Extracting CKM $\gamma$ phase from $B^{\pm }\to K^{\pm }{\pi }^{+}{\pi }^{-}$ and $B^0$, ${\bar{B}}^0\to K_s{\pi }^{+}{\pi }^{-}$

Abstract

We discuss some aspects of the search for CP asymmetry in the three body B decays, revealed through the interference among neighbor resonances in the Dalitz plot. We propose a competitive method to extract the CKM $\gamma$ angle combining Dalitz plot amplitude analysis of $B^{\pm }\to K^{\pm }{\pi }^{+}{\pi }^{-}$ and untagged $B^0$, ${\bar{B}}^0\to K_s{\pi }^{+}{\pi }^{-}$. The method also obtains the ratio and phase difference between the {\it tree} and {\it penguin} contributions from $B^0$ and ${\bar{B}}^0\to K^{\ast \pm }{\pi }^{\mp }$ decays and the CP asymmetry between $B^0$ and $\overline{B^0}$. From Monte Carlo studies of 100K events for the neutral mesons, we show the possibility of measuring $\gamma$.

Revised enlarged version to appear at Phys Rev D

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• Localized direct CP violation in $B^{\pm }\to {\rho }^0(\omega ){\pi }^{\pm }\to {\pi }^{+}{\pi }^{-}{\pi }^{\pm }$
• CP violation in the B system
• Contributions of $K_0^{\ast }(1430)$ and $K_0^{\ast }(1950)$ in the three-body decays $B\to K\pi h$
• Study of $CP$ Violation in $B^{-}\to K^{-}{\pi }^{+}{\pi }^{-}$ and $B^{-}\to K^{-}\sigma (600)$ decays in the QCD factorization approach
• Observation of $B_s^0\to K^{\ast \pm }{K}^{\mp }$ and evidence for $B_s^0\to K^{\ast -}{\pi }^{+}$ decays
• Recent Developments on the CKM Matrix
• Observation of the decay ${\Xi }_b^{-}\to p{K}^{-}{K}^{-}$