  B decays are a subject of active research since they provide useful
information on the dynamics of strong and electroweak interactions for testing
the Standard Model (SM) and models beyond and are ideally suited for a critical
analysis of CP violation phenomena. Within the standard model, there exist
certain relations between CP violating rate differences in B decays in the
SU(3) limit, as for example $\Delta (\bar{B}^0 \to \pi^+ \pi^-) = - \Delta
(\bar{B}^0 \to \pi^+ K^-)$. The goal of this letter is to study the direct CP
violation asymmetry in a class of processes where there has been recent
theoretical progress, as for example the B decays into two light pseudoscalars
mesons and into a light pseudoscalar and a light vector meson. We identify
relations between rate asymmetries which are valid in the SU(3) limit in the
standard model and we compute SU(3) breaking corrections to them, going beyond
the naive factorization by using the QCD improved factorization model of Beneke
{\it et al.}. Finally, in some processes as for example $BR(B^- \to
\eta^{\prime} K^-)$, we claim that one has to add SUSY contributions to the
Wilson coefficients. In these cases, we end with a $BR$ depending on three
parameters, whose values are constrained by the experimental data.
