Measurement of the branching fraction of and search for a $CP$-violating asymmetry in ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$ at BESIII

The rare decay ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$ is studied using a sample of $1.3×{10}^{9}\text{}\text{}J/\psi $ events collected with the BESIII detector at BEPCII in 2009 and 2012. The branching fraction is measured with improved precision to be $\left(2.42±0.0{5}_{\mathrm{stat}}±0.0{8}_{\mathrm{syst}}\right)×{10}^{-3}$. Due to the inclusion of new data, this result supersedes the last BESIII result on this branching fraction. In addition, the $CP$-violating asymmetry in the angle between the decay planes of the ${\pi }^{+}{\pi }^{-}$-pair and the ${e}^{+}{e}^{-}$-pair is investigated. A measurable value would indicate physics beyond the standard model; the result is ${A}_{CP}=\left(2.9±3.{7}_{\mathrm{stat}}±1.{1}_{\mathrm{syst}}\right)%$, which is consistent with the standard model expectation of no $CP$-violation. The precision is comparable to the asymmetry measurement in the ${K}_{L}^{0}\to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$ decay where the observed $\left(14±2\right)%$ effect is driven by a standard model mechanism.