to perform a study comparing the use of SU (2) versus SU (3) HM χ PT for the extrapolation of B -meson decay constants and mixing matrix elements to the physical quark masses in a future analysis when we have lighter data with smaller statistical errors in order to see which procedure leads to a more accurate determination of these quantities. Although we know that HM χ PT is the correct low-energy effective description of the lattice theory when the simulated quark masses are sufficiently light, we do not know a priori at what mass the range of validity of HM χ PT ends. Studies of the light pseudoscalar meson sector on the RBC/UKQCD domain-wall ensembles show that NLO χ PT does not describe the numerical data for the masses and decay constants when the pion masses are above about 420 MeV [34]. Since the lightest pion mass in our analysis is approximately 430 MeV, this suggests that most of our data may be too heavy for NLO HM χ PT to apply and that the inclusion of NNLO terms may be necessary. Unfortunately, because we only have three data points for each of the SU (3)-breaking ratios, we do not have enough data points to reliably constrain the values of the higher-order terms (there are two free parameters at NNLO in the SU (3) HM χ PT expressions, and even more at NNLO in SU(2) HM χ PT). When the masses of the light pseudoscalar mesons in the chiral logarithms are sufficiently heavy, however, the logarithms can be well-approximated by polynomials. We therefore choose to fit the data to a linear fit function that is constrained to be equal to one in the SU (3) limit ( m$_{l}$ → m$_{s}$ ) and then match this result onto the NLO SU (2) HM χ PT expression at the location of our lightest data point ( am$_{l}$ = 0 . 01), which we believe is sufficiently light that NLO SU (2) HM χ PT should apply. Although the behavior of the data is unlikely to be strictly linear in the heavy-mass region, the statistical errors in our data points are sufficiently large (as great as ∼ 8%) that we can successfully perform a linear fit and obtain a good χ $^{2}$/ dof without the addition of higher-order polynomial terms. 3 Furthermore, we cannot reliably determine the size of a quadratic term if we include one in the fit. Given our poor statistical errors, however, we cannot exclude the possibility of other fit functions, and we use alternate fit forms as one way to estimate the chiral extrapolation error. We also vary the location of the SU (2) HM χ PT matching point and the parameters that enter the SU (2) HM χ PT expressions, and consider matching onto SU (3) HM χ PT. All of these 3 Because the data points for the SU (3)-breaking ratios in Tables V and VI were generated on three different sea-quark ensembles, they are statistically independent; thus the uncorrelated χ $^{2}$/ dof correctly reflects the goodness-of-fit. 26