Measurement of the branching fractions for $J/\psi \to \gamma {\pi }^0$, $\gamma \eta$ and $\gamma {\eta }^{\prime }$

The decay modes $J/\psi \to \gamma {\pi }^0$, $\gamma \eta$ and $\gamma {\eta }^{\prime }$ are analyzed using a data sample of $58\times {10}^6$ $J/\psi$ decays collected with the BESII detector at the BEPC. The branching fractions are determined to be: $Br(J/\psi \to \gamma {\pi }^0)=({3.13}_{-0.47}^{+0.65})\times {10}^{-5}$, $Br(J/\psi \to \gamma \eta )=(11.23\pm 0.89)\times {10}^{-4}$, and $Br(J/\psi \to \gamma {\eta }^{\prime })=(5.55\pm 0.44)\times {10}^{-3}$, where the errors are combined statistical and systematic errors. The ratio of partial widths $\Gamma (J/\psi \to \gamma {\eta }^{\prime })/\Gamma (J/\psi \to \gamma \eta )$ is measured to be $4.94\pm 0.40$, and the singlet-octet pseudoscalar mixing angle of $\eta -{\eta }^{\prime }$ system is determined.

Figure 1

Distribution of (a) $\cos {\theta }_v$ and (b) ${\theta }_{\min }$. The open histograms are $J/\psi$ data, the shaded histograms are background from $e^{+}{e}^{-}\to \gamma \gamma (\gamma )$, and the dashed lines are simulated $J/\psi \to \gamma {\pi }^0\to \gamma \gamma \gamma$ events (not normalized).

Figure 2

Invariant mass distribution of the $\gamma \gamma$ with the smallest opening angle for $J/\psi \to \gamma \gamma \gamma$ candidate events. The solid squares with error bars are data, the histogram is the best fit described in the text, and the dashed line is the background.

Figure 3

The invariant mass distribution of $\gamma \gamma$ pairs with the smallest opening angle in $J/\psi \to \gamma \gamma \gamma$ events selected from the four-photon event sample.

Figure 4

Invariant mass distribution of the $\gamma \gamma$ with the smallest opening angle of $J/\psi \to \gamma \gamma \gamma$ candidates. Solid squares with error bars are data, the histogram is the fit result, and the dashed line is the background.

Figure 5

The $\gamma \gamma$ invariant mass distribution for $J/\psi \to \gamma \gamma \gamma$ candidate events (three entries per event). The solid squares with error bars indicate data, the histogram is the fit result, and the dashed line is the non-combinatorial background.

Figure 6

Scatter-plot of $M_{\gamma \gamma }$ versus $M_{\gamma \gamma {\pi }^{+}{\pi }^{-}}$ for the $J/\psi \to \gamma \gamma \gamma {\pi }^{+}{\pi }^{-}$ candidates.

Figure 7

The $\gamma \gamma {\pi }^{+}{\pi }^{-}$ invariant mass distribution for $J/\psi \to \gamma \gamma \gamma {\pi }^{+}{\pi }^{-}$ candidates that satisfy the requirement $M_{\gamma \gamma }\in [0.088,0.182]\mathrm{GeV}/c^2$. The solid squares with error bars indicate the data, the histogram is the fit result, and the dashed line is the background.

Figure 8

The $\gamma \gamma {\pi }^{+}{\pi }^{-}$ invariant mass distribution for events with $\gamma \gamma$ mass in the $\eta$ mass region ($M_{\gamma \gamma }\in [0.484,0.612]\mathrm{GeV}/c^2$). The solid squares with error bars are data, the histogram is the fit result, and the dashed line is the background.

Figure 9

The $\gamma {\pi }^{+}{\pi }^{-}$ invariant mass distribution for selected $J/\psi \to \gamma \gamma {\pi }^{+}{\pi }^{-}$ events. The solid squares with error bars are data, the histogram is the fit result, and the dashed line is the background.

Figure 10

Comparisons of (a) $Br(J/\psi \to \gamma {\pi }^0)$, (b) $Br(J/\psi \to \gamma \eta )$, and (c) $Br(J/\psi \to \gamma {\eta }^{\prime })$ between BESII and previous measurements [12]. The shaded regions are the world averages from the PDG [12].