Search for the electromagnetic Dalitz decays ${\chi }_{cJ}\to e^{+}{e}^{-}\phi$

Using a data sample of $(2.712\pm 0.014)\times {10}^9$ $\psi (3686)$ events collected at $\sqrt{s}=3.686$ GeV by the BESIII detector, we search for the rare electromagnetic Dalitz decays ${\chi }_{cJ}\to e^{+}{e}^{-}\phi (J=0,1,2)$ via the radiative transitions $\psi (3686)\to \gamma {\chi }_{cJ}$. No statistically significant ${\chi }_{cJ}\to e^{+}{e}^{-}\phi$ signals are observed. The upper limits on the branching fractions of ${\chi }_{cJ}\to e^{+}{e}^{-}\phi (J=0,1,2)$, excluding the $\phi$ resonance to $e^{+}{e}^{-}$ final states, are set to be $2.4\times {10}^{-7},6.7\times {10}^{-7}$ and $4.1\times {10}^{-7}$ at 90% confidence level, respectively. This is the first search for the electromagnetic Dalitz transition of P-wave charmonium ${\chi }_{cJ}$ states to a light vector meson.