(untitled) (International Journal of Mathematics and Physics, 2013)
On the basis of the investigation of the asymptotic behavior of the correlation functions of the corresponding field currents with the necessary quantum numbers the analytic method for the determination of the mass spectrum and decay constants of mesons consisting of c and b quarks with relativistic corrections is proposed. The dependence of the constituent mass of quarks on the current mass and on the orbital and radial quantum numbers is analytically derived. The mass and wave functions of the mesons are determined via the eigenvalues of nonrelativistic Hamiltonian in which the kinetic energy term is defined by the constituent mass of the bound state forming particles and the potential energy term is determined by the contributions of every possible type of Feynman diagrams with an exchange of gauge field. In the framework of our approach the mass splitting between the singlet and triplet states is determined, and the width of E1 transition rates in the cc, bb and bc systems are calculated. The obtained results are satisfactorily agree with the experimental data.