  The decay constants for the $D$ and $D_S$ mesons, denoted $f_D$ and $f_{D_S}$
respectively, are equal in the $SU(3)_V$ limit, as are the hadronic amplitudes
for $B_S-\bar B_S$ and $B^0-\bar B^0$ mixing. The leading $SU(3)_V$ violating
contribution to $\left( f_{D_S} / f_D \right)$ and to the ratio of hadronic
matrix elements relevant for $B_S-\bar B_S$ and $B^0-\bar B^0$ mixing
amplitudes are calculated in chiral perturbation theory. We discuss the
formalism needed to include both meson and anti-meson fields in the heavy quark
effective theory.
