Evidence for ${\eta }_c\to \gamma \gamma$ and measurement of $J/\psi \to 3\gamma$

The decay of $J/\psi$ to three photons is studied using $\psi (3686)\to {\pi }^{+}{\pi }^{-}J/\psi$ in a sample of $1.0641\times {10}^8$ $\psi (3686)$ events collected with the BESIII detector. Evidence of the direct decay of ${\eta }_c$ to two photons, ${\eta }_c\to \gamma \gamma$, is reported, and the product branching fraction is determined to be $\mathcal{B}(J/\psi \to \gamma {\eta }_c,{\eta }_c\to \gamma \gamma )=(4.5\pm 1.2\pm 0.6)\times {10}^{-6}$, where the first error is statistical and the second is systematic. The branching fraction for $J/\psi \to 3\gamma$ is measured to be $(11.3\pm 1.8\pm 2.0)\times {10}^{-6}$ with improved precision.

Figure 1

Scatter plots of $M(\gamma \gamma {)}_{\lg }$ versus $M(\gamma \gamma {)}_{\mathrm{sm}}$ for data before (c) and after (e) removal of backgrounds from $J/\psi \to \gamma {\pi }^0/\eta /{\eta }^{\prime }$ and MC simulations of the processes (a) $J/\psi \to \gamma {\pi }^0/\eta /{\eta }^{\prime }\to 3\gamma$, (b) $J/\psi \to \gamma f_2(1270)\to \gamma (\gamma \gamma {)}_{{\pi }^0}(\gamma \gamma {)}_{{\pi }^0}$, (d) $J/\psi \to 3\gamma$, and (f) $J/\psi \to \gamma {\eta }_c\to 3\gamma$. The vertical lines indicate the mass windows to reject ${\pi }^0$, $\eta$ and ${\eta }^{\prime }$.

Figure 2

The ${\pi }^0{\pi }^0$ invariant mass spectrum (left) and the angular distribution of the ${\pi }^0$ in the laboratory frame (right) for the $\psi (3686)\to {\pi }^{+}{\pi }^{-}J/\psi$, $J/\psi \to \gamma {\pi }^0{\pi }^0$ control sample, for data (points with error bars) and PWA results (solid line).

Figure 3

Projection of the two-dimensional fit to ${\chi }_{4\mathrm{C}}^2$ (left) and $M(\gamma \gamma {)}_{\lg }$ (right) for data (points with error bars) and the fit results (thick solid line). The (dark red) dotted-dashed, (red) dashed and (blue) dotted lines show contributions from $J/\psi \to 3\gamma$, $J/\psi \to \gamma {\eta }_c\to 3\gamma$, and $J/\psi \to \gamma {\pi }^0{\pi }^0$, respectively. The stacked histogram represents the backgrounds from $J/\psi \to \gamma {\pi }^0/\eta /{\eta }^{\prime }$ (light shaded and green) and non-$J/\psi$ decays (dark shaded and violet).

Figure 4

The ${\pi }^{+}{\pi }^{-}$ recoil mass spectrum $M({\pi }^{+}{\pi }^{-}{)}_{\mathrm{recoil}}$ from the control channel $\psi (3686)\to {\pi }^{+}{\pi }^{-}J/\psi$, $J/\psi \to \gamma (\gamma \gamma {)}_{\eta }$ for data (points with error bars) and MC simulation (dashed histogram). The event selection is the same as for $J/\psi \to 3\gamma$ but with the requirement that the $\gamma \gamma$ mass $M(\gamma \gamma )$ has to lie within $[0.5,0.6]\mathrm{GeV}/{\mathrm{c}}^2$. For comparison, a simulation of $J/\psi \to \gamma (\gamma \gamma {)}_{\eta }$ is shown (solid histogram) with the area scaled to that of the full $\psi (3686)$ decay chain simulation. The arrows indicate the signal region for selection of $J/\psi$ events.

Figure 5

The energy spectrum of $J/\psi \to 3\gamma$ inclusive photons in the $J/\psi$ rest frame. The points with error bars represent the partial branching fractions as a function of the ratio $2E_{\gamma }/M_{J/\psi }$ measured in data. Here, $E_{\gamma }$ is the photon energy and $M_{J/\psi }$ is the $J/\psi$ mass. The solid line shows the theoretical calculation according to the orthopositronium decay formula [20].