Helicity amplitude analysis of ${\chi }_{cJ}\to \phi \phi$

Using (447.9 $\pm$ 2.3) million $\psi$(3686) events collected with the BESIII detector, the decays of ${\chi }_{cJ}\to \phi \phi$ ($J$=0, 1, 2) have been studied via the decay $\psi (3686)\to \gamma {\chi }_{cJ}$. The branching fractions of the decays ${\chi }_{cJ}\to \phi \phi$ ($J$=0, 1, 2) are determined to be $(8.48\pm 0.26\pm 0.27)\times {10}^{-4}$, $(4.36\pm 0.13\pm 0.18)\times {10}^{-4}$, and $(13.36\pm 0.29\pm 0.49)\times {10}^{-4}$, respectively, which are the most precise measurements to date. From a helicity amplitude analysis of the process $\psi (3686)\to \gamma {\chi }_{cJ},{\chi }_{cJ}\to \phi \phi ,\phi \to K^{+}{K}^{-}$, the polarization parameters of the ${\chi }_{cJ}\to \phi \phi$ decays are determined for the first time.