Improved measurements of the Dalitz decays $\eta /{\eta }^{\prime }\to \gamma {e}^{+}{e}^{-}$

Based on a data sample of 10 billion $J/\psi $ events collected with the BESIII detector, improved measurements of the Dalitz decays $\eta /{\eta }^{\prime }\to \gamma {e}^{+}{e}^{-}$ are performed, where the $\eta $ and ${\eta }^{\prime }$ are produced through the radiative decays $J/\psi \to \gamma \eta /{\eta }^{\prime }$. The branching fractions of $\eta \to \gamma {e}^{+}{e}^{-}$ and ${\eta }^{\prime }\to \gamma {e}^{+}{e}^{-}$ are measured to be $\left(7.07±0.05±0.23\right)×{10}^{-3}$ and $\left(4.83±0.07±0.14\right)×{10}^{-4}$, respectively. Within the single-pole model, the parameter of electromagnetic transition form factor for $\eta \to \gamma {e}^{+}{e}^{-}$ is determined to be ${\Lambda }_{\eta }=\left(0.749±0.027±0.007\right)\text{}\text{}\mathrm{GeV}/{c}^{2}$. Within the multipole model, we extract the electromagnetic transition form factors for ${\eta }^{\prime }\to \gamma {e}^{+}{e}^{-}$ to be ${\Lambda }_{{\eta }^{\prime }}=\left(0.802±0.007±0.008\right)\text{}\text{}\mathrm{GeV}/{c}^{2}$ and ${\gamma }_{{\eta }^{\prime }}=\left(0.113±0.010±0.002\right)\text{}\text{}\mathrm{GeV}/{c}^{2}$. The results are consistent with both theoretical predictions and previous measurements. The characteristic sizes of the interaction regions for the $\eta $ and ${\eta }^{\prime }$ are calculated to be $\left(0.645±0.023±0.007\right)\text{}\text{}\mathrm{fm}$ and $\left(0.596±0.005±0.006\right)\text{}\text{}\mathrm{fm}$, respectively. In addition, we search for the dark photon in $\eta /{\eta }^{\prime }\to \gamma {e}^{+}{e}^{-}$, and the upper limits of the branching fractions as a function of the dark photon are given at 90% confidence level.