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

We report measurement of the cross section of $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\psi (2S)$ between 4.0 and $5.5\mathrm{G}\mathrm{e}\mathrm{V}$, based on an analysis of initial state radiation events in a $980\mathrm{f}{\mathrm{b}}^{-1}$ 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: $M_{Y(4360)} = (4347\pm 6\pm 3) {\rm MeV}/c^2$,$\Gamma_{Y(4360)} = (103\pm 9\pm 5) {\rm MeV}$,$M_{Y(4660)} = (4652\pm10\pm 8) {\rm MeV}/c^2$,$\Gamma_{Y(4660)} = (68\pm 11\pm 1) \rm MeV$; 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${\cal{B}}[Y(4660)\to \pi^+\pi^-\psi(2S)]\cdot \Gamma_{Y(4660)}^{e^+e^-} = (8.1\pm 1.1\pm 0.5) \rm eV$foronesolution;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 a charged charmoniumlike structure at $4.05\mathrm{G}\mathrm{e}\mathrm{V}\mathrm{/}{c}^2$ is observed in the ${\pi }^{\pm }\psi (2S)$ intermediate state in the $Y(4360)$ decays.