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

Abstract: Using a sample of about 10 billion $J/\psi$ events collected at a center-of-mass energy $\sqrt s = 3.097$ GeV with the BESIII detector, the electromagnetic 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 $J/\psi\to e^+e^-X(1835)$ is presented for the first time. The intermediate states $X(2120)$ and $X(2370)$ are also observed in the $\pi^+ \pi^- \eta'$ invariant mass spectrum with significances of $5.3\sigma$ and $7.3\sigma$. The corresponding product branching fractions for $J/\psi\to e^+e^-X$, $X\to\pi^+\pi^-\eta'$ $(X=X(1835), X(2120)$ and $X(2370))$, are reported.