Search for ${\eta }_1(1855)$ in ${\chi }_{cJ}\to \eta \eta {\eta }^{\prime }$ decays

Abstract

Based on a sample of $2.7\times 10^9$ $\psi (3686)$ events collected by the BESIII detector operating at the BEPCII collider, an analysis of the decay $\psi (3686)\to \gamma {\chi }_{cJ},{\chi }_{cJ}\to \eta \eta {\eta }^{\prime }$ is performed. The decay modes ${\chi }_{c1}$ and ${\chi }_{c2}\to \eta \eta {\eta }^{\prime }$ are observed for the first time, and their corresponding branching fractions are determined to be $\mathcal{B}({\chi }_{c1}\to \eta \eta {\eta }^{\prime })=(1.40\pm 0.13(\text{stat.})\pm 0.09(\text{sys.}))\times 10^{-4}$ and $\mathcal{B}({\chi }_{c2}\to \eta \eta {\eta }^{\prime })=(4.18\pm 0.84(\text{stat.})\pm 0.48(\text{sys.}))\times 10^{-5}$. An upper limit on the branching fraction of ${\chi }_{c0}\to \eta \eta {\eta }^{\prime }$ is set as $2.59\times 10^{-5}$ at 90\% confidence level (CL). A partial wave analysis (PWA) of the decay ${\chi }_{c1}\to \eta \eta {\eta }^{\prime }$ is performed to search for the $1^{-+}$ exotic state ${\eta }_1(1855)$. The PWA result indicates that the structure in the $\eta {\eta }^{\prime }$ mass spectrum is mainly attributed to the $f_0(1500)$, while in the $\eta \eta$ mass spectrum, it is primarily the $0^{++}$ phase space. The upper limit of $\mathcal{B}({\chi }_{c1}\to {\eta }_1(1855)\eta )\cdot \mathcal{B}({\eta }_1(1855)\to \eta {\eta }^{\prime })<9.79\times 10^{-5}$ is set based on the PWA at 90\% CL.