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

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