Determining the Weak Phase $\gamma$ using the decays $B_d$, $B^+ \to K \eta (\eta')$ and $B_s \to \pi \eta (\eta')$

Abstract

We suggest two methods (based on flavor SU(3) symmetry) to determine the CKM angle $\gamma$ using the decays $B_d$, $B^+ \to K \eta (\eta')$ and $B_s \to \pi \eta (\eta')$, respectively. Rescattering effects are partly included -- we neglect annihilation amplitudes, but do not assume any other relation between the SU(3) invariant amplitudes. We use the fact that the amplitude (including the Electroweak Penguin contribution) for $B_d$, $B^+ \to \pi K$ with final state $I (isospin) =3/2$ is known as a function of $\gamma$ from the decay rate $B^+ \to \pi^0 \pi^+$.