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 $B\to PP$ decays without assuming the smallness of the annihilation contributions. These relations provide important tests for the Standard Model of CP violation.

Comments: Revtex, 16 pages, Several changes about references are made