor interactions in the framework of the Breit-Fermi quasi-relativistic approximation with the screened quark interaction potential are calculated. Wave functions and matrix elements of spin-spin, spin-orbital and tensor interactions were calculated numerically.
Results. It is found that the energies of the S and P levels and the magnitude of the «fine» and «hyperfine» splitting depend essentially on the mixing constant λ of scalar and vector long-range screening potential and the constant of the strong interaction α_s (whose value is almost unchanged within the B_c meson family). Increasing the contribution of the Lorentz vector potential to operators of spin-orbital, spin-spin and tensor interactions leads to increase of the magnitude of the corresponding splittings of energy levels. The obtained value of the mixing constant λ = 0.3 indicates that the confined screened potential has a predominantly scalar Lorentz nature (about 70 %), and the Coulomb-like potential of one-gluon exchange is purely a Lorentz vector.
Conclusions. The calculated energy levels of the system b¯c can be used for experimental search for B_c mesons

Keywords: mesons, Breit-Fermi hamiltonian, mass spectrum, screening potential

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