The ratio (${\mathit{f}}_{\mathit{B}\mathit{s}}$/${\mathit{f}}_{\mathit{B}}$)/(${\mathit{f}}_{\mathit{D}\mathit{s}}$/${\mathit{f}}_{\mathit{D}}$) and its implications for B-B¯ mixing

We observe that quantities like (${\mathit{f}}_{\mathit{B}\mathit{s}}$/${\mathit{f}}_{\mathit{B}}$)/(${\mathit{f}}_{\mathit{D}\mathit{s}}$/${\mathit{f}}_{\mathit{D}}$) are predicted to be unity both by heavy quark and by light quark flavor symmetries. Hence, the deviation from the symmetry prediction must be simultaneously small in both symmetry breaking parameters, i.e., order of the ratio of light to heavy quark masses. We estimate the size of the correction. We observe that the ratio of (ΔM/Γ) for ${\mathit{B}}_{\mathit{s}\mathrm{-}}$B${\mathrm{¯}}_{\mathit{s}}$ to B-B¯ mixing can be expressed in terms of the measurable ratio ${\mathit{f}}_{\mathit{D}\mathit{s}}$/${\mathit{f}}_{\mathit{D}}$ with good precision. We comment on applications of these ideas to other processes.