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 state radiation events in a $980 rm fb^{-1}$ data sample recorded with the Belle detector. The properties of the $Y(4360)$ and $Y(4660)$ states are determined. Fitting the mass spectrum of $pi^+pi^-psi(2S)$ with two coherent Breit-Wigner functions, we find two solutions with identical mass and width but different couplings to electron-positron pairs: $M_{Y(4360)} = (4347pm 6pm 3) {rm MeV}/c^2$, $Gamma_{Y(4360)} = (103pm 9pm 5) {rm MeV}$, $M_{Y(4660)} = (4652pm10pm 8) {rm MeV}/c^2$, $Gamma_{Y(4660)} = (68pm 11pm 1) rm MeV$; and ${cal{B}}[Y(4360)to pi^+pi^-psi(2S)]cdot Gamma_{Y(4360)}^{e^+e^-} = (10.9pm 0.6pm 0.7) rm eV$ and ${cal{B}}[Y(4660)to pi^+pi^-psi(2S)]cdot Gamma_{Y(4660)}^{e^+e^-} = (8.1pm 1.1pm 0.5) rm eV$ for one solution; or ${cal{B}}[Y(4360)to pi^+pi^-psi(2S)]cdot Gamma_{Y(4360)}^{e^+e^-} = (9.2pm 0.6pm 0.6) rm eV$ and ${cal{B}}[Y(4660)to pi^+pi^-psi(2S)]cdot Gamma_{Y(4660)}^{e^+e^-} = (2.0pm 0.3pm 0.2) rm eV$ for the other. Here, the first errors are statistical and the second systematic. Evidence for a charged charmoniumlike structure at $4.05 {rm GeV}/c^2$ is observed in the $pi^{pm}psi(2S)$ intermediate state in the $Y(4360)$ decays.
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