Extraction of the CP-violating phase $γ$ using $B \to K ππ$ and $B \to K K {\bar K}$ decays

Abstract

Using the B{\sc a}B{\sc ar}\ measurements of the Dalitz plots for $B^0 \to K^+π^0π^-$, $B^0 \to K^0π^+π^-$, $B^+ \to K^+π^+π^-$, $B^0 \to K^+ K^0 K^-$, and $B^0 \to K^0 K^0 {\bar K}^0$ decays, we demonstrate that it is possible to cleanly extract the weak phase $γ$. We find four possible solutions. Three of these -- $32^\circ$, $259^\circ$, and $315^\circ$ -- are in disagreement with the SM, while one -- $77^\circ$ -- is consistent with the SM. An advantage of this Dalitz-plot method is that one can obtain many independent measurements of $γ$, thereby reducing its statistical error. An accurate determination of the errors, however, requires detailed knowledge of the data.