Search for $η_{1}(1855)$ in $χ_{cJ}\toηηη^{\prime}$ decays

Abstract: Based on a sample of $2.7\times10<sup>{9}$ $\psi(3686)$ events collected by the BESIII detector operating at the BEPCII collider, an analysis of the decay $$\psi(3686)\to\gamma\chi_{cJ}, \chi_{cJ}\to\eta\eta\eta<sup>{\prime}$$ is performed. The decay modes $\chi_{c1}$ and $\chi_{c2}\to\eta\eta\eta<sup>{\prime}$ are observed for the first time, and their corresponding branching fractions are determined to be $$\mathcal{B}(\chi_{c1}\to\eta\eta\eta^{\prime}) = (1.40\, \pm 0.13\, (\text{stat.}) \pm 0.09\, (\text{sys.})) \times 10<sup>{-4}$$ and $$\mathcal{B}(\chi_{c2}\to\eta\eta\eta^{\prime}) = (4.18\, \pm 0.84\, (\text{stat.}) \pm 0.48\, (\text{sys.})) \times 10<sup>{-5}$$. An upper limit on the branching fraction of $\chi_{c0}\to\eta\eta\eta<sup>{\prime}$ is set as $2.59 \times 10<sup>{-5}$ at 90\% confidence level (CL). A partial wave analysis (PWA) of the decay $\chi_{c1}\to\eta\eta\eta<sup>{\prime}$ is performed to search for the $1<sup>{-+}$ exotic state $\eta_1(1855)$. The PWA result indicates that the structure in the $\eta\eta<sup>{\prime}$ mass spectrum is mainly attributed to the $f_0(1500)$, while in the $\eta\eta$ mass spectrum, it is primarily the $0<sup>{++}$ phase space. The upper limit of $\mathcal{B}(\chi_{c1}\to\eta_{1}(1855)\eta) \cdot \mathcal{B}(\eta_{1}(1855)\to\eta\eta^{{\prime})&lt;} 9.79 \times 10<sup>{-5}$ is set based on the PWA at 90\% CL.