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

Abstract

With 10 billion $J/\psi$ events collected at \mbox{BESIII}, the decay of $X(2370)\rightarrow K^{*}(892)^{0}\bar{K}^{0}+\mathrm{c.c.}$ is searched for via the $J/\psi\rightarrow\gamma K_{S}^{0}K_{S}^{0}\pi^{0}$ process. No evidence of this decay mode is found, with $\mathcal{B}[J/\psi\rightarrow\gamma X(2370)] \times \mathcal{B}[ X(2370) \rightarrow K^{*}(892)^{0}\bar{K}^{0}+\mathrm{c.c.} \rightarrow K^{0}_{S}K^{0}_{S}\pi^{0}] < 2.7\times 10^{-6}$ at the $90\%$ confidence level. The suppression of the $K^{*}(892)\bar{K}$ mode indicates the $X(2370)$ as a flavor-singlet state. It is the first flavor-singlet light hadron observed above $1~\textrm{GeV}/c^{2}$. 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 $J/\psi$ radiative decays, decay pattern similarities to that of $\eta_{c}$, flavor-singlet property, narrow partial decay width, and suppression of radiative decays to $\omega$ and $\phi$, 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 $X(2370)$.