Strong decays of charmonia

In this work, we calculate the charmonium spectrum and strong decay widths of $c\overline{c}$ states. The calculations are performed using the quark potential model which incorporates the relativistic effects. The resulting $c\overline{c}$ spectrum exhibits a good agreement with experimental data. The open flavor strong decay widths are calculated employing the $^{3}{P}_{0}$ model. We adopt two choices of wave functions to determine the observables: the first involves the utilization of realistic wave functions obtained by solving the relativistic Schr"odinger equation, while the second employs simple harmonic oscillator wave functions whose parameters are fitted to the realistic wave functions. We find that the decay widths of higher charmonia states above the threshold value of open charm mesons are well described with these wave functions. We provide a comprehensive analysis of the strong decay widths and assigned specific charmonium states: $X(3940)$ is assigned to the ${\ensuremath{\eta}}_{c}(3S)$ state, $Y(4660)$ to the $\ensuremath{\psi}(5S)$ state, $X(3915)$ to the ${\ensuremath{\chi}}_{0}(2P)$ state, ${Z}_{c}(3900)$ to the ${h}_{c}(2P)$ state, $X(4350)$ to the ${\ensuremath{\chi}}_{2}(3P)$ state, and $X(3842)$ to the ${\ensuremath{\psi}}_{3}(1D)$ state. We also compare our results with available experimental data and theoretical predictions of other models.