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

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 $γ$ angle combining Dalitz plot amplitude analysis of $B^{\pm} \to K^{\pm} π^+ π^-$ and untagged $B^0$, $\bar B^0 \to K_s π^+ π^-$. 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^{*\pm} π^{\mp} $ decays and the CP asymmetry between $B^0$ and $\bar{B^0}$. From Monte Carlo studies of 100K events for the neutral mesons, we show the possibility of measuring $γ$.