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Study of the $ω$/$ω_3$, $ρ$/$ρ_3$ and the newly observed $ω$-like state $X(2220)$

We study the excited states of $ω$ and $ω_3$ by comparison with the $ρ$ and $ρ_3$ families, and discuss the possibility of $X(2220)$ as $ω$ excitation by analyzing the mass spectra and strong decay behaviors. In addition, we predict the masses and widths of $ω(2D)$ and $ω_3$and $ρ_3(4D)$, $ρ_3(1G)$, $ω_3$ and $ρ_3(2G)$ and $ω_3(3G)$ and $ρ_3(3G)$. The abundant information of their two-body strong decays predicted in this work will be helpful to further study of these $ω$ and $ω_3$ and $ρ$ and $ρ_3$ states in experiment and theory.