Study of electromagnetic Dalitz decays ${\chi }_{cJ}\to {\mu }^{+}{\mu }^{-}J/\psi $

Using $4.48×{10}^{8}\text{}\text{}\psi \left(3686\right)$ events collected with the BESIII detector, we search for the decays ${\chi }_{cJ}\to {\mu }^{+}{\mu }^{-}J/\psi $ through the radiative decays $\psi \left(3686\right)\to \gamma {\chi }_{cJ}$, where $J=0$, 1, 2. The decays ${\chi }_{c1,2}\to {\mu }^{+}{\mu }^{-}J/\psi $ are observed, and the corresponding branching fractions are measured to be $B\left({\chi }_{c1}\to {\mu }^{+}{\mu }^{-}J/\psi \right)=\left(2.51±0.18±0.20\right)×{10}^{-4}$ and $B\left({\chi }_{c2}\to {\mu }^{+}{\mu }^{-}J/\psi \right)=\left(2.33±0.18±0.29\right)×{10}^{-4}$, where the first uncertainty is statistical and the second one systematic. No significant ${\chi }_{c0}\to {\mu }^{+}{\mu }^{-}J/\psi $ decay is observed, and the upper limit on the branching fraction is determined to be $2.0×{10}^{-5}$ at 90% confidence level. Also, we present a study of dimuon invariant mass dependent transition form factor for the decays ${\chi }_{c1,2}\to {\mu }^{+}{\mu }^{-}J/\psi $.