Effects of $A_t$ and $\mu$ phases on B and K physics in the effective supersymmetric models

In the minimal supersymmetric standard model (MSSM), the $\mu -$parameter and the trilinear coupling $A_t$ may be generically complex and can affect various observables at B factories. Working in the effective SUSY models and imposing the edm constraints from Chang-Keung-Pilaftsis (CKP) mechanism, we find that (i) there is no new large phase shift in the $B^0-\overline{B^0}$ mixing from the A_t and $\mu$ phases, (ii) CP violating dilepton asymmetry is smaller than 0.1%, (iii) the direct CP violation in $B\to X_s\gamma$ can be as large as $\sim \pm 16$, (iv) the $\mathrm{B}\mathrm{r}(B\to X_s{l}^{+}{l}^{-})$ can be enhanced by upto $\sim 85$ compared to the standard model (SM) prediction, and its correlation with $\mathrm{B}\mathrm{r}(B\to X_s\gamma )$ is distinctly different from the minimal supergravity scenario. Also, we find $1 \leq \epsilon_K / \epsilon_K^{SM} \leq 1.4$,and$\epsilon_K$cannotbesaturatedbythe{A}_{t}and$\mu$ phases alone : namely, $\mathrm{\mid }{ϵ}_K^{\mathrm{S}\mathrm{U}\mathrm{S}\mathrm{Y}}\mathrm{\mid }\le O({10}^{-5})$ if the phases of $\mu$ and A_t are the sole origin of CP violation.