Observation of the Electromagnetic Dalitz Transition $h_c \rightarrow e^+e^-η_c$

Using $(27.12\pm 0.14)\times10^8$ $ψ(3686)$ decays and data samples of $e^+e^-$ collisions with $\sqrt{s}$ from 4.130 to 4.780~GeV collected with the BESIII detector, we report the first observation of the electromagnetic Dalitz transition $h_c\to e^+e^-η_c$ with a statistical significance of $5.4σ$. We measure the ratio of the branching fractions $\frac{\mathcal{B}(h_c\rightarrow e^+e^-η_c)}{\mathcal{B}(h_c\rightarrow γη_c)}$ separately for the $h_c$ samples produced via $ψ(3686)\toπ^0h_c$ and $e^+e^-\toπ^+π^-h_c$. The average ratio is determined to be $(0.59\pm0.10(\text{stat.})\pm0.04(\text{syst.}))\%$, where the uncertainty includes both statistical and systematic components.