Measurement of Prominent $\eta$-Decay Branching Fractions

The decay $\psi (2S)\to \eta J/\psi$ is used to measure, for the first time, all prominent $\eta$-meson branching fractions with the same experiment in the same dataset, thereby providing a consistent treatment of systematics across branching fractions. We present results for $\eta$ decays to $\gamma \gamma$, ${\pi }^{+}{\pi }^{-}{\pi }^0$, $3{\pi }^0$, ${\pi }^{+}{\pi }^{-}\gamma$ and $e^{+}{e}^{-}\gamma$, accounting for 99.9% of all $\eta$ decays. The precision of several of the branching fractions and their ratios is improved. Two channels, ${\pi }^{+}{\pi }^{-}\gamma$ and $e^{+}{e}^{-}\gamma$, show results that differ at the level of three standard deviations from those previously determined.

Figure 1

Top to bottom: $\gamma \gamma$, $3{\pi }^0$, ${\pi }^{+}{\pi }^{-}{\pi }^0$, ${\pi }^{+}{\pi }^{-}\gamma$, $e^{+}{e}^{-}\gamma$. For each channel, left to right: Goodness-of-fit for $J/\psi$ vertex and mass fit, and for $\psi (2S)$ vertex and mass fit. Points: data. Dotted line: Signal MC predictions. Solid line: Sum of all MC predictions. Arrows indicate selection requirements. Cuts have been applied to all quantities with the exception of the one plotted.

Figure 2

Distributions for individual channels. Top row: $3{\pi }^0$, highest and lowest photon energies. Second row: ${\pi }^{+}{\pi }^{-}{\pi }^0$, kinematic distribution of the three pions, and two-photon invariant mass; $y$ is a function of the kinetic energy of the ${\pi }^0$ ($T_0$) and the sum of the kinetic energies of all pions ($Q$): $y=(3T_0/Q)-1$. Third row: ${\pi }^{+}{\pi }^{-}\gamma$, invariant mass of the two pions and photon energy. Fourth row: $e^{+}{e}^{-}\gamma$, invariant mass of the two electrons on different horizontal and vertical scales. Symbols as in Fig. 1.

Figure 3

Top to bottom: $\gamma \gamma$, $3{\pi }^0$, ${\pi }^{+}{\pi }^{-}{\pi }^0$, ${\pi }^{+}{\pi }^{-}\gamma$, $e^{+}{e}^{-}\gamma$. For each channel, left to right: $J/\psi$ momentum, $\eta$ mass, polar angle of the positive lepton from the $J/\psi$ decay, and polar angle of an $\eta$ decay product (most energetic shower for $\gamma \gamma$ and $3{\pi }^0$, positive track for ${\pi }^{+}{\pi }^{-}{\pi }^0$, ${\pi }^{+}{\pi }^{-}\gamma$, and $e^{+}{e}^{-}\gamma$). Symbols as in Fig. 1.

Figure 4

Comparison of the results obtained in this analysis with the most precise measurements from other experiments [2, 14] (top) and the PDG 2006 global fits [2].