28 predictions in SM4 compared to SM, enhanced or diminished by a factor of O (3). Note also that enhanced branching fractions correspond to a large CP asymmetry in B$_{s}$ → ψφ and smaller branching fractions correspond to smaller asymmetry. The corresponding upper limit on the branching fractions are given by, However, when S$_{ψφ}$ is close to its SM value i.e when the CP violating phase, φ s t ′ , of V$_{t}$ ′ s is close to zero, the branching fractions reduce from their SM value since | C tot 10 | and δ ′ in eq. 91 are reduced from its SM value due to destructive interference with SM4 counterpart. The decays B → X$_{s}$ν ¯ ν are the theoretically cleanest decays in the field of rare B -decays. They are dominated by the same Z $^{0}$-penguin and box diagrams involving top quark ex- changes which we encounter in the case of K$_{L}$ → π $^{0}$ν ¯ ν , since the change of the external quark flavors has no impact on the m$_{t/t}$ ′ dependence, the later is fully described by the function X ( x$_{t/t}$ ′ ) which includes the NLO corrections. The charm contribution is negligible here. The effective Hamiltonian for the decay B → X$_{s}$ν ¯ ν is given by with The calculation of the branching fractions for B → X$_{s}$ν ¯ ν can be done in the spectator model corrected for short distance QCD effects. Normalizing it to Br ( B → X$_{c}$ν ¯ ν ) and summing over three neutrino flavors one finds [56, 109] Br ( B → X$_{s}$ν ¯ ν ) Br B X$_{c}$e ¯ ν = 3 α 2 4 π $^{2}$sin$^{4}$Θ$_{W}$ ¯ η f ( z ) κ ( z ) 1 | V$_{cb}$ | 2 ∣ λ$_{t}$X ( x$_{t}$ ) + λ$_{t}$ ′ X ( x$_{t}$ ′ ) ∣ ∣$^{2}$ = ˜ C $^{2}$¯ η | V$_{cb}$ | $^{2}$f ( z ) κ ( z ) , (95) X ( x ) = x 8 [ 2 + x x − 1 + 3 x − 6 ( x 1) 2 ln x ] (94) H eff = G$_{F}$ √$_{2}$ α 2 π sin $^{2}$Θ$_{w}$ ( V ∗ $_{tb}$V$_{ts}$ X ( x$_{t}$ ) + V ∗ t ′ $_{s}$V$_{t}$ ′ $_{d}$X ( x$_{t}$ ′ )) ( ¯ bs )$_{V}$ − $_{A}$(¯ νν )$_{V}$ − A + h.c. (93) G. Branching fraction B → X$_{s}$ν ¯ ν Br ( B$_{s}$ → µ $^{+}$µ − ) < 8 . 0 × 10 − 9 m$_{t}$ ′ = 400 GeV , < 1 . 2 × 10 − $^{8}$, m$_{t}$ ′ = 600 GeV , Br ( B$_{s}$ → τ $^{+}$τ − ) < 1 . 8 × 10 − 6 m$_{t}$ ′ = 400 GeV , < 2 . 4 × 10 − $^{6}$, m$_{t}$ ′ = 600 GeV . (92)