Measurements of $C\!P$ violation in the three-body phase space of charmless $B^{\pm}$ decays
The charmless three-body decay modes $B^{\pm} \rightarrow K^{\pm} π^{+} π^{-}$, $B^{\pm} \rightarrow K^{\pm} K^{+} K^{-}$, $B^{\pm} \rightarrow π^{\pm} K^{+} K^{-}$ and $B^{\pm} \rightarrow π^{\pm} π^{+} π^{-}$ are reconstructed using data, corresponding to an integrated luminosity of 3.0\;$\mbox{\,fb}^{-1}$, collected by the LHCb detector. The inclusive $C\!P$ asymmetries of these modes are measured to be $$ A_{C\!P}(B^{\pm} \rightarrow K^{\pm} π^{+} π^{-})= +0.025 \pm 0.004 \pm 0.004 \pm 0.007 \\ A_{C\!P}(B^{\pm} \rightarrow K^{\pm} K^{+} K^{-}) = -0.036 \pm 0.004 \pm 0.002 \pm 0.007 \\ A_{C\!P}(B^{\pm} \rightarrow π^{\pm} π^{+} π^{-})= +0.058 \pm 0.008 \pm 0.009 \pm 0.007 \\ A_{C\!P}(B^{\pm} \rightarrow π^{\pm} K^{+} K^{-})= -0.123 \pm 0.017 \pm 0.012 \pm 0.007 $$ %% where the first uncertainty is statistical, the second systematic, and the third is due to the $C\!P$ asymmetry of the $B^{\pm} \rightarrow J/ψK^{\pm}$ 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.