Measurements of the branching fractions of $χ_{cJ}\to φφη, φφη^{\prime}$ and $φK^+K^-η$

Abstract

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