Measurements of branching ratios for $\eta$ decays into charged particles

The WASA-at-COSY experiment has collected $3\times {10}^7$ events with $\eta$ mesons produced via the reaction $pd\to {}^3\mathrm{He}\eta$ at $\mathrm{T}=1.0\mathrm{GeV}$. Using this data set, we evaluate the branching ratios of the decays $\eta \to {\pi }^{+}{\pi }^{-}\gamma$, $\eta \to e^{+}{e}^{-}\gamma$, $\eta \to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$, and $\eta \to e^{+}{e}^{-}{e}^{+}{e}^{-}$. The branching ratios are normalized to the $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ decay. In addition an upper limit on a $CP$-violating asymmetry in $\eta \to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$ is extracted.

Figure 1

A cross-sectional scheme of the WASA detector with the beam coming from the left. Hadronic ejectiles are measured with the forward detector on the right while meson decay products are measured with the central detector on the left. Components are described in the text.

Figure 2

Initial spectrum of the ${}^3\mathrm{He}$ missing mass. The prominent peak is due to $\eta$ meson production, while the broad background distribution is from production of two and three $\pi$ mesons. The dashed (red) line shows a fit of the background (incorporating the shapes of double and triple $\pi$ meson production, as described in the text) and the inset shows the peak after background subtraction with the $\eta$ mass marked by the dotted (blue) line.

Figure 3

Time difference between the FD ${}^3\mathrm{He}$ track and a charged particle track in CD. The red lines indicate the applied selection.

Figure 4

Reconstructed vertex $z$ position for nonresonant ${\pi }^{+}{\pi }^{-}$ events. Simulations for $pd\to {}^3\mathrm{He}{\pi }^{+}{\pi }^{-}$ are shown in red.

Figure 5

Charge-signed momentum versus energy deposit in the (a) plastic scintillator barrel (PSB) and (b) calorimeter (SEC). The bands corresponding to $e^{+/-}$ and $\pi$ mesons are labeled.

Figure 6

Posterior probabilities for events passing the $\eta \to e^{+}{e}^{-}\gamma$ kinematic fit hypothesis showing the discrimination of $\pi$ mesons from electrons. The red and blue lines are simulations of $\eta \to e^{+}{e}^{-}\gamma$ and $\eta \to {\pi }^{+}{\pi }^{-}\gamma$ respectively and the shaded area is the sum of both simulations.

Figure 7

Condition on conversion suppression shown for (a) simulations and (b) data. For the simulations, the multicolored plot is for the $\eta \to e^{+}{e}^{-}\gamma$ signal while the red dots are for $\eta \to \gamma \gamma$ where a photon converts in the beam pipe. The demarcation lines shown in each plot are the same.

Figure 8

Missing mass of ${}^3\mathrm{He}$ for events passing the kinematic fit probability condition for the hypothesis $pd\to {}^3\mathrm{He}{\pi }^{+}{\pi }^{-}\gamma \gamma$. The background fit is described by a dashed line and is derived using the method described in the text.

Figure 9

${}^3\mathrm{He}$ missing mass distribution for events passing all selection conditions for $\eta \to e^{+}{e}^{-}\gamma$. The background fit is described by the dashed line.

Figure 10

The $\mathrm{MM}\left({}^3\mathrm{He}\right)$ distribution for events passing all selection conditions for the $\eta \to e^{+}{e}^{-}{e}^{+}{e}^{-}$ signal. The background coming from $\pi$-meson production is described by the horizontal red line. The region between the vertical dashed lines was excluded from the fit of the background.

Figure 11

Diagrams for triangle and box anomalies.

Figure 12

The experimental ${\mathrm{MM}}^2\left({}^3\mathrm{He}{\pi }^{+}{\pi }^{-}\right)$ distribution for the $pd\to {}^3\mathrm{He}\eta$ events after the kinematic fit probability cut for the $pd\to {}^3\mathrm{He}{\pi }^{+}{\pi }^{-}\gamma$ hypothesis (points) compared to MC of the $\eta \to {\pi }^{+}{\pi }^{-}\gamma$ (light shaded) signal and the $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ background (dark shaded). The red curve is the sum of the simulations. Kinematic variables used to obtain the distributions are not corrected by the kinematic fit.

Figure 13

The $\mathrm{MM}\left({}^3\mathrm{He}\right)$ distribution for events passing selection conditions for $\eta \to {\pi }^{+}{\pi }^{-}\gamma$. The function used to subtract the continuum background is shown as a dashed line.

Figure 14

Definition of the dihedral angle $\varphi$ for the $\eta \to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$ decay in the $\eta$ meson rest frame.

Figure 15

The $\mathrm{MM}\left({}^3\mathrm{He}\right)$ distribution for events passing the $\eta \to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$ selection criteria. The background fit is shown as a dashed line (red) and the shape of the peak from simulations of the $pd\to {}^3\mathrm{He}\eta$ events is shown as a dotted line (blue).

Figure 16

$sin\varphi cos\varphi$ distribution for the data and Monte Carlo simulation of the $\eta \to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$ with a flat $\varphi$ distribution.