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The Electric Dipole Moment and CP Violation in $B \to X_s l^+ l^-$ in SUGRA Models with Nonuniversal Gaugino Masses

The constraints of electric dipole moments (EDMs) of electron and neutron on the parameter space in supergravity (SUGRA) models with nonuniversal gaugino masses are analyzed. It is shown that with a light sparticle spectrum, the sufficient cancellations in the calculation of EDMs can happen for all phases being order of one in the small tan$β$ case and all phases but $ϕ_μ$ ($|ϕ_μ| <\sim π/6$) order of one in the large tan$β$ case. This is in contrast to the case of mSUGRA in which in the parameter space where cancellations among various SUSY contributions to EDMs happen $|ϕ_μ|$ must be less than $π/10$ for small $tanβ$ and ${\cal{O}}(10^{-2})$ for large $tanβ$. Direct CP asymmetries and the T-odd polarization of lepton in $B\to X_s l^+l^-$ are investigated in the models. In the large tan$β$ case, $A_{CP}^2$ and $P_N$ for l=$μ$ ($τ$) can be enhanced by about a factor of ten (ten) and ten (three) respectively compared to those of mSUGRA.