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

Using $4.48\times {10}^8$ $\psi (3686)$ events collected with the BESIII detector, we search for the decays ${\chi }_{cJ}\to {\mu }^{+}{\mu }^{-}J\mathrm{/}\psi$ through the radiative decays $\psi (3686)\to \gamma {\chi }_{cJ}$, where $J=0,1,2$. The decays ${\chi }_{c1,2}\to {\mu }^{+}{\mu }^{-}J\mathrm{/}\psi$ are observed, and the corresponding branching fractions are measured to be $$\mathcal{B}$(\chi_{c1} \rightarrow \mu^{+}\mu^{-}J/\psi) = (2.51 \pm 0.18 \pm 0.20)\times10^{-4}$and$$\mathcal{B}$(\chi_{c2} \rightarrow \mu^{+}\mu^{-}J/\psi) = (2.33 \pm 0.18 \pm 0.29)\times10^{-4}$, where the first uncertainty is statistical and the second one systematic. No significant ${\chi }_{c0}\to {\mu }^{+}{\mu }^{-}J\mathrm{/}\psi$ decay is observed, and the upper limit on the branching fraction is determined to be $2.0\times {10}^{-5}$ at 90% confidence level. Also, we present a study of di-muon invariant mass dependent transition form factor for the decays $\chi_{c1,2} \rightarrow \mu^{+}\mu^{-}J/\psi$.