Study of the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\eta$ using initial state radiation

We study the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\eta \gamma$, where the photon is radiated from the initial state. About 8000 fully reconstructed events of this process are selected from the BABAR data sample with an integrated luminosity of $469{\mathrm{fb}}^{-1}$. Using the ${\pi }^{+}{\pi }^{-}\eta$ invariant mass spectrum, we measure the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\eta$ cross section in the $e^{+}{e}^{-}$ center-of-mass energy range from 1.15 to 3.5 GeV. The cross section is well described by the Vector-Meson dominance model with four $\rho$-like states. We observe $49\pm 9$ events of the $J/\psi$ decay to ${\pi }^{+}{\pi }^{-}\eta$ and measure the product ${\mathrm{\Gamma }}_{J/\mathrm{\Psi }\to e^{+}{e}^{-}}{\mathcal{B}}_{J/\mathrm{\Psi }\to {\pi }^{+}{\pi }^{-}\eta }=2.34\pm 0.43_{\mathrm{stat}}\pm 0.16_{\mathrm{syst}}\mathrm{eV}$.

Figure 1

The Feynman diagram for the process $e^{+}{e}^{-}\to {\gamma }_{\mathrm{ISR}}{\pi }^{+}{\pi }^{-}\gamma \gamma$ via the $\rho \eta$ intermediate state in the Vector-Meson dominance model.

Figure 2

The distributions of ${\chi }_{4\mathrm{C}}^2$ for events from the invariant mass ranges $1.15<m_{{\pi }^{+}{\pi }^{-}\eta }<200\mathrm{GeV}/c^2$ (a) and $2.0<m_{{\pi }^{+}{\pi }^{-}\eta }<3.5\mathrm{GeV}/c^2$ (b). The points with error bars are data. The open histogram represents the sum of the simulated distributions for signal and backgrounds events. The shaded histogram represents non-ISR background, while the hatched area shows ISR background.

Figure 3

The distribution of $m_{2\gamma }^{{\pi }^0}$ for region I (a) and for region II (b). The points with error bars are data. The open histogram represents signal simulation, the shaded and hatched areas shows simulated non-ISR and ISR background contributions, respectively.

Figure 4

The distributions of the invariant mass for all combinations of the ISR-photon candidate with any other photon in an event in $e^{+}{e}^{-}\to q\overline{q}$ simulation (a) and data (b). The curves are the results of the fits described in the text.

Figure 5

The two-photon invariant mass distribution for events from region I (a), and region II (b) after all selections. The points with error bars represent data. The histograms cumulatively show simulated contributions for peaking background (shaded), nonpeaking background (hatched), and signal $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\eta \gamma$ events (open).

Figure 6

The two-photon invariant mass spectrum for data events (points with error bars) from the three $m_{{\pi }^{+}{\pi }^{-}\eta }$ intervals: $1.300–1.325\mathrm{GeV}/c^2$ (a), $1.500–1.525\mathrm{GeV}/c^2$ (b), and $3.4–3.5\mathrm{GeV}/c^2$ (c). The solid curve is the result of the fit described in the text. The dashed curve represents the fitted background.

Figure 7

The measured ${\pi }^{+}{\pi }^{-}\eta$ invariant mass spectrum (solid circles). The open circles show the same distribution for the peaking background obtained using MC simulation.

Figure 8

The two-pion invariant mass distribution for data (points with error bars) and simulated (histogram) events from the mass range $1.4<m_{{\pi }^{+}{\pi }^{-}\eta }<2.0\mathrm{GeV}/c^2$.

Figure 9

The $\cos {\theta }_{\eta }$ distribution for data (points with error bars) and simulated (histogram) events from the mass range $1.4<m_{{\pi }^{+}{\pi }^{-}\eta }<2.0\mathrm{GeV}/c^2$. The curve is the result of the fit described in the text.

Figure 10

The detection efficiency ${ϵ}_{\mathrm{MC}}$ obtained using MC simulation as a function of $E_{\mathrm{c}.\mathrm{m}.}$ The lines are fits to a fourth-order polynomial for $E_{\mathrm{c}.\mathrm{m}.}<2\mathrm{GeV}$ and to a constant for $E_{\mathrm{c}.\mathrm{m}.}>2\mathrm{GeV}$.

Figure 11

The $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\eta$ cross section measured in this work (BABAR) in comparison with most precise previous measurements: CMD-2 [9], the independent BABAR (2007) [12], SND [11]) at $E_{\mathrm{c}.\mathrm{m}.}<2.15\mathrm{GeV}$ (a) and $E_{\mathrm{c}.\mathrm{m}.}>1.9\mathrm{GeV}$ (b).

Figure 12

The measured $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\eta$ cross section fitted with the four models described in the text.

Figure 13

(a) The fit to the ${\pi }^{+}{\pi }^{-}\eta$ mass spectrum for data events from the $J/\psi$ region. (b) The $m_{{\pi }^{+}{\pi }^{-}}$ invariant mass distribution for data events with $3.05<m_{{\pi }^{+}{\pi }^{-}\eta }<3.15\mathrm{GeV}/{\mathrm{c}}^2$ (points with error bars) and simulated signal events generated using the model with the $\rho (770)\eta$ intermediate state (histogram).