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 3.0fb-1, collected by the LHCb detector. The inclusive CP asymmetries of these modes are measured to be ACP(B±→K±π+π-)=+0.025±0.004±0.004±0.007,ACP(B±→K±K+K-)=-0.036±0.004±0.002±0.007,ACP(B±→π±π+π-)=+0.058±0.008±0.009±0.007,ACP(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/ψK± 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.