Analytical calculations of ground and excited states of unequal mass heavy pseudoscalar and vector mesons mass spectra using Bethe-Salpeter formalism

Considering the fact that, a wide range of variation in masses of various states of heavy pseudoscalar and vector mesons can be seen in different models and the experimental data on masses of many of these states is not yet currently available, in this paper, we study the analytical calculation of heavy pseudoscalar and vector mesons mass spectra ( such as $\eta_{c}$, $B_{c}$, $\eta_{b}$, $J/\psi$, $B^{*}_{c}$ and $\Upsilon$) and their corresponding wave functions in the framework of Bethe-Salpeter equation under the covariant instantaneous ansatz. The parameters of the framework were determined by a fit to the heavy pseudoscalar and vector mesons mass spectrum of ground states. These input parameters so fixed were found to give good agreements with data on mass spectra of ground and excited states of these mesons mass spectra.