2% × $^{(}$˜ m$_{s}$ − ˜ m$_{d}$ ) / Λ$_{QCD}$ ∼ 0 . 4% error in the SU (3)-breaking ratios f$_{B}$$_{s}$/f$_{B}$$_{d}$ and ξ . In order to obtain the total systematic error in f$_{B}$$_{s}$/f$_{B}$$_{d}$ and ξ due to the light- and strange-quark masses, we add the three estimates for the light-quark error, the strange valence-quark error, and the strange sea-quark error in quadrature. This leads to an error in f$_{B}$$_{s}$/f$_{B}$$_{d}$ of 0.6% for both the APE and HYP data and an error in ξ of 0.6% (0.5%) for the APE (HYP) data. pseudoscalar meson masses and decay constants. We can therefore estimate the effect of the incorrect strange sea-quark mass on f$_{B}$$_{s}$/f$_{B}$$_{d}$ and ξ based on observations in the light pseudoscalar meson sector. Preliminary studies by RBC and UKQCD find that reweighting to the physical strange sea-quark mass leads to no statistically significant change in m$_{π}$ and a 2% change in f$_{π}$ [78]. If we assume that the unphysical strange sea-quark mass leads to a 2% error in the decay constants and matrix elements, then it will lead to a 2% × m$_{s}$ − m$_{d}$ ) / Λ$_{QCD}$ ∼ 0 . 4% error in the SU (3)-breaking ratios f$_{B}$$_{s}$/f$_{B}$$_{d}$ and ξ . We estimate the uncertainties in the ratios f$_{B}$$_{s}$/f$_{B}$$_{d}$ and ξ due to finite volume effects using one-loop finite-volume HM χ PT. The effect of the finite spatial lattice volume is simply to turn the one-loop integrals that appear in the HM χ PT expressions into sums, which we show in Eqs. (D13)-(D14). It is therefore straightforward to compute the corrections to our data given the parameters of our simulations. We find that the one-loop finite volume corrections are about 1% at our lightest quark mass and even less at heavier masses. We therefore take 1% to be the systematic uncertainty in f$_{B}$$_{s}$/f$_{B}$$_{d}$ and ξ due to the finite spatial lattice volume. Because we work in the static heavy-quark limit, our results for f$_{B}$$_{s}$/f$_{B}$$_{d}$ and ξ neglect relativistic effects due to the finite b -quark mass. We therefore estimate the size of the omitted relativistic corrections using power-counting. The leading 1 /m$_{b}$ corrections to the decay constants and matrix elements are of O (Λ$_{QCD}$ /m$_{b}$ ). Because we are only computing the SU (3)-breaking ratios f$_{B}$$_{s}$/f$_{B}$$_{d}$ and ξ , however, relativistic effects in these quantities are further suppressed by a factor of ( m$_{s}$ − m$_{d}$ ) / Λ$_{QCD}$. Therefore we expect the relativistic 41 H. 1 /m$_{b}$ corrections G. Finite-volume errors