Mass spectrum, root-mean-square radii, form factors, and charge radii of mesons

In this work, properties of charmonium, bottomonium, and charmed-bottom mesons for S, P, and D states are calculated with the selection of suitable trial wave functions for the semi-relativistic potential model along with the incorporation of spin and spin–orbit interactions. These trial wave functions are tested by calculating the masses of ground, radial, and orbital excited states of mesons with the variational method. Relativistic effects are incorporated in the potential model through lowest order perturbation theory. The predictions for the masses of mesons show good agreement with the available experimental data and theoretical predictions found by different methods. This indicates that these trial wave functions are appropriate for the further study of mesons. These trial wave functions are used to calculate RMS radii, form factors, and charged radii. Results show that RMS radii and charge radii have inverse relation with the masses of mesons, i.e., heavier mesons have smaller radii and vice versa. Momentum dependence of the form factors is studied graphically and numerically.