Study of the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0$ process using initial state radiation with BABAR

The process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0\gamma$ has been studied at a center-of-mass energy near the ${\rm Y}(4S)$ resonance using a $89.3{\mathrm{f}\mathrm{b}}^{-1}$ data sample collected with the BABAR detector at the PEP-II collider. From the measured $3\pi$ mass spectrum we have obtained the products of branching fractions for the $\omega$ and $\varphi$ mesons, $\mathcal{B}(\omega \to e^{+}{e}^{-})\mathcal{B}(\omega \to 3\pi )=(6.70\pm 0.06\pm 0.27)\times {10}^{-5}$ and $\mathcal{B}(\varphi \to e^{+}{e}^{-})\mathcal{B}(\varphi \to 3\pi )=(4.30\pm 0.08\pm 0.21)\times {10}^{-5}$ and evaluated the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0$ cross section for the $e^{+}{e}^{-}$ center-of-mass energy range 1.05 to 3.00 GeV. About 900 $e^{+}{e}^{-}\to J/\psi \gamma \to {\pi }^{+}{\pi }^{-}{\pi }^0\gamma$ events have been selected and the branching fraction $\mathcal{B}(J/\psi \to {\pi }^{+}{\pi }^{-}{\pi }^0)=(2.18\pm 0.19)\%$ has been measured.

Figure 1

The diagram for the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0\gamma$ process.

Figure 2

The ${\chi }^2$ distributions for data (points with error bars) and simulated (histogram) events from the $\omega$ mass region. The shaded histogram shows the distribution for simulated background events.

Figure 3

The ${\chi }^2$ distributions for data from the mass range $1.05<M_{3\pi }<3.00\mathrm{G}\mathrm{e}\mathrm{V}/{\mathrm{c}}^2$. The shaded histogram shows events rejected by background suppression cuts.

Figure 4

The ${\chi }^2$ distribution for events from the mass range $1.05<M_{3\pi }<3.00\mathrm{G}\mathrm{e}\mathrm{V}/{\mathrm{c}}^2$ after background suppression cuts. The points with error bars show the data distribution. The histogram is the sum of simulated distributions for $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0\gamma$ and background processes. The dark and lightly shaded histograms show the distributions for $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0{\pi }^0$ and other background processes, respectively.

Figure 5

The $3\pi$ mass spectrum for data events with ${\chi }^2<40$. The lightly shaded histogram shows the mass spectrum for calculated background. The dark histogram is $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0{\pi }^0$ background.

Figure 6

The $M_{3\pi }$ spectrum for events with $100<{\chi }^2<500$ and $E_{{\pi }^0}>1\mathrm{G}\mathrm{e}\mathrm{V}$. The points with error bars are data. The histogram is the sum of spectra for simulated events of $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0\gamma$ and background processes. The lightly shaded histogram is the sum of all background processes. The difference between the dark and lightly shaded histograms shows the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0{\pi }^0\gamma$ contribution.

Figure 7

${\pi }^{+}{\pi }^{-}$ invariant mass spectrum for events with $100<{\chi }^2<500$ and$0.85<M_{3\pi }<1.05\mathrm{G}\mathrm{e}\mathrm{V}/{\mathrm{c}}^2$. The points with error bars are data. The histogram is the sum of spectra for simulated events of $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0\gamma$ and background processes. The lightly shaded histogram is the sum of all background processes. The difference between the dark and lightly shaded histogram shows the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\gamma$ contribution.

Figure 8

The $3\pi$ mass spectrum for data obtained after the statistical background-subtraction procedure.

Figure 9

The $3\pi$ mass spectrum for background events obtained from the statistical background-subtraction procedure (points with error bars). The histogram shows the background mass distribution expected from MC simulation.

Figure 10

The $3\pi$ mass dependence of the detection efficiency obtained from MC simulation. The line is the fit to a second-order polynomial.

Figure 11

The $3\pi$ mass spectrum for events with $40<{\chi }^2<500$. Points with error bars show the data distribution. The solid line shows the sum of the distributions for simulated $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0\gamma$ and background processes. The shaded histogram shows the distribution for background processes.

Figure 12

The $3\pi$ mass distribution for events selected without using the photons from the ${\pi }^0$ decay that are reconstructed (left) and not reconstructed (right) with our standard kinematic fit procedure. Points with error bars show the data distribution. The solid line is a fit result. The shaded histogram is the fitted background contribution.

Figure 13

Distributions of the ISR photon energy (1st row) and polar angle (2nd row) for data (points with error bars) and simulation (solid line) events with ${\chi }^2<20$. The left and right columns correspond to the mass regions $0.75<M_{3\pi }<0.82\mathrm{G}\mathrm{e}\mathrm{V}/{\mathrm{c}}^2$ and $1.40<M_{3\pi }<1.80\mathrm{G}\mathrm{e}\mathrm{V}/{\mathrm{c}}^2$, respectively. Shaded histograms show the calculated background contributions.

Figure 14

Distributions of ${\pi }^0$ energy (1st row), charged-pion momentum (2nd row), and angle between the normal to the $3\pi$ plane in the three-pion rest frame and the direction of the $3\pi$ system in the laboratory frame (3rd row) for data (points with error bars) and simulation (solid line) events with ${\chi }^2<20$. The left and right columns correspond to the mass regions $0.75<M_{3\pi }<0.82\mathrm{G}\mathrm{e}\mathrm{V}/{\mathrm{c}}^2$ and $1.40<M_{3\pi }<1.80\mathrm{G}\mathrm{e}\mathrm{V}/{\mathrm{c}}^2$, respectively. Shaded histograms show the calculated background contributions.

Figure 15

Distributions of ${\pi }^{+}{\pi }^{-}$ (left column) and ${\pi }^{\pm }{\pi }^0$ (right column) invariant masses for data (points with error bars) and simulation (solid line) for events with ${\chi }^2<20$. The rows correspond to the mass regions: $0.75<M_{3\pi }<0.82\mathrm{G}\mathrm{e}\mathrm{V}/{\mathrm{c}}^2$ (1st row), $1.00<M_{3\pi }<1.04\mathrm{G}\mathrm{e}\mathrm{V}/{\mathrm{c}}^2$ (2nd row), $1.10<M_{3\pi }<1.40\mathrm{G}\mathrm{e}\mathrm{V}/{\mathrm{c}}^2$ (3rd row), and $1.40<M_{3\pi }<1.80\mathrm{G}\mathrm{e}\mathrm{V}/{\mathrm{c}}^2$ (4th row). Shaded histograms show the calculated background contributions.

Figure 16

The distribution of the difference between measured and true $3\pi$ mass for simulated events with ${\chi }^2<40$ from the mass region near the $\omega$. The curve is a fit to a triple-Gaussian function.

Figure 17

The background-subtracted $3\pi$ mass spectrum for masses between 0.70 and $1.05\mathrm{M}\mathrm{e}\mathrm{V}/{\mathrm{c}}^2$ (upper plot) and for masses from 1.05 to $1.80\mathrm{M}\mathrm{e}\mathrm{V}/{\mathrm{c}}^2$ (lower plot). The curves are the result of the fit described in the text.

Figure 18

The $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0$ cross section measured in this work (filled circles), by SND (open circles), and DM2 (open triangles).

Figure 19

$3\pi$ mass spectrum for selected $e^{+}{e}^{-}\to J/\psi \gamma \to {\pi }^{+}{\pi }^{-}{\pi }^0\gamma$ events.

Figure 20

The Dalitz plot for $J/\psi \to 3\pi$ candidates in data (left) and simulation (right).