Measurements of the branching fractions of ${\chi }_{cJ}\to 2K^{+}2K^{-}\omega$ and $\phi K^{+}{K}^{-}\omega$ decays

Using a data sample of $(2712.4\pm 14.3)\times {10}^6$ $\psi (3686)$ events collected with the BESIII detector operating at the BEPCII collider, we report the first observation of the decays ${\chi }_{cJ}\to 2K^{+}2K^{-}\omega$ and ${\chi }_{cJ}\to \phi K^{+}{K}^{-}\omega$ ($J=0,1,2$) via the radiative transitions $\psi (3686)\to \gamma {\chi }_{cJ}$. The branching fractions of these decays are measured for the first time, and the statistical significance for each signal exceeds $10\sigma$.