Measurements of $C\text{\hspace{0.17em}⁣}P$ violation in the three-body phase space of charmless $B^{\pm }$ decays

The charmless three-body decay modes $B^{\pm} \rightarrow K^{\pm} \pi^{+} \pi^{-}$,$B^{\pm} \rightarrow K^{\pm} K^{+} K^{-}$,$B^{\pm} \rightarrow \pi^{\pm} K^{+} K^{-}$and$B^{\pm} \rightarrow \pi^{\pm} \pi^{+} \pi^{-}$ are reconstructed using data, corresponding to an integrated luminosity of 3.0;$f{b}^{-1}$, collected by the LHCb detector. The inclusive $C\text{\hspace{0.17em}⁣}P$ asymmetries of these modes are measured to be $$A_{C\text{\hspace{0.17em}⁣}P}(B^{\pm }\to K^{\pm }{\pi }^{+}{\pi }^{-})=+0.025\pm 0.004\pm 0.004\pm 0.007A_{C\text{\hspace{0.17em}⁣}P}(B^{\pm }\to K^{\pm }{K}^{+}{K}^{-})=-0.036\pm 0.004\pm 0.002\pm 0.007A_{C\text{\hspace{0.17em}⁣}P}(B^{\pm }\to {\pi }^{\pm }{\pi }^{+}{\pi }^{-})=+0.058\pm 0.008\pm 0.009\pm 0.007A_{C\text{\hspace{0.17em}⁣}P}(B^{\pm }\to {\pi }^{\pm }{K}^{+}{K}^{-})=-0.123\pm 0.017\pm 0.012\pm 0.007$$ %% where the first uncertainty is statistical, the second systematic, and the third is due to the $C\text{\hspace{0.17em}⁣}P$ asymmetry of the $B^{\pm }\to J\mathrm{/}\psi K^{\pm }$ reference mode. The distributions of these asymmetries are also studied as functions of position in the Dalitz plot and suggest contributions from rescattering and resonance interference processes.