affect NNLO terms that are of higher-order than we consider. We therefore vary f between f$_{0}$ = 115 MeV [34] and f$_{K}$ = 155 . 5 MeV [6] in order to estimate the systematic uncertainty due to the omission of higher-order terms in the chiral expansion. The use of f$_{0}$ in the SU (2) chiral limit, which the RBC and UKQCD Collaborations find to be about 10% lower than f$_{π}$ , leads to a difference from the central value for f$_{B}$$_{s}$/f$_{B}$$_{d}$ of 2.1% (2.2%) for APE (HYP) and from the central value for ξ of 2.3% for both APE and HYP. The use of f$_{K}$ leads to similar changes in f$_{B}$$_{s}$/f$_{B}$$_{d}$ of 2.1% and in ξ of 2.2%. We take the largest of the uncertainties enumerated above, which is obtained from the difference between the preferred linear plus NLO SU (2) HM χ PT fit and the purely linear fit, for the final estimate of the chiral extrapolation error; this leads to the values in the row labeled “chiral extrapolation” in Tab. VIII. Although we fix the value of the B $^{∗}$- B - π coupling (and hence the coefficient of the one- loop chiral logarithms) in the chiral extrapolation of our lattice data, g$_{B}$ ∗ Bπ is in fact poorly known from phenomenology. Hence we must vary the value of g$_{B}$ ∗ Bπ over a sensible range based on lattice QCD calculations and phenomenology in order to estimate the systematic errors in f$_{B}$$_{s}$/f$_{B}$$_{d}$ and ξ due to the uncertainty in the coefficient of the one-loop chiral logarithms. There has only been one unquenched lattice QCD calculation of the B $^{∗}$- B - π coupling with a complete associated error budget, which gives g$_{B}$ ∗ Bπ = 0 . 516(5)(50), where the first uncertainty is statistical and the second is systematic [62]. Although this value was computed in the static heavy-quark limit and neglects the effects of the dynamical strange quark, we take this as our central value because of its small statistical errors and full systematic error budget, as well as because it lies in the middle of the range of values presented in the literature. Another recent determination of g$_{B}$ ∗ Bπ = 0 . 44 ± 0 . 03 +0 . 07 − 0 00 in the static limit in two-flavor lattice QCD, where the errors are due to statistics and the chiral extrapolation uncertainty, is consistent with this result [65]. QCD sum rules and the relativistic quark model give a slightly lower value of g$_{B}$ ∗ Bπ ≈ 0 . 38 ± 0 . 08 [66]. The value of the B $^{∗}$- B - π coupling is expected to be close to the D $^{∗}$- D - π coupling because of heavy-quark symmetry. We can therefore also use lattice QCD calculations and phenomenological extractions of 35 B. Uncertainty due to g$_{B}$ ∗ Bπ