Measurements of the branching fractions of $\chi_{cJ}\to \phi\phi\eta, \phi\phi\eta^{\prime}$ and $\phi K^+K^-\eta$

Abstract

Using a sample of $(2712.4 \pm 14.3)\times 10^6 ~\psi$(3686) events collected by the BESIII detector at the BEPCII collider, we measure the branching fractions of the decays $\chi_{cJ}\to \phi\phi\eta,~\phi\phi\eta^{\prime}$, and~$\phi K^+K^-\eta $ ($J = 0, 1, 2$). The obtained branching fractions are $\mathcal{B}(\chi_{c0} \to \phi\phi\eta) = (7.40 \pm 0.23 \pm 0.55)\times10^{-4}$, $\mathcal{B}(\chi_{c1} \to \phi\phi\eta) = (3.33 \pm 0.14 \pm 0.25)\times10^{-4}$, $\mathcal{B}(\chi_{c2} \to \phi\phi\eta) = (5.46 \pm 0.17 \pm 0.40)\times10^{-4}$, $\mathcal{B}(\chi_{c0} \to \phi\phi\eta^\prime) = (2.96 \pm 0.23 \pm 0.29)\times10^{-4}$, $\mathcal{B}(\chi_{c1} \to \phi\phi\eta^\prime) = (0.69 \pm 0.10 \pm 0.08)\times10^{-4}$, $\mathcal{B}(\chi_{c2} \to \phi\phi\eta^\prime) = (0.65 \pm 0.09 \pm 0.07)\times10^{-4}$, $\mathcal{B}(\chi_{c0} \to \phi K^+K^-\eta) = (1.23 \pm 0.08 \pm 0.10)\times10^{-4}$, $\mathcal{B}(\chi_{c1} \to \phi K^+K^-\eta) = (1.00 \pm 0.07 \pm 0.07)\times10^{-4}$, and $\mathcal{B}(\chi_{c2} \to \phi K^+K^-\eta) = (1.82 \pm 0.09 \pm 0.14)\times10^{-4}$, where $K^+K^-$ is not from the decay of a $\phi$ meson, the first uncertainties are statistical and the second systematic. The branching fractions of $\chi_{cJ}\to \phi\phi\eta$ are measured with precision improved by factors of $1.5-1.9$, and those of $\chi_{cJ}\to \phi\phi\eta^\prime$ and $\phi K^+K^-\eta$ are measured for the first time.