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 GeV, based on an analysis of initial state radiation events in a $980{\mathrm{fb}}^{-1}$ 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: $M_{Y(4360)}=(4347\pm 6\pm 3)\mathrm{MeV}/c^2$, ${\mathrm{\Gamma }}_{Y(4360)}=(103\pm 9\pm 5)\mathrm{MeV}$, $M_{Y(4660)}=(4652\pm 10\pm 8)\mathrm{MeV}/c^2$, ${\mathrm{\Gamma }}_{Y(4660)}=(68\pm 11\pm 1)\mathrm{MeV}$; and $\mathcal{B}[Y(4360)\to {\pi }^{+}{\pi }^{-}\psi (2S)]·{\mathrm{\Gamma }}_{Y(4360)}^{e^{+}{e}^{-}}=(10.9\pm 0.6\pm 0.7)\mathrm{eV}$ and $\mathcal{B}[Y(4660)\to {\pi }^{+}{\pi }^{-}\psi (2S)]·{\mathrm{\Gamma }}_{Y(4660)}^{e^{+}{e}^{-}}=(8.1\pm 1.1\pm 0.5)\mathrm{eV}$ for one solution; or $\mathcal{B}[Y(4360)\to {\pi }^{+}{\pi }^{-}\psi (2S)]·{\mathrm{\Gamma }}_{Y(4360)}^{e^{+}{e}^{-}}=(9.2\pm 0.6\pm 0.6)\mathrm{eV}$ and $\mathcal{B}[Y(4660)\to {\pi }^{+}{\pi }^{-}\psi (2S)]·{\mathrm{\Gamma }}_{Y(4660)}^{e^{+}{e}^{-}}=(2.0\pm 0.3\pm 0.2)\mathrm{eV}$ for the other. Here, the first errors are statistical and the second systematic. Evidence for a charged charmoniumlike structure at $4.05\mathrm{GeV}/c^2$ is observed in the ${\pi }^{\pm }\psi (2S)$ intermediate state in the $Y(4360)$ decays.

Figure 1

Invariant-mass distributions of the candidate $\psi (2S)$ signals in (a) the ${\pi }^{+}{\pi }^{-}J/\psi$ mode and (b) the ${\mu }^{+}{\mu }^{-}$ mode. Dots with error bars are data and the curves are the best fits.

Figure 2

The ISR characteristics of the selected events. The first row is for the ${\pi }^{+}{\pi }^{-}J/\psi$ mode and the second for the ${\mu }^{+}{\mu }^{-}$ mode. Panels (a) and (d) show the square of the mass recoiling against the ${\pi }^{+}{\pi }^{-}\psi (2S)$ system; (b) and (e) show the visible energy in the detector; (c) and (f) show the polar-angle distribution of the ${\pi }^{+}{\pi }^{-}\psi (2S)$ system in the $e^{+}{e}^{-}$ center-of-mass frame. Points with error bars (histograms) represent the data (MC simulation, described in Sec. 1). The backgrounds, estimated from the normalized $\psi (2S)$ mass sidebands, have been subtracted from the distributions.

Figure 3

Invariant mass of the ${\pi }^{+}{\pi }^{-}$ recoiling against the $\psi (2S)$ versus the invariant mass of the ${\pi }^{+}{\pi }^{-}\psi (2S)$ in the ${\pi }^{+}{\pi }^{-}J/\psi$ mode (a) and ${\mu }^{+}{\mu }^{-}$ mode (b). The horizontal dashed lines show the belt of $f_0(980)$, while the vertical solid lines demarcate the regions with the $Y(4360)$ and $Y(4660)$ states and the higher-mass combinations.

Figure 4

Invariant-mass distributions of ${\pi }^{+}{\pi }^{-}$ from $Y(4360)$ and $Y(4660)$ decays in the ${\pi }^{+}{\pi }^{-}J/\psi$ mode. Points with error bars (open histograms) represent the data (MC simulation, described in Sec. 1); the shaded histograms represent the background estimated from the scaled sidebands. Panel (a) is for the events in the region $4.0\mathrm{GeV}/c^2<M_{{\pi }^{+}{\pi }^{-}\psi (2S)}<5.5\mathrm{GeV}/c^2$, (b) for events in the $Y(4360)$ region (4.0 to $4.5\mathrm{GeV}/c^2$), and (c) for the events in $Y(4660)$ region (4.5 to $5.5\mathrm{GeV}/c^2$).

Figure 5

Angular distributions of $\pi$ in the ${\pi }^{+}{\pi }^{-}$ system in ${\pi }^{+}{\pi }^{-}J/\psi$ mode. Panel (a) is for the events in the region $4.0\mathrm{GeV}/c^2<M_{{\pi }^{+}{\pi }^{-}\psi (2S)}<5.5\mathrm{GeV}/c^2$, (b) for events in the $Y(4360)$ region (4.0 to $4.5\mathrm{GeV}/c^2$), and (c) for the events in $Y(4660)$ region (4.5 to $4.9\mathrm{GeV}/c^2$). The dots with error bars are data and the histograms are from MC simulation.

Figure 6

Angular distributions of the ${\pi }^{+}{\pi }^{-}$ in ${\pi }^{+}{\pi }^{-}\psi (2S)$ system in the ${\pi }^{+}{\pi }^{-}J/\psi$ mode. Panel (a) is for the events in the region $4.0\mathrm{GeV}/c^2<M_{{\pi }^{+}{\pi }^{-}\psi (2S)}<5.5\mathrm{GeV}/c^2$, (b) for events in the $Y(4360)$ region (4.0 to $4.5\mathrm{GeV}/c^2$), and (c) for the events in $Y(4660)$ region (4.5 to $4.9\mathrm{GeV}/c^2$). The dots with error bars are data, while the histograms are MC simulation.

Figure 7

The effective luminosity of ISR production with the full data sample.

Figure 8

The efficiency curves and the fit to third-order polynomials. Plot (a) is ${\pi }^{+}{\pi }^{-}J/\psi$ mode, and (b) is ${\mu }^{+}{\mu }^{-}$ mode.

Figure 9

The ${\pi }^{+}{\pi }^{-}\psi (2S)$ invariant-mass distributions and the simultaneous fit results described in the text. From left to right: (a) the ${\pi }^{+}{\pi }^{-}J/\psi$ mode, (b) the ${\mu }^{+}{\mu }^{-}$ mode, and (c) the sum. The points with error bars show the data while the shaded histograms are the scaled sideband backgrounds. The solid red curves show the best fits; the dashed curves, which are from the two fit solutions, show the contributions from the two Breit-Wigner components (described in the text). The interference between the two resonances is not shown.

Figure 10

The four solutions from the fit to the ${\pi }^{+}{\pi }^{-}\psi (2S)$ invariant-mass spectra with the $Y(4260)$ included. The curves show the best fit and the dashed curves show the contributions from the three Breit-Wigner components.

Figure 11

The measured $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\psi (2S)$ cross section for $\sqrt{s}=4.0$ to 5.5 GeV. The errors are the sum in quadrature of the summed statistical errors of the numbers of signal and background events and the systematic errors.

Figure 12

The scatter plots of $M_{{\pi }^{-}\psi (2S)}$ versus $M_{{\pi }^{+}\psi (2S)}$ for the $Y(4360)$-subsample events in (a) the ${\pi }^{+}{\pi }^{-}J/\psi$ mode and (b) the ${\mu }^{+}{\mu }^{-}$ mode. Panels (c) and (d) show the sum of the $M_{{\pi }^{+}\psi (2S)}$ and $M_{{\pi }^{-}\psi (2S)}$ distributions in the ${\pi }^{+}{\pi }^{-}J/\psi$ and ${\mu }^{+}{\mu }^{-}$ modes, respectively. The shaded histograms are the backgrounds from the normalized $\psi (2S)$ mass sidebands.

Figure 13

The distribution of $M_{\max }({\pi }^{\pm }\psi (2S))$ from $Y(4360)$-subsample decays. The points with error bars represent the data; the histogram is from the sidebands and normalized to the signal region; the solid curve is the best fit and the dashed curve is the signal parametrized by a Breit-Wigner function.

Figure 14

The scatter plots of $M_{{\pi }^{-}\psi (2S)}$ versus $M_{{\pi }^{+}\psi (2S)}$ for the $Y(4660)$ events in the (a) ${\pi }^{+}{\pi }^{-}J/\psi$ mode and (b) the ${\mu }^{+}{\mu }^{-}$ mode. Panels (c) and (d) show the sum of the $M_{{\pi }^{+}\psi (2S)}$ and $M_{{\pi }^{-}\psi (2S)}$ distributions in the ${\pi }^{+}{\pi }^{-}J/\psi$ and ${\mu }^{+}{\mu }^{-}$ modes, respectively. The shaded histograms are the backgrounds from the normalized sidebands.

Figure 15

The ${\pi }^{+}{\pi }^{-}\psi (2S)$ invariant-mass distributions and the fit results for the ${\pi }^{+}{\pi }^{-}J/\psi$ mode only. The details of the plot are the same as those in Fig. 9.

Figure 16

The four solutions from the fit to the ${\pi }^{+}{\pi }^{-}\psi (2S)$ invariant-mass spectra with the $Y(4260)$ included but for the ${\pi }^{+}{\pi }^{-}J/\psi$ mode only. The details are the same as those in Fig. 10.