On Measuring CP Violating Phase $γ$ Using Neutral $B$ Decays

Abstract

We propose two independent methods to determine the CKM phase $γ$ and the tree and penguin amplitudes using neutral $B$ decays, assuming that the phase $β$ is known. Based on flavor SU(3) symmetry and SU(3) breaking effect, one method uses the decay processes $B^0(t) \rightarrow π^0 K_S$, $B^0 \rightarrow ηK^0 \; (K_S \rightarrow ππ)$ and their charge-conjugate processes, and the other uses the processes $B^0(t) \rightarrow π^0 K_S$, $B^0 \rightarrow π^0 π^0$ and their charge-conjugate processes. From SU(3) breaking consideration, the latter method would be more useful.