content_image/331903.jpg content_image/331901.jpg content_image/331900.jpg content_image/331899.jpg
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, 

<img src='content_image/331903.jpg'>

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 

<img src='content_image/331901.jpg'>

## G. Branching fraction B → X$_{s}$ν ¯ ν 

<img src='content_image/331900.jpg'>

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] 

<img src='content_image/331899.jpg'>

