SU(3) Analysis of Annihilation Contributions and CP Violating Relations in $B \to PP$ Decays

Abstract

Several methods proposed to measure the angle $\gamma$ in the KM unitarity triangle assumed that the tree contribution to $B^-\to \pi^-\bar K^0 $ is purely due to annihilation contributions and is negligibly small. This assumption has to be tested in order to have a correct interpretation of the experimental data. In this paper we show that using SU(3) symmetry, the smallness of the tree contribution can be tested in a dynamic model independent way. We also derive several relations between CP violating rate differences for $B\to P P$ decays without assuming the smallness of the annihilation contributions. These relations provide important tests for the Standard Model of CP violation.