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

Abstract

We discuss direct CP violation in three-body decays of $B$ meson such as $B^{\pm }\to K^{\pm }{\pi }^{+}{\pi }^{-}$, which involves various intermediate resonance states, such as $B^{\pm }\to K_i^{\ast }{\pi }^{\pm }$ and $B^{\pm }\to \rho K^{\pm }$, where $K_i^{\ast }$ represents the $\pi K$ 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 $K_i^{\ast }$ and $\rho$ resonances overlap. By examining a Dalitz plot of this mode and combining a measurement of the branching ratio for $B^{\pm }\to {\rho }^{\pm }K$, it is possible to extract the weak phase, ${\varphi }_3$= arg$(-V_{ud}{V}_{ub}^{\ast }/(V_{cd}{V}_{cb}^{\ast }))$, of the Kobayashi-Maskawa matrix.

12 pages, 1 figures. Argument to determine the CKM angle is changed. Also available via anonymous ftp at ftp://ftp.kek.jp/kek/preprints/TH/TH-549

Cited by in corpus (5)

• CP Violation in the B System and Relations to $K\to \pi \nu \bar{\nu }$ Decays
• The CP violating asymmetry in $B^{\pm }\to M\bar{M}{\pi }^{\pm }$ decays
• The penguin operators in nonresonant $B^{-}\to M\bar{M}{\pi }^{-}$ $(M={\pi }^{-},K^{-},K^0)$ decays
• CP violating phase $\gamma$ and the partial widths asymmetry in $B^{-}\to {\pi }^{+}{\pi }^{-}{K}^{-}$ and $B^{-}\to K^{+}{K}^{-}{K}^{-}$ decays
• Looking for nonstandard CP violation in B^\pm -> D_s^\pm D^0 pi^0 decays