TABLE VIII: Total error budget for the SU (3)-breaking ratios f$_{B}$$_{s}$/f$_{B}$$_{d}$ and ξ . Each source of uncertainty is discussed in Sec. VI, and is rounded to the nearest percentage. f$_{B}$$_{s}$/f$_{B}$$_{d}$ ξ uncertainty APE HYP APE HYP statistics 8% 4% 6% 5% chiral extrapolation 7% 7% 7% 7% uncertainty in g$_{B}$ ∗ Bπ 3% 3% 2% 2% discretization error 3% 3% 4% 4% renormalization factors 0% 0% 2% 2% scale and quark mass uncertainties 1% 1% 1% 1% finite volume error 1% 1% 1% 1% 1 /m$_{b}$ corrections 2% 2% 2% 2% total systematics 9% 9% 9% 9% corrections to these quantities to be approximately where the scale Λ$_{QCD}$ cancels in the ratio, and we use the average MS quark masses listed in the PDG [6]. Using the experimentally-measured ratio of masses m$_{B}$ 0 $_{s}$/m$_{B}$ 0 d = 5366 . 6 / 5279 . 5 = 1 . 0165 [6], we obtain the following values for the SU (3)-breaking ratios of B -meson decay constants and mixing matrix elements: 42 VII. RESULTS AND CONCLUSIONS f$_{B}$$_{s}$ f$_{B}$$_{d}$ =   $^{1}$$^{.}$$^{16(09)(10)}$ APE 1 . 14(05)(10) HYP and ξ =   $^{1}$$^{.}$$^{13(07)(10)}$ APE 1 . 13(05)(10) HYP , (85) where the first errors are statistical and the second are the sum of the individual systematic errors added in quadrature. We find good agreement between the different link-smearings, indicating that, despite the use of a single lattice spacing, discretization errors are small Λ$_{QCD}$ m$_{b}$ × m$_{s}$ − m$_{d}$ Λ$_{QCD}$ ∼ 2% , (84)