Improved Factorization Method in Studying B-meson Decays

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.