Using a sample of $(225.2\pm 2.8)\times {10}^6$ $J/\psi$ events collected with the Beijing Spectrometer at the Beijing Electron-Positron Collider, $CP$ and $P$ violating decays of $\eta$, ${\eta }^{\prime }$, and ${\eta }_c$ into ${\pi }^{+}{\pi }^{-}$ and ${\pi }^0{\pi }^0$ are searched for in $J/\psi$ radiative decays. No significant $\eta$, ${\eta }^{\prime }$, or ${\eta }_c$ signal is observed, and $90\%$ confidence level upper limits of $\mathcal{B}(\eta \to {\pi }^{+}{\pi }^{-})<3.9\times {10}^{-4}$, $\mathcal{B}({\eta }^{\prime }\to {\pi }^{+}{\pi }^{-})<5.5\times {10}^{-5}$, $\mathcal{B}({\eta }_c\to {\pi }^{+}{\pi }^{-})<1.3\times {10}^{-4}$, $\mathcal{B}(\eta \to {\pi }^0{\pi }^0)<6.9\times {10}^{-4}$, $\mathcal{B}({\eta }^{\prime }\to {\pi }^0{\pi }^0)<4.5\times {10}^{-4}$, and $\mathcal{B}({\eta }_c\to {\pi }^0{\pi }^0)<4.2\times {10}^{-5}$ are obtained.

• Received 25 June 2011

DOI:https://doi.org/10.1103/PhysRevD.84.032006