Abstract
On the basis of an investigation into the asymptotic behavior of the correlation functions of the corresponding field currents with the necessary quantum numbers, an analytic method for determining 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 the wave function (WF) mesons are determined from the Schrodinger equation with a mass of constituent components particles. We calculate the splitting of the mass spectrum for the singlet and triplet states mesons, as well as to determine the width of the lepton and radiation decays due E1 transition for $$\left( {\bar cc} \right)$$ , $$\left( {\bar bb} \right)$$ , $$\left( {\bar bc} \right)$$ systems. Our results for the mass spectrum of mesons consisting of c and b quarks are in satisfactory agreement with the available experimental data.