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

Abstract

We suggest two methods (based on flavor SU(3) symmetry) to determine the CKM angle $\gamma$ using the decays $B_d$, $B^{+}\to K\eta ({\eta }^{\prime })$ and $B_s\to \pi \eta ({\eta }^{\prime })$, 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 $B^{+}\to {\pi }^0{\pi }^{+}$.

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