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 $\gamma$.

Comments: Revised enlarged version to appear at Phys Rev D