27  3e-07  6e-07  9e-07  1.2e-06  1.5e-06  1.8e-06  2.1e-06  2.4e-06 -1 -0.8 -0.6 -0.4 -0.2  0 Br( B s  ->  + -  ) S  2e-09  4e-09  6e-09  8e-09  1e-08  1.2e-08 -1 -0.8 -0.6 -0.4 -0.2  0 Br( B s  ->   ) S FIG. 7: Correlation between branching fraction in B$_{s}$ → µ $^{+}$µ − (left panel) and B$_{s}$ → τ $^{+}$τ − (right panel) with S$_{ψφ}$ , where the red and blue regions correspond to m$_{t}$ ′ = 400 and 600 GeV respectively, the horizontal lines represent the SM limit for Br ( B$_{s}$ → ℓ $^{+}$ℓ − ) whereas the vertical lines represent the 2 σ experimental range for S$_{ψφ}$ . SM4, the branching ratio of B$_{s}$ → l $^{+}$l − is given by The branching ratio of B$_{s}$ → l $^{+}$l − can be predicted with higher accuracy by correlating it with the B$_{s}$ − ¯ B$_{s}$ mixing and then considerable uncertainty due to mixing angle and f$_{B}$$_{s}$ gets removed. We have where B$_{bs}$ is the “Bag-parameter” for B$_{s}$ mesons for which lattice result is given by [108], however, in order to be conservative we use the value 1 . 33 ± 0 . 15 . In eq. 89 the parameter Δ ′ is defined as, In fig. 7 we have shown the correlation between the branching fraction Br ( B$_{s}$ → ℓ $^{+}$ℓ − ) and CP asymmetry in B$_{s}$ → ψφ , it is clear that there are possibilities for appreciably different Δ ′ = [ η$_{t}$S$_{0}$ ( x$_{t}$ ) + η$_{t}$ ′ ( V$_{t}$ ′ $_{s}$V ∗ t ′ $_{b}$) 2 ( V$_{ts}$V ∗ $_{tb}$) 2 S$_{0}$ ( x$_{t}$ ′ ) + 2 η$_{tt}$ ′ ( V$_{t}$ ′ $_{s}$V ∗ t ′ $_{b}$) ( V$_{ts}$V ∗ $_{tb}$) S$_{0}$ ( x$_{t}$, x$_{t}$ ′ ) ] . (91) B$_{bs}$ = 1 . 33 ± 0 . 06 , (90) Br ( B$_{s}$ → l $^{+}$l − ) = 3 α $^{2}$τ$_{B}$$_{s}$ m 2 l 8 πB$_{bs}$m 2 W √ 1 − 4 m 2 l m 2 B$_{s}$ ∣ C tot 10 ∣ ∣$^{2}$ | Δ $^{′}$| Δ M$_{s}$ , (89) Br ( B$_{s}$ → l $^{+}$l − ) = G 2 $_{F}$α $^{2}$m$_{B}$$_{s}$ m 2 $_{l}$f 2 $_{B$_{s}$}$τ$_{B}$$_{s}$ 16 π 3 | V$_{tb}$V ∗ ts | 2 √ 1 − 4 m 2 l m 2 B$_{s}$ ∣ C tot 10 ∣ ∣$^{2}$ . (88)