Study of electromagnetic Dalitz decays $\ddot{I}{‡}_{cJ}\to \hat{I}{¼}^{+}\hat{I}{¼}^{-}J/\ddot{I}ˆ$

Abstract

Using $4.48\times 10^8$ $\ddot{I}ˆ(3686)$ events collected with the BESIII detector, we search for the decays $\ddot{I}{‡}_{cJ}\to \hat{I}{¼}^{+}\hat{I}{¼}^{-}J/\ddot{I}ˆ$ through the radiative decays $\ddot{I}ˆ(3686)\to {\hat{I}}^3\ddot{I}{‡}_{cJ}$, where $J=0,1,2$. The decays $\ddot{I}{‡}_{c1,2}\to \hat{I}{¼}^{+}\hat{I}{¼}^{-}J/\ddot{I}ˆ$ are observed, and the corresponding branching fractions are measured to be $\mathcal{B}(\ddot{I}{‡}_{c1}\to \hat{I}{¼}^{+}\hat{I}{¼}^{-}J/\ddot{I}ˆ)=(2.51\pm 0.18\pm 0.20)\times 10^{-4}$ and $\mathcal{B}(\ddot{I}{‡}_{c2}\to \hat{I}{¼}^{+}\hat{I}{¼}^{-}J/\ddot{I}ˆ)=(2.33\pm 0.18\pm 0.29)\times 10^{-4}$, where the first uncertainty is statistical and the second one systematic. No significant $\ddot{I}{‡}_{c0}\to \hat{I}{¼}^{+}\hat{I}{¼}^{-}J/\ddot{I}ˆ$ 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 $\ddot{I}{‡}_{c1,2}\to \hat{I}{¼}^{+}\hat{I}{¼}^{-}J/\ddot{I}ˆ$.