Study of the $\omega$/$\omega_3$, $\rho$/$\rho_3$ and the newly observed $\omega$-like state $X(2220)$

We study the excited states of $\omega$ and $\omega_3$ by comparison with the $\rho$ and $\rho_3$ families, and discuss the possibility of $X(2220)$ as $\omega$ excitation by analyzing the mass spectra and strong decay behaviors. In addition, we predict the masses and widths of $\omega(2D)$ and $\omega_3$and $\rho_3(4D)$, $\rho_3(1G)$, $\omega_3$ and $\rho_3(2G)$ and $\omega_3(3G)$ and $\rho_3(3G)$. The abundant information of their two-body strong decays predicted in this work will be helpful to further study of these $\omega$ and $\omega_3$ and $\rho$ and $\rho_3$ states in experiment and theory.