Search for the reaction ${e}^{+}{e}^{-}\to {\chi }_{cJ}{\pi }^{+}{\pi }^{-}$ and a charmoniumlike structure decaying to ${\chi }_{cJ}{\pi }^{±}$ between 4.18 and 4.60 GeV

We search for the process ${e}^{+}{e}^{-}\to {\chi }_{cJ}{\pi }^{+}{\pi }^{-}$ ($J=0$, 1, 2) and for a charged charmoniumlike state in the ${\chi }_{cJ}{\pi }^{±}$ subsystem. The search uses datasets collected with the BESIII detector at the BEPCII storage ring at center-of-mass energies between 4.18 GeV and 4.60 GeV. No significant ${\chi }_{cJ}{\pi }^{+}{\pi }^{-}$ signals are observed at any center-of-mass energy, and thus upper limits are provided which also serve as limits for a possible charmoniumlike structure in the invariant ${\chi }_{cJ}{\pi }^{±}$ mass.