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

TL;DR

This paper proposes two methods based on flavor SU(3) symmetry to determine the CKM angle gamma using specific B meson decays, incorporating rescattering effects and electroweak penguin contributions.

Contribution

It introduces novel methods leveraging flavor SU(3) symmetry and known decay amplitudes to extract the CKM angle gamma from B meson decay data.

Findings

Methods provide a way to determine gamma from B decay rates.

Rescattering effects are partially included in the analysis.

The approach relates B decay amplitudes to known decay processes.

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 $B^+ \to \pi^0 \pi^+$.