Effect of SUSY phases on the $B_d^0-{\bar{B}}_d^0$ mixing in the minimal supergravity model

We investigate the effect of SUSY phases (${\theta }_A$ and ${\theta }_{\mu }$) on the $B_d^0-{\bar{B}}_d^0$ mixing in the minimal supergravity model. It is known that the complex phase ${\theta }_A$ $=$ arg($A$) ($A$ is the universal coefficient of the trilinear scalar couplings) is essentially unconstrained by the electric dipole moment experiment, while the phase ${\theta }_{\mu }$ $=$ arg($\mu$) ($\mu$ is the supersymmetric Higgsino mass) is strongly constrained to zero. We found that ${\theta }_A$ does not affect the phase of the $B^0_d - \bar{B}^0_d$mixingmatrixelement$M_{12}(B)$ by numerical analysis of the renormalization group equations. This means that the measurement of the $B^0_d

• \bar{B}^0_d$ mixing at the future B-factory could give the direct information on the parameters of the CKM matrix even in the framework of the minimal supergravity model with the SUSY phase ${\theta }_A$.