Chiral Perturbation Theory for $f_{D_S}/f_D$ and $B_{B_S}/B_B$

Abstract

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.

10 pages, 2 figures