We discuss (Formula presented) decay in both constrained and unconstrained supersymmetric models with explicit (Formula presented) violation within the minimal flavor violation scheme by including (Formula presented)-enhanced large contributions beyond the leading order. In this analysis, we take into account the relevant cosmological and collider bounds, as well as electric dipole moment constraints. In the unconstrained model, there are portions of the parameter space yielding a large (Formula presented) asymmetry at leading order (LO). In these regions, we find that the (Formula presented) phases satisfy certain sum rules, e.g., the sum of the phases of the (Formula presented) parameter and the top squark trilinear coupling centralize around (Formula presented) with a width determined by the experimental bounds. In addition, at large values of (Formula presented) the sign of the (Formula presented) asymmetry tracks the sign of the gluino mass, and the (Formula presented) asymmetry is significantly larger than the LO prediction. In the constrained minimal supersymmetric standard model based on minimal supergravity, we find that the decay rate is sensitive to the phase of the universal trilinear coupling. This sensitivity decreases at large values of the universal gauino mass. We also show that, for a given set of the mass parameters, there exists a threshold value of the phase of the universal trilinear coupling which grows with (Formula presented) and beyond which the experimental bounds are satisfied. In both supersymmetric scenarios, the allowed ranges of the (Formula presented) phases are wide enough to have phenomenological consequences.
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