Search for $\hat{I}{\cdot }_c(2S)\to 2(\ddot{I}{€}^{+}\ddot{I}{€}^{-})$ and improved measurement of $\ddot{I}{‡}_{cJ}\to 2(\ddot{I}{€}^{+}\ddot{I}{€}^{-})$

Abstract

We search for the hadronic decay $\hat{I}{\cdot }_c(2S)\to 2(\ddot{I}{€}^{+}\ddot{I}{€}^{-})$ in the $\ddot{I}ˆ(3686)\to {\hat{I}}^3\hat{I}{\cdot }_c(2S)$ radiative decay using $(27.12\pm 0.14)\times 10^8$ $\ddot{I}ˆ(3686)$ events collected by the BESIII detector at the BEPCII collider. No significant signal is found, and the upper limit of $\mathcal{B}[\ddot{I}ˆ(3686)\to {\hat{I}}^3\hat{I}{\cdot }_c(2S)]\mathcal{B}[\hat{I}{\cdot }_c(2S)\to 2(\ddot{I}{€}^{+}\ddot{I}{€}^{-})]$ is determined to be $0.78\times 10^{-6}$ at the 90\% confidence level. Using $\ddot{I}ˆ(3686)\to {\hat{I}}^3\ddot{I}{‡}_{cJ}$ transitions, we also measure the branching fractions of $\mathcal{B}[\ddot{I}{‡}_{cJ(J=0,1,2)}\to 2(\ddot{I}{€}^{+}\ddot{I}{€}^{-})]$, which are $\mathcal{B}[\ddot{I}{‡}_{c0}\to 2(\ddot{I}{€}^{+}\ddot{I}{€}^{-})]=(2.127\pm 0.002(stat.)\pm 0.101(syst.))$\%, $\mathcal{B}[\ddot{I}{‡}_{c1}\to 2(\ddot{I}{€}^{+}\ddot{I}{€}^{-})]=(0.685\pm 0.001(stat.)\pm 0.031syst.))$\%, and $\mathcal{B}[\ddot{I}{‡}_{c2}\to 2(\ddot{I}{€}^{+}\ddot{I}{€}^{-})]=(1.153\pm 0.001(stat.)\pm 0.063(syst.))$\%.