Search for the $X(2370)$ and observation of ${\eta }_c\to \eta \eta \eta \prime$ in $J/\psi \to \gamma \eta \eta \eta \prime$

Using a sample of $1.31\times {10}^{9}J/\psi$ events collected with the BESIII detector, we perform a study of $J/\psi \to \gamma \eta \eta {\eta }^{\prime }$ to search for the $X(2370)$ and ${\eta }_c$ in the $\eta \eta {\eta }^{\prime }$ invariant mass distribution. No significant signal for the $X(2370)$ is observed, and we set an upper limit for the product branching fraction of $\mathcal{B}(J/\psi \to \gamma X(2370)·\mathcal{B}(X(2370)\to \eta \eta {\eta }^{\prime })<9.2\times {10}^{-6}$ at the 90% confidence level. A clear ${\eta }_c$ signal is observed for the first time, yielding a product branching fraction of $\mathcal{B}(J/\psi \to \gamma {\eta }_c)·\mathcal{B}({\eta }_c\to \eta \eta {\eta }^{\prime })=(4.86\pm 0.62(\mathrm{stat})\pm 0.45(\mathrm{sys}))\times {10}^{-5}$.

Figure 1

Invariant mass distributions for the selected candidates of $J/\psi \to \gamma \eta \eta {\eta }^{\prime }$. Plots (a) and (b) are the invariant mass distributions of $\gamma {\pi }^{+}{\pi }^{-}$ and $\eta \eta {\eta }^{\prime }$ for ${\eta }^{\prime }\to \gamma {\pi }^{+}{\pi }^{-}$, respectively. (c) and (d) are the invariant mass distributions of ${\pi }^{+}{\pi }^{-}\eta$ and $\eta \eta {\eta }^{\prime }$ for ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\eta$, respectively. The dots with error bars are data and the histograms are for the signal MC samples (arbitrary normalization).

Figure 2

Plots (a) and (b) are efficiency curves for the decays of ${\eta }^{\prime }\to \gamma {\pi }^{+}{\pi }^{-}$ and ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\eta$ obtained from $J/\psi \to \gamma X\to \gamma \eta \eta {\eta }^{\prime }$ MC simulation, where X means $0^{-+}$ nonresonant state. Plots (c) and (d) are the simultaneous fit results for the $X(2370)$ in the invariant mass distribution of $\eta \eta {\eta }^{\prime }$ for the decays of ${\eta }^{\prime }\to \gamma {\pi }^{+}{\pi }^{-}$ and ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\eta$, respectively. Plots (e) and (f) are the fit results for ${\eta }_c$ in the invariant mass distribution of $\eta \eta {\eta }^{\prime }$ for the decays of ${\eta }^{\prime }\to \gamma {\pi }^{+}{\pi }^{-}$ and ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\eta$, respectively. The dots with error bars represent the data, the red solid curves show the fit results, the hatched areas represent the signal of the $X(2370)$ scaled to the upper limit or the signal of the ${\eta }_c$, the brown dashed lines show the events from ${\eta }^{\prime }$ sideband, the green hyphenated lines represent the Chebychev polynomial function or the ARGUS function.