Measurements of CP Violation in the Three-Body Phase Space of Charmless B± Decays

The charmless three-body decay modes B± → K± π+ π−, B± → K± K+ K−, B± → π± K+ K− and B± → π± π+ π− are reconstructed using data, corresponding to an integrated luminosity of 3.0 fb^−1, collected by the LHCb detector. The inclusive CP asymmetries of these modes are measured to be A_CP(B± → K± π+ π−) = +0.025 ± 0.004 ± 0.004 ± 0.007, A_CP(B± → K± K+ K−) = −0.036 ± 0.004 ± 0.002 ± 0.007, A_CP(B± → π± π+ π−) = +0.058 ± 0.008 ± 0.009 ± 0.007, A_CP(B± → π± K+ K−) = −0.123 ± 0.017 ± 0.012 ± 0.007, where the first uncertainty is statistical, the second systematic, and the third is due to the CP asymmetry of the B± → J/ψ K± 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