Observation of $\hat{I}{\cdot }_c(2S)\to 3(\ddot{I}{€}^{+}\ddot{I}{€}^{-})$ and measurements of $\ddot{I}{‡}_{cJ}\to 3(\ddot{I}{€}^{+}\ddot{I}{€}^{-})$ in $\ddot{I}ˆ(3686)$ radiative transitions

Abstract

The hadronic decay $\hat{I}{\cdot }_c(2S)\to 3(\ddot{I}{€}^{+}\ddot{I}{€}^{-})$ is observed with a statistical significance of 9.3 standard deviations using $(448.1\pm 2.9)\times 10^6$ $\ddot{I}ˆ(3686)$ events collected by the BESIII detector at the BEPCII collider. The measured mass and width of $\hat{I}{\cdot }_c(2S)$ are $(3643.4\pm 2.3(stat.)\pm 4.4(syst.))$ MeV/$c^2$ and $(19.8\pm 3.9(stat.)\pm 3.1(syst.))$ MeV, respectively, which are consistent with the world average values within two standard deviations. The product branching fraction $\mathcal{B}[\ddot{I}ˆ(3686)\to {\hat{I}}^3\hat{I}{\cdot }_c(2S)]\times \mathcal{B}[\hat{I}{\cdot }_c(2S)\to 3(\ddot{I}{€}^{+}\ddot{I}{€}^{-})]$ is measured to be $(9.2\pm 1.0(stat.)\pm 0.9(syst.))\times 10^{-6}$. Using $\mathcal{B}[\ddot{I}ˆ(3686)\to {\hat{I}}^3\hat{I}{\cdot }_c(2S)]=(7.0_{-2.5}^{+3.4})\times 10^{-4}$, we obtain $\mathcal{B}[\hat{I}{\cdot }_c(2S)\to 3(\ddot{I}{€}^{+}\ddot{I}{€}^{-})]=(1.31\pm 0.15(stat.)\pm 0.13(syst.){(}_{-0.47}^{+0.64})(\mathrm{extr}))\times 10^{-2}$, where the third uncertainty is from $\mathcal{B}[\ddot{I}ˆ(3686)\to {\hat{I}}^3\hat{I}{\cdot }_c(2S)]$. We also measure the $\ddot{I}{‡}_{cJ}\to 3(\ddot{I}{€}^{+}\ddot{I}{€}^{-})$ ($J=0,1,2$) decays via $\ddot{I}ˆ(3686)\to {\hat{I}}^3\ddot{I}{‡}_{cJ}$ transitions. The branching fractions are $\mathcal{B}[\ddot{I}{‡}_{c0}\to 3(\ddot{I}{€}^{+}\ddot{I}{€}^{-})]=(2.080\pm 0.006(stat.)\pm 0.068(syst.))\times 10^{-2}$, $\mathcal{B}[\ddot{I}{‡}_{c1}\to 3(\ddot{I}{€}^{+}\ddot{I}{€}^{-})]=(1.092\pm 0.004(stat.)\pm 0.035(syst.))\times 10^{-2}$, and $\mathcal{B}[\ddot{I}{‡}_{c2}\to 3(\ddot{I}{€}^{+}\ddot{I}{€}^{-})]=(1.565\pm 0.005(stat.)\pm 0.048(syst.))\times 10^{-2}$.

12 pages, 5 figures