Observation of ${\eta }^{\prime }$ Decays to ${\pi }^{+}{\pi }^{-}{\pi }^0$ and ${\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$

Using $\psi (2S)\to {\pi }^{+}{\pi }^{-}J/\psi$, $J/\psi \to \gamma {\eta }^{\prime }$ events acquired with the CLEO-c detector at the CESR $e^{+}{e}^{-}$ collider, we make the first observations of the decays ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}{\pi }^0$ and ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$, measuring absolute branching fractions $({37}_{-9}^{+11}\pm 4)\times {10}^{-4}$ and $({25}_{-9}^{+12}\pm 5)\times {10}^{-4}$, respectively. For ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}{\pi }^0$, this result probes the mechanism of isospin violation and the roles of ${\pi }^0/\eta /{\eta }^{\prime }$-mixing and final state rescattering in strong decays. We also set upper limits on branching fractions for ${\eta }^{\prime }$ decays to ${\pi }^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-}$, $2({\pi }^{+}{\pi }^{-})$, ${\pi }^{+}{\pi }^{-}2{\pi }^0$, $2({\pi }^{+}{\pi }^{-}){\pi }^0$, $3({\pi }^{+}{\pi }^{-})$, and invisible final states.

Figure 1

Distributions in $M({\eta }^{\prime })$ for (a) ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}{\pi }^0$ and (b) ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$. Solid circles represent data (nonzero bin entries only), the dashed histogram is the sum of a linear background normalized to the sideband populations in data and feedacross from ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\gamma$ normalized by branching fraction, the dotted histogram is the signal MC shape normalized to the observed signal level, and the solid line is the sum of dotted and dashed histograms. Solid (dashed) arrows indicate nominal signal (sideband) region boundaries; sidebands extend to the edges of the plots. All selection criteria are applied here except to $M({\eta }^{\prime })$.

Figure 2

Distributions in (a) the invariant mass of the two photons in the ${\pi }^0$ candidate in ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}{\pi }^0$; (b) Dalitz variables $y$ vs $|x|$ for ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}{\pi }^0$ (uncorrected for efficiency) for data, where box absence or size indicates 0, 1, or 2 events in each 0.1-by-0.1 bin, and (c) from a phase-space MC simulation, where bin shading indicates relative population; (d) the $e^{+}{e}^{-}$ invariant mass for ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$; (e) the ${\pi }^{+}{\pi }^{-}$ invariant mass for ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$. In (a), (d), and (e), solid circles represent the data, the dotted histogram is the MC signal shape normalized to the yields found in Table 1, and the solid line is the sum of MC signal and predicted ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\gamma$ feedacross. The region between the arrows indicates the selected region in (a) and an excluded region in (d). All selection criteria, including that upon $M({\eta }^{\prime })$, are applied here, except to $M(\gamma \gamma )$ in (a) and to $M(e^{+}{e}^{-})$ in (d). The quantities $x$ and $y$ are defined as $x\equiv \sqrt{3}(T_{+}-T_{-})/Q$, $y\equiv (3T_0/Q)-1$, $T_0$ ($T_{\pm }$) is the ${\pi }^0$ (${\pi }^{\pm }$) kinetic energy in the ${\eta }^{\prime }$ center of mass, and $Q\equiv T_0+T_{+}+T_{-}$.

Figure 3

Distribution of $E_{\gamma }^{*}$ (see text) for $J/\psi \to \gamma {\eta }^{\prime }$, ${\eta }^{\prime }\to \mathcal{I}$ candidate events. Solid circles represent data (nonzero bin entries only), the dashed histogram is the linear background normalized to the sideband populations in data, the dotted histogram is the signal MC shape normalized to the 90% C.L. upper limit, and the solid line is the sum of dotted and dashed histograms. Solid (dashed) arrows indicate nominal signal (sideband) region boundaries; sidebands extend to the edges of the plot. All selections are applied here except to $E_{\gamma }^{*}$.