Effect of supersymmetric CP phases on the $B \to X_s \gamma$ and $B \to X_s l^+ l^-$ decays in the minimal supergravity model

Abstract

We investigate the effect of supersymmetric CP violating phases on the $B\to X_s \gamma$ and $B\to X_s l^+l^-$ decays in the minimal supergravity model. We show that the phase of the trilinear scalar coupling constant for top squarks is strongly suppressed and aligned to that of the gaugino mass due to a renormalization effect from the Planck scale to the electroweak scale. As a result, the effect of supersymmetric CP violating phases on the $B \to X_s \gamma$ and $B \to X_s l^+ l^-$ decays are small taking into account the neutron and the electron electric dipole moment constraints. For the $B \to X_s\gamma$ decay, the amplitude has almost no new CP violating phase and the direct CP asymmetry is less than 2 %. For the $B \to X_s l^+ l^-$ decay, the branching ratio can be sizably different from that in the standard model only when the sign of the $B \to X_s \gamma$ amplitude is opposite to that in the standard model.