B0−B¯0mixing and violations ofCPsymmetry

In view of a possible long lifetime for $B$ mesons, ${\tau }_B\sim {10}^{-12\mathrm{}}$ sec, we reexamine predictions of the standard model for $B^0-{\overline{B}}^0$ mixing. We estimate theoretical uncertainties in the computation of the relevant matrix element by comparing the vacuum-saturation approximation with predictions obtained in the bag model and in the harmonic-oscillator model with and without relativistic corrections. For the $B_d-{\overline{B}}_d$ system we find mixing leading to a like-sign dilepton yield of at most a few percent of the opposite-sign dilepton rate; $B_s-{\overline{B}}_s$ mixing should be stronger. While very little $\mathrm{CP}$ violation is expected in $B^0-{\overline{B}}^0$ mixing, we find that certain $\mathrm{CP}$ asymmetries in on-shell $B_d$ decays could reach a level of 10% or more.