New Physics in $B_{d,s}$-${\text{Bbar}}_{d,s}$ mixings and $B_{d,s}\to {\mu }^{+}{\mu }^{-}$ decays

A new way of probing new physics in the $B$ meson system is provided. We define double ratios for the observables of $B_{d,s}$-${\text{Bbar}}_{d,s}$ mixings and $B_{d,s}\to {\mu }^{+}{\mu }^{-}$ decays, and find simple relations between the observables. By using the relations we predict the yet-to-be measured branching ratio of $B_d\to {\mu }^{+}{\mu }^{-}$ to be $(0.809\sim 1.03)\times {10}^{-10}$, up to the new physics models.