9 In addition to the operators relevant for b → sγ , there are two new operators: The amplitude for the decay B → X$_{s}$ l $^{+}$l − in SM4 is given by where P$_{L,R}$ = (1 ∓ γ$_{5}$ ) / 2 and q is the sum of l + and l − momenta. Here the Wilson coefficients are evaluated at µ = m$_{b}$ . The differential branching ratio is given by where Here z ≡ q $^{2}$/m2 $_{b}$, t ≡ m$_{l}$/m$_{b}$ and ˆ m$_{q}$ = m$_{q}$/m$_{b}$ for all quarks q . In the framework of SM4, the Wilson coefficients C tot 7 , C tot 9 and C tot 10 are given by where the function Y ( z ) is given in [55]. The measurements of the B → X$_{s}$ℓ $^{+}$ℓ − in the two regions, so called low q 2 ( q 2 < ∼ 6 GeV $^{2}$) and high q 2 ( q 2 > ∼ 14 GeV $^{2}$), are complementary as they have different sensitivities to the short distance physics. Compared to small q $^{2}$, the rate in the large q 2 region has a smaller renormalization scale dependence and m$_{c}$ dependence. Although the rate is smaller at large q $^{2}$, the experimental efficiency is better. Large q 2 constrains the X$_{s}$ to have small invariant mass, m$_{X}$$_{s}$ , which suppresses the background from B → X$_{c}$ℓ − ¯ ν → X$_{s}$ℓ $^{+}$ℓ − ν ¯ ν . To suppress this background at small q 2 region an upper cut on m$_{X}$$_{s}$ is required, complicating the theoretical description due to the dependence of the measured rate on the shape function, C tot 7 , 10 = C$_{7}$$_{,}$$_{10}$ ( m$_{b}$ ) + V ∗ t ′ $_{s}$V$_{t}$ ′ b V ∗ $_{ts}$V$_{tb}$ C t ′ 7 , $_{10}$( m$_{b}$ ) , (23) C tot 9 = C$_{9}$ ( m$_{b}$ ) + Y ( z ) + V ∗ t ′ $_{s}$V$_{t}$ ′ b V ∗ $_{ts}$V$_{tb}$ C t ′ 9 ( m$_{b}$ ) , (24) D ( z ) = | C tot 9 | 2 ( 1 + 2 t 2 z ) (1 + 2 z ) + 4 | C tot 7 | 2 ( 1 + 2 t 2 z )( 1 + 2 z ) + | C tot 10 | 2 [ (1 + 2 z ) + 2 t 2 z (1 − 4 z ) ] + 12Re( C tot 7 C $^{tot}$∗ 9 ) ( 1 + 2 t 2 z ) . (22) d Br ( B → X$_{s}$ l $^{+}$l − ) d z = α $^{2}$B ( B → X$_{c}$e ¯ ν ) 4 π $^{2}$f ( ˆ m$_{c}$ ) κ ( ˆ m$_{c}$ ) (1 − z ) 2 ( 1 − 4 t 2 z ) 1 / 2 | V ∗ $_{tb}$V$_{ts}$ | 2 | V$_{cb}$ | 2 D ( z ) , (21) M = G$_{F}$ α √$_{2}$$_{π}$ V ∗ $_{ts}$V$_{tb}$ [ C tot 9 ¯ sγ$_{µ}$P$_{L}$b ¯ lγ$_{µ}$l + C tot 10 ¯ sγ$_{µ}$P$_{L}$b ¯ lγ$_{µ}$γ$_{5}$l − 2 m$_{b}$ C tot 7 q 2 ¯ siσ$_{µν}$q $^{ν}$P$_{R}$ b ¯ lγ$_{µ}$l ] , (20) Q$_{9}$ = (¯ sb )$_{V}$ − $_{A}$( ¯ ll )$_{V}$ , Q$_{10}$ = (¯ sb )$_{V}$ − $_{A}$( ¯ ll )$_{V}$ . (19)