SU(3) - Flavor Symmetry in $B \to VP$ Decays

In the framework of SU(3) symmetry, we present a general analysis of $B$ meson decays into two lighter uncharmed mesons (both pairs of pseudoscalar mesons and pairs of vector and pseudoscalar mesons). From the analysis we find constraints on $\gamma$ and discuss their validity. The most useful new constraint is obtained by considering the decay modes $B^{0} \to K\pi$ and $B^{+} \to \pi^{0}\pi^{+}$. In decays into pairs of vector and pseudeuscalar mesons, no constraints can be obtained using SU(3) symmetry alone and further assumptions are needed. Based on these assumptions, we obtain new (weaker) constraints using $B^{0} \to \rho K/B^{0} \to K^{*}\pi$ and $B^{+} \to \rho\pi$. We show that no other constraints can be obtained. We also suggest a method to measure $\gamma$ using $B^{0}_{s} \to \rho\pi$ and $B^{0} \to K^{*\pm}K^{\mp}$.