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Using a sample of about 10 billion $J/\psi$ events collected at acenter-of-mass energy $\sqrt s = 3.097$ GeV with the BESIII detector, theelectromagnetic Dalitz decays $J/\psi \to e^+e^- \pi^+ \pi^- \eta'$, with$\eta'\to\gamma\pi^+ \pi^-$ and $\eta'\to\pi^+\pi^-\eta$, have been studied.The decay $J/\psi \to e^+ e^- X(1835)$ is observed with a significance of$15\sigma$, and the transition form factor of $J/\psi\to e^+e^-X(1835)$ ispresented for the first time. The intermediate states $X(2120)$ and $X(2370)$are also observed in the $\pi^+ \pi^- \eta'$ invariant mass spectrum withsignificances of $5.3\sigma$ and $7.3\sigma$. The corresponding productbranching fractions for $J/\psi\to e^+e^-X$, $X\to\pi^+\pi^-\eta'$ $(X=X(1835),X(2120)$ and $X(2370))$, are reported.

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