Measurement of $C\!P$ violation in the phase space of $B^{\pm} \to K^{\pm} \pi^{+} \pi^{-}$ and $B^{\pm} \to K^{\pm} K^{+} K^{-}$ decays

The charmless decays $B^{\pm}\to K^{\pm}\pi^+\pi^-$ and $B^{\pm}\to K^{\pm}K^+K^-$ are reconstructed using data, corresponding to an integrated luminosity of 1.0 fb$^{-1}$, collected by LHCb in 2011. The inclusive charge asymmetries of these modes are measured as $A_{C\!P}(B^{\pm}\to K^{\pm}\pi^+\pi^-) = 0.032 \pm 0.008 {\mathrm{\,(stat)}} \pm 0.004 {\mathrm{\,(syst)}} \pm 0.007 (J/\psi K^{\pm})$ and $A_{C\!P}(B^{\pm}\to K^{\pm}K^+K^-) = -0.043 \pm 0.009 {\mathrm{\,(stat)}} \pm 0.003 {\mathrm{\,(syst)}} \pm 0.007 (J/\psi K^{\pm})$, where the third uncertainty is due to the $C\!P$ asymmetry of the $B^{\pm}\to J/\psi K^{\pm}$ reference mode. The significance of $A_{C\!P}(B^{\pm}\to K^{\pm}K^+K^-)$ exceeds three standard deviations and is the first evidence of an inclusive $C\!P$ asymmetry in charmless three-body $B$ decays. In addition to the inclusive $C\!P$ asymmetries, larger asymmetries are observed in localised regions of phase space.