Search for vector charmonium(-like) states in the $e^+e^- rightarrow eta J/psi$ line shape

The cross section of $e^+e^- rightarrow eta J/psi$ has been measured by BESIII and Belle experiments. Fit to the $e^+e^- rightarrow eta J/psi$ line shape, three resonant structures are evident. The parameters for the three resonant structures are $M_{1}=(3980pm17pm7)$ MeV/$c^{2}$, $Gamma_{1}=(104pm32pm13)$ MeV; $M_{2}=(4219pm5pm4)$ MeV/$c^{2}$, $Gamma_{2}=(63pm9pm3)$ MeV; $M_{3}=(4401pm12pm4)$ MeV/$c^{2}$, $Gamma_{3}=(49pm19pm4)$ MeV, where the first uncertainties are statistical and the second systematic. We attribute the three structures to $psi(4040)$, $Y(4220)$ and $psi(4415)$ states. The branching fractions $mathcal{B}(psi(4040) rightarrow eta J/psi)$ and $mathcal{B}(psi(4415) rightarrow eta J/psi)$ are given. If $Y(4220)$ is taken as $psi(4S)$ state, the branching fraction $mathcal{B}(psi(4S) rightarrow eta J/psi)$ is also given. Combining all $Y(4220)$ parameters obtained from different decays, we give average parameters for $Y(4220)$, which are $M_{Y(4220)}=(4220.8pm2.4)$ MeV/$c^{2}$, $Gamma_{Y(4220)}=(54.8pm3.3)$ MeV.