Helicity amplitude analysis of $χ_{cJ} \rightarrow ϕϕ$
Using (447.9 $\pm$ 2.3) million $ψ$(3686) events collected with the BESIII detector, the decays of $χ_{cJ} \rightarrow ϕϕ$ ($J$=0, 1, 2) have been studied via the decay $ψ(3686)\rightarrowγχ_{cJ}$. The branching fractions of the decays $χ_{cJ} \rightarrow ϕϕ$ ($J$=0, 1, 2) are determined to be $(8.48\pm0.26\pm0.27)\times10^{-4}$, $(4.36\pm0.13\pm0.18)\times10^{-4}$, and $(13.36\pm0.29\pm0.49)\times10^{-4}$, respectively, which are the most precise measurements to date. From a helicity amplitude analysis of the process $ψ(3686) \rightarrow γχ_{cJ}, χ_{cJ}\rightarrow ϕϕ, ϕ\rightarrow K^{+}K^{-}$, the polarization parameters of the $χ_{cJ} \rightarrow ϕϕ$ decays are determined for the first time.