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which is absent at large q $^{2}$. In the low q 2 region the dominant contribution to B$_{s}$ → X$_{s}$ℓ $^{+}$ℓ − comes from virtual photon and much less from Z . It is the Z that is very sensitive to m$_{t}$ ′ as that amplitude grow with m 2 t ′ . The photonic contribution cares only about the electric charge, modulo logarithmic QCD corrections. For these reasons we will be using the branching ratio only in the high q 2 region to constrain SM4. 

The theoretical calculations shown above for the branching ratio of B → X$_{s}$ l $^{+}$l − are rather uncertain in the intermediate q 2 region (7 GeV 2 < q 2 < 12 GeV $^{2}$) owing to the vicinity of charmed resonances. The predictions are relatively more robust in the low- q 2 (1 GeV 2 < q 2 < 6 GeV $^{2}$) and the high- q 2 (14 . 4 GeV 2 < q 2 < m 2 $_{b}$) regions. 

For m$_{t}$ ′ > 300 GeV, Br ( B → X$_{s}$ l $^{+}$l − ) is completely dominated by the Wilson coefficient C tot 10 . Hence in our numerical analysis, we neglect the small z -dependence in C tot 9 . 

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Within SM, B$_{q}$ − ¯ B$_{q}$ mixing ( q = d, s ) proceeds to an excellent approximation only through the box diagrams with internal top quark exchanges. In case of four generations there is an additional contribution to B$_{q}$ − ¯ B$_{q}$ mixing coming from the virtual exchange of the fourth generation up quark t ′ . The mass difference Δ M$_{q}$ in SM4 is given by 

where 

where x$_{t}$ = m 2 $_{t}$/m 2 $_{W}$, x$_{t}$ ′ = m 2 t ′ /M 2 W and 

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