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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 

<img src='content_image/354468.jpg'>

<img src='content_image/354469.jpg'>

<img src='content_image/354467.jpg'>

where 

<img src='content_image/354466.jpg'>

Here z ≡ q $^{2}$/m2 $_{b}$, t ≡ m$_{l}$/m$_{b}$ and ˆ m$_{q}$ = m$_{q}$/m$_{b}$ for all quarks q . tot tot 

In the framework of SM4, the Wilson coefficients C 7 , C 9 and C tot 10 are given by 

where the function Y ( z ) is given in [55]. 

<img src='content_image/354464.jpg'>

<img src='content_image/354465.jpg'>

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, 

