Ratios of $B$ and $D$ Meson Decay Constants in Improved Mock Meson Model

Abstract

We calculate the ratio $f_{B_s}/f_{B_d}$ by following the Oakes' method which is based on chiral symmetry breaking, but we improve his calculation by performing the calculation of the factor $<0|{\bar{b}}{\gamma}_5s|B_s>$/$<0|{\bar{b}}{\gamma}_5d|B_d>$ in the mock meson model. In this calculation we improved the mock meson model by using the value of the parameter $\beta$ which is obtained by the variational method in the relativistic quark model. We also calculate $f_{D_s}/f_{D_d}$, and then $(f_{B_s}/f_{B_d})\, /\, (f_{D_s}/f_{D_d})$. In this method we also obtain the ratio $f_{B_s}/f_{D_s}$ and $f_{B_d}/f_{D_d}$ which are important for the knowledge of CP violation and $B$-$\bar{B}$ mixing.