Study on the resonant parameters of $Y(4220)$ and $Y(4390)$

Many vector charmonium-like states have been reported recently in the cross sections of $e^{+}{e}^{-}\to \omega {\chi }_{c0}$, ${\pi }^{+}{\pi }^{-}{h}_c$, ${\pi }^{+}{\pi }^{-}J\mathrm{/}\psi$, ${\pi }^{+}{\pi }^{-}\psi (3686)$ and ${\pi }^{+}{D}^0{D}^{\ast -}+c\mathrm{.}c\mathrm{.}$ To better understand the nature of these states, a combined fit is performed to these cross sections by using three resonances $Y(4220)$, $Y(4390)$ and $Y(4660)$. The resonant parameters for the three resonances are obtained. We emphasize that two resonances $Y(4220)$ and $Y(4390)$ are sufficient to explain these cross sections below 4.6 GeV. The lower limits of $Y(4220)$ and $Y(4390)$'s leptonic decay widths are also determined to be $(36.4\pm 2.0\pm 4.2)$ and $(123.8\pm 6.5\pm 9.0)$ eV.