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

Abstract

Results in the quenched approximation for SU(3) breaking ratios of the heavy-light decay constants and the $\Delta F=2$ mixing matrix elements are reported. Using lattice simulations at $6/g^2=5.7$, 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 $M_{bs}/M_{bd}=1.76(10{)}_{-42}^{+57}$. 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, $f_{bs}/f_{bd}=1.17(2{)}_{-6}^{+12}$. For the B parameters we find $B_{bs}(2GeV)=B_{bd}(2GeV)=1.02(13)$; we cannot resolve the SU(3) breaking effects in this case.

Comments: 16 pages, 5 ps figures, Latex