The $B \to K\pi$ Puzzle and Supersymmetric Models

In the light of new experimental results on $B \to K\pi$ decays, we study the decay processes $B \to K \pi$ in the framework of both R-parity conserving (SUGRA) and R-parity violating supersymmetric models. We find that any possible deviations from the Standard Model indicated by the current data for the branching ratios and the direct CP asymmetries of $B \to K\pi$ can be explained in both R-parity conserving SUGRA and R-parity violating SUSY models. However, there is a difference between the predictions of both models to the time-dependent CP asymmetry observable $S_{K_{_S} \pi^0}$ whose current experimental results include large uncertainties. We demonstrate that this difference can be useful for testing both models with more accurate data for $S_{K_{S} \pi^0}$ and $A_{CP}^{+-}$ in the near future.