Lightest $0^{-+}$ Glueball as Dominant Constituent of $X(2370)$

Abstract

With 10 billion $J/\ddot{I}ˆ$ events collected at \mbox{BESIII}, the decay of $X(2370)\to K^{\ast }(892{)}^0{\bar{K}}^0+c.c.$ is searched for via the $J/\ddot{I}ˆ\to {\hat{I}}^3{K}_S^0{K}_S^0\ddot{I}{€}^0$ process. No evidence of this decay mode is found, with $\mathcal{B}[J/\ddot{I}ˆ\to {\hat{I}}^{3}X(2370)]\times \mathcal{B}[X(2370)\to K^{\ast }(892{)}^0{\bar{K}}^0+c.c.\to K_S^0{K}_S^0\ddot{I}{€}^0]<2.7\times 10^{-6}$ at the $90\%$ confidence level. The suppression of the $K^{\ast }(892)\bar{K}$ mode indicates the $X(2370)$ as a flavor-singlet state. It is the first flavor-singlet light hadron observed above $1\text{GeV}/c^2$. All \mbox{BESIII} measurements on the $X(2370)$ are summarized. A dominant component of the lightest $0^{-+}$ glueball is essential for a natural and complete explanation of the properties of the $X(2370)$~\textemdash~the mass, spin-parity, high production rate in $J/\ddot{I}ˆ$ radiative decays, decay pattern similarities to that of $\hat{I}{\cdot }_c$, flavor-singlet property, narrow partial decay width, and suppression of radiative decays to $\ddot{I}‰$ and $\ddot{I}•$, since these properties are all consistent with the features of the lightest $0^{-+}$ glueball while other interpretations at present are disfavored. This supports that the lightest $0^{-+}$ glueball is the dominant constituent of the $X(2370)$.