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We report on the investigation of the rare decay$\eta\rightarrow\pi^0+\text{e}^++\text{e}^-$ which is of interest to study both$C$ violation in the electromagnetic interaction and to search forcontributions from physics beyond the Standard Model, since the allowed decayvia a two-photon intermediate state is strongly suppressed. The experiment hasbeen performed using the WASA-at-COSY installation, located at the COSYaccelerator of the Forschungszentrum J\"ulich, Germany. In total $3\times10^7$events of the reaction $\text{p}+\text{d}\rightarrow{^3\text{He}}+\eta$ havebeen recorded at an excess energy of $Q = 59.8\,\textrm{MeV}$. Based on thisdata set the $C$ parity violating decay$\eta\rightarrow\pi^0+\gamma^*\rightarrow\pi^0+\textrm{e}^++\textrm{e}^-$ via asingle-photon intermediate state has been searched for, resulting in new upperlimits of $\Gamma\left(\eta\rightarrow\pi^0+\textrm{e}^++\textrm{e}^-\right)/\Gamma\left(\eta\rightarrow\pi^++\pi^-+\pi^0\right) < 3.28\times10^{-5}$ and$\Gamma\left(\eta\rightarrow\pi^0+\textrm{e}^++\textrm{e}^-\right)/\Gamma\left(\eta\rightarrow\textrm{all}\right) < 7.5\times10^{-6}\ (\textrm{CL}= 90\,\%)$, respectively.

Search for $C$ violation in the decay $\eta\rightarrow\pi^0+e^++e^-$ with WASA-at-COSY