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

TL;DR

This paper analytically calculates the mass spectra and wave functions of heavy pseudoscalar and vector mesons using the Bethe-Salpeter formalism, fitting parameters to known data and predicting excited states.

Contribution

It provides a novel analytical approach to compute heavy meson spectra within the Bethe-Salpeter framework, including excited states, with parameters fitted to experimental data.

Findings

Good agreement with experimental mass spectra for ground and excited states

Parameters successfully fitted to known meson masses

Analytical expressions for wave functions of heavy mesons

Abstract

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.