SU(3) flavor breaking in hadronic matrix elements forB−B¯oscillations

Results in the quenched approximation for SU(3) breaking ratios of the heavy-light decay constants and the $\Delta F=2\mathrm{}$ mixing matrix elements are reported. Using lattice simulations at ${6/g}^2=5.7\mathrm{}$, 5.85, 6.0, and 6.3, we directly compute the mixing matrix element $M_{\mathrm{hl}}=〈P_{\mathrm{hl}}|\overline{h}{\gamma }_{\mu }\left(1\mathrm{}-{\gamma }_5\right)l\overline{h}{\gamma }_{\mu }\left(1\mathrm{}-{\gamma }_5\right)l|P_{\mathrm{hl}}〉.$ Extrapolating to the physical $B$ meson states, $B^0$ and $B_s^0,$ we obtain $M_{\mathrm{bs}}{/M}_{\mathrm{bd}}{=1.76\mathrm{}\left(10\right)\mathrm{}}_{-42}^{+57\mathrm{}}$ 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, $f_{\mathrm{bs}}{/f}_{\mathrm{bd}}{=1.17\mathrm{}\left(2\right)\mathrm{}}_{-6}^{+12\mathrm{}}.$ For the $B$ parameters we find $B_{\mathrm{bs}}\left(2\mathrm{GeV}{)=B}_{\mathrm{bd}}\right(2\mathrm{GeV})=1.02\mathrm{}(13);$ we cannot resolve the SU(3) breaking effects in this case.