total error budgets for both quantities are given at the end of the section in Table VIII. As described in the previous section, we extrapolate our data to the physical quark masses using a linear fit matched onto NLO SU (2) HM χ PT at the value of our lightest data point. The SU (2) expressions are derived using the symmetries of the lattice theory; therefore they contain the correct dependence of the B -meson decay constants and mixing matrix elements on the quark mass and lattice spacing through NLO when the quark masses are sufficiently light. Given the large light-quark masses used in our simulations, however, it may be that the SU (2) chiral logarithms do not become important until the pion mass is even lighter than the range of our data. Thus we vary the location of the matching point as one way to estimate the systematic uncertainty due to the chiral extrapolation. In addition, because we use NLO SU (2) HM χ PT to obtain our central value, we must estimate the systematic uncertainty due to the truncation of higher-orders in HM χ PT. We do this in several ways: (i) by explicitly adding higher-order terms to the linear plus SU (2) HM χ PT fit function, (ii) by matching the linear fit onto the NLO SU (3) HM χ PT expressions, and (iii) by varying the value of the low-energy constant f in the coefficient of the NLO chiral logarithms. Because we do not know a priori at what mass the SU (2) chiral logarithms become important, we vary the point at which we match the linear fit onto NLO SU (2) HM χ PT in order to estimate the systematic uncertainty due to the choice of matching point. At the matching point used in the preferred fit, the ratio of the light up-down quark mass to the strange valence-quark mass is am$_{l}$/am$_{s}$ ≈ 0 . 28 and to the strange sea quark mass is am$_{l}$/am$_{h}$ = 0 . 25. Since both of these quantities are small, we expect the strange quark can be integrated out of the chiral effective theory and that SU (2) HM χ PT is applicable in this region. As the light-quark mass decreases, SU (2) becomes an even better approximation. At light-quark masses above this point, however, the ratios am$_{l}$/am$_{s}$ and am$_{l}$/am$_{h}$ are no longer small expansion parameters, and SU (2) will eventually cease to apply. Therefore, when we estimate the systematic error due to the choice of matching point, we only consider extrapolations in which the matching point is closer to the chiral limit than in the preferred fit. The limiting case is where the matching point is at the chiral limit, which corresponds to a purely linear extrapolation. Although the choice of a linear fit is not based on effective 31 A. Chiral extrapolation fit ansatz