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We report measurement of the cross section of $e^+e^-\to \pi^+\pi^-\psi(2S)$between 4.0 and $5.5 {\rm GeV}$, based on an analysis of initial stateradiation events in a $980 \rm fb^{-1}$ data sample recorded with the Belledetector. The properties of the $Y(4360)$ and $Y(4660)$ states are determined.Fitting the mass spectrum of $\pi^+\pi^-\psi(2S)$ with two coherentBreit-Wigner functions, we find two solutions with identical mass and width butdifferent couplings to electron-positron pairs: $M_{Y(4360)} = (4347\pm 6\pm 3){\rm MeV}/c^2$, $\Gamma_{Y(4360)} = (103\pm 9\pm 5) {\rm MeV}$, $M_{Y(4660)} =(4652\pm10\pm 8) {\rm MeV}/c^2$, $\Gamma_{Y(4660)} = (68\pm 11\pm 1) \rm MeV$;and ${\cal{B}}[Y(4360)\to \pi^+\pi^-\psi(2S)]\cdot \Gamma_{Y(4360)}^{e^+e^-} =(10.9\pm 0.6\pm 0.7) \rm eV$ and ${\cal{B}}[Y(4660)\to \pi^+\pi^-\psi(2S)]\cdot\Gamma_{Y(4660)}^{e^+e^-} = (8.1\pm 1.1\pm 0.5) \rm eV$ for one solution; or${\cal{B}}[Y(4360)\to \pi^+\pi^-\psi(2S)]\cdot \Gamma_{Y(4360)}^{e^+e^-} =(9.2\pm 0.6\pm 0.6) \rm eV$ and ${\cal{B}}[Y(4660)\to \pi^+\pi^-\psi(2S)]\cdot\Gamma_{Y(4660)}^{e^+e^-} = (2.0\pm 0.3\pm 0.2) \rm eV$ for the other. Here,the first errors are statistical and the second systematic. Evidence for acharged charmoniumlike structure at $4.05 {\rm GeV}/c^2$ is observed in the$\pi^{\pm}\psi(2S)$ intermediate state in the $Y(4360)$ decays.

Measurement of $e^+e^- \to \pi^+\pi^-\psi(2S)$ via Initial State Radiation at Belle