SU(3) Flavor Breaking in Hadronic Matrix Elements for $B-\bar{B}$ Oscillations

Results in the quenched approximation for SU(3) breaking ratios of the heavy-light decay constants and the $\mathrm{\Delta }F=2$ mixing matrix elements are reported. Using lattice simulations at $6\mathrm{/}{g}^2=5.7$, 5.85, 6.0, and 6.3, we directly compute the mixing matrix element $M_{hl}=< \bar P_{hl}|\bar h \gamma_\mu (1-\gamma_5)l \bar h \gamma_\mu(1-\gamma_5)l|P_{hl}>$. Extrapolating to the physical B meson states, $B^0$ and $B_s^0$, we obtain $M_{bs}/M_{bd} =1.76(10)^{+57}{-42}$. in the continuum limit. The systematic error includes the errors within the quenched approximation but not the errors of quenching. We also obtain the ratio of decay constants, $f_{bs}\mathrm{/}{f}_{bd}=1.17(2{)}_{-6}^{+12}$. For the B parameters we find $B{bs}(2 GeV)=B_{bd}(2 GeV)=1.02(13)$; we cannot resolve the SU(3) breaking effects in this case.