10 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 . 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 S$_{0}$ ( x$_{t}$ ) = 4 x$_{t}$ − 11 x 2 t + x 3 t 4(1 − x$_{t}$ ) 2 − 3 2 x 3 $_{t}$ln x$_{t}$ (1 − x$_{t}$ ) 3 , (27) S$_{0}$ ( x$_{t}$ ′ ) = S$_{0}$ ( x$_{t}$ → x$_{t}$ ′ ) , (28) S$_{0}$ ( x$_{t}$, x$_{t}$ ′ ) = x$_{t}$x$_{t}$ ′ { ln x$_{t}$ ′ x$_{t}$ ′ − x$_{t}$ [ 1 4 + 3 2 1 1 − x$_{t}$ ′ − 3 4 1 (1 − x$_{t}$ ′ ) 2 ] − ln x$_{t}$ x$_{t}$ ′ − x$_{t}$ [ 1 4 + 3 2 1 1 − x$_{t}$ − 3 4 1 (1 − x$_{t}$ ) 2 ] − 3 4 1 (1 − x$_{t}$ )(1 − x$_{t}$ ′ ) } . (29) M$_{12}$ = G 2 $_{F}$m 2 W 12 π 2 m$_{B}$$_{q}$B$_{bq}$f 2 B$_{q}$ { η$_{t}$ ( V$_{tq}$V ∗ $_{tb}$) $^{2}$S$_{0}$ ( x$_{t}$ ) + η$_{t}$ ′ ( V$_{t}$ ′ $_{q}$V ∗ t ′ $_{b}$) $^{2}$S$_{0}$ ( x$_{t}$ ′ ) +2 η$_{tt}$ ′ ( V$_{tq}$V ∗ $_{tb}$) ( V$_{t}$ ′ $_{q}$V ∗ t ′ $_{b}$) S$_{0}$ ( x$_{t}$, x$_{t}$ ′ ) } , (26) Δ M$_{q}$ = 2 | M$_{12}$ | , (25) E. B$_{q}$ − ¯ B$_{q}$ mixing