Direct CP violation in three-body decays of the B meson by resonance effects

We discuss direct CP violation in three-body decays of B meson such as B±→K±π+π−, which involves various intermediate resonance states, such as B±→K∗iπ± and B±→ρK±, where K∗i represents the πK resonance. Due to the large final state interaction phases of the resonances, the CP asymmetry can be as large as the 25% level near the kinematical region where the K∗i and ρ resonances overlap. By examining a Dalitz plot of this mode and combining a measurement of the branching ratio for B±→ρ±K, it is possible to extract the weak phase, φ3=arg(−VudVub∗/(VcdVcb∗)), of the Kobayashi-Maskawa matrix.