Observation of the Electromagnetic Dalitz Transition $h_c\to e^{+}{e}^{-}{\eta }_c$

Using $(27.12\pm 0.14)\times {10}^8$ $\psi (3686)$ 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 $h_c\to e^{+}{e}^{-}{\eta }_c$ with a statistical significance of $5.4\sigma$. We measure the ratio of the branching fractions $\frac{\mathcal{B}(h_c\to e^{+}{e}^{-}{\eta }_c)}{\mathcal{B}(h_c\to \gamma {\eta }_c)}$ separately for the $h_c$ samples produced via $\psi (3686)\to {\pi }^0{h}_c$ and $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{h}_c$. The average ratio is determined to be $(0.59\pm 0.10(\text{stat.})\pm 0.04(\text{syst.}))\mathrm{\%}$, where the uncertainty includes both statistical and systematic components.