Observation of $J/\psi $ Electromagnetic Dalitz Decays to $X\left(1835\right)$, $X\left(2120\right)$, and $X\left(2370\right)$

Using a sample of about ${10}^{10}\text{}\text{}J/\psi $ events collected at a center-of-mass energy $\sqrt{s}=3.097\text{}\text{}\mathrm{GeV}$ with the BESIII detector, the electromagnetic Dalitz decays $J/\psi \to {e}^{+}{e}^{-}{\pi }^{+}{\pi }^{-}{\eta }^{\prime }$, with ${\eta }^{\prime }\to \gamma {\pi }^{+}{\pi }^{-}$ and ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\eta $, have been studied. The decay $J/\psi \to {e}^{+}{e}^{-}X\left(1835\right)$ is observed with a significance of $15\sigma $, and also an ${e}^{+}{e}^{-}$ invariant-mass dependent transition form factor of $J/\psi \to {e}^{+}{e}^{-}X\left(1835\right)$ is presented for the first time. The intermediate states $X\left(2120\right)$ and $X\left(2370\right)$ are also observed in the ${\pi }^{+}{\pi }^{-}{\eta }^{\prime }$ invariant-mass spectrum with significances of $5.3\sigma $ and $7.3\sigma $. The corresponding product branching fractions for $J/\psi \to {e}^{+}{e}^{-}X$, $X\to {\pi }^{+}{\pi }^{-}{\eta }^{\prime }$ [$X=X\left(1835\right)$, $X\left(2120\right)$, and $X\left(2370\right)\right]$ are reported.