Search for the reaction $e^{+}e^{-} rightarrow pi ^{+}pi ^{-} chi_{cJ}$ and a charmonium-like structure decaying to $chi_{cJ}pi ^{pm}$ between 4.18 and 4.60 GeV

We search for the process $e^{+}e^{-}rightarrow pi ^{+}pi ^{-} chi_{cJ}$ ($J=0,1,2$) and for a charged charmonium-like state in the $pi ^{pm} chi_{cJ}$ subsystem. The search uses data sets 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 $pi ^{+}pi ^{-} chi_{cJ}$ signals are observed at any center-of-mass energy, and thus upper limits are provided which also serve as limits for a possible charmonium-like structure in the invariant $pi ^{pm} chi_{cJ}$ mass.