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Search for new physics in $ΔS = 2$ two - body (VV, PP, VP) decays of the B^- - meson

The $ΔS = 2$ $b \to \bar d ss$ 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 $ΔS = 2$ 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 $10^{-9} - 10^{-6}$.