The $\Delta S = 2$ $b \to \bar d ss$ transition proceeds via the box - diagram in the Standard Model with a branching ratio calculated to be below $10^{ -11}$, thus providing an appropriate testing ground for physics beyond the Standard Model. We analyze the $\Delta S = 2$ two - body $B^- \to K^{ *-} \bar K^{ *0}$, $B^- \to K^- \bar K^{ 0}$, $B^- \to K^{ *-} \bar K^{ 0}$ and $B^- \to K^{ -} \bar K^{ *0}$ exclusive decays which are driven by the $b \to \bar d ss$ transition, both in the Standard Model and in several extensions of it. The models considered are the minimal supersymmetric model with and without ${ \cal R}$ parity conservation and two Higgs doublet models. All four modes are found to have a branching ratio of the order of $10^{ -13}$ in the Standard Model, while the expected branching ratio in the different extensions vary between $10^{ -9} - 10^{ -6}$.
Categories: hep-ph