Observation of the Exotic State $\ddot{I}{€}_1(1600)$ in $\ddot{I}ˆ(2S)\to {\hat{I}}^3\ddot{I}{‡}_{c1},\ddot{I}{‡}_{c1}\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\hat{I}{\cdot }^{\prime }$

Abstract

A partial wave analysis of the process $\ddot{I}ˆ(2S)\to {\hat{I}}^3\ddot{I}{‡}_{c1},\ddot{I}{‡}_{c1}\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\hat{I}{\cdot }^{\prime }$ is performed using $(2712.4\pm 14.3)\times 10^6$ $\ddot{I}ˆ(2S)$ events collected with the BESIII detector. An isovector state with exotic quantum numbers $J^{PC}=1^{-+}$, denoted as $\ddot{I}{€}_1(1600)$, is observed for the first time in the charmonium decay of $\ddot{I}{‡}_{c1}\to \ddot{I}{€}_1^{\pm }(1600)\ddot{I}{€}^{\mp }$, $\ddot{I}{€}_1^{\pm }(1600)\to \ddot{I}{€}^{\pm }\hat{I}{\cdot }^{\prime }$ with a statistical significance over $21\ddot{I}ƒ$. Its mass and width are determined to be $1828\pm 8(\mathrm{stat}{)}_{-33}^{+11}(\mathrm{syst})\mathrm{MeV}/c^2$ and $638\pm 26(\mathrm{stat}{)}_{-86}^{+35}(\mathrm{syst})\mathrm{MeV}$, respectively, using a relativistic Breit-Wigner function with a mass-dependent width. The corresponding product of branching fractions is determined to be $\mathcal{B}\left[\ddot{I}{‡}_{c1}\to \ddot{I}{€}_1(1600{)}^{\pm }\ddot{I}{€}^{\mp }\right]\times \mathcal{B}\left[\ddot{I}{€}_1(1600{)}^{\pm }\to \ddot{I}{€}^{\pm }\hat{I}{\cdot }^{\prime }\right]=\left(4.30\pm 0.14(\mathrm{stat}{)}_{-1.03}^{+1.04}(\mathrm{syst})\right)\times 10^{-4}$.