B0-B¯0mixing and theεKparameter in the minimal supergravity model

${\mathit{B}}^0$-B${\mathrm{¯}}^0$ mixing and a CP violation parameter in ${\mathit{K}}^0$-K${\mathrm{¯}}^0$ mixing, ${\mathrm{\epsilon }}_{\mathit{K}}$, are studied in the minimal supergravity model. We solve the one-loop renormalization group equations for the minimal supersymmetric standard model parameters numerically in order to determine the masses and mixings of the supersymmetric particles, while all off-diagonal (generation mixing) elements and phases of Yukawa coupling matrices and those of squark mass matrices are taken into account. Applying the radiative electroweak symmetry-breaking condition and phenomenological constraints including the recent measurement of the b→sγ inclusive branching ratio, we obtain the allowed parameter region. We have found that the present constraints still allow a parameter region where both ${\mathit{B}}^0$-B${\mathrm{¯}}^0$ mass splitting Δ${\mathit{M}}_{\mathit{B}}$ and ${\mathrm{\epsilon }}_{\mathit{K}}$ are ∼20% larger than the standard model values. By explicit numerical calculations, we have also found that the complex phase of the ${\mathit{B}}^0$-B${\mathrm{¯}}^0$ mixing matrix element in this model is almost the same as the standard model value within good accuracy in the whole allowed parameter region. It is shown that Δ${\mathit{M}}_{\mathit{B}}$ and ${\mathrm{\epsilon }}_{\mathit{K}}$ can put useful constraints on the supersymmetry’s parameter space when the Cabibbo-Kobayashi-Maskawa matrix elements are determined through the measurements of CP violations in B decay with future B factories. ©1996 The American Physical Society.