content_image/350947.jpg content_image/350946.jpg content_image/350945.jpg content_image/350944.jpg content_image/350943.jpg content_image/350942.jpg content_image/350941.jpg content_image/350939.jpg
The quark level transition b → sγ induces the inclusive B → X$_{s}$γ decay. The effective Hamiltonian for b → sγ can be written in the following form 

<img src='content_image/350947.jpg'>

where the form of operators O$_{i}$ ( µ ) and the expressions for calculating the Wilson coefficients C$_{i}$ ( µ ) are given in [55]. The introduction of fourth generation changes the values of Wilson coefficients C$_{7}$ and C$_{8}$ via the virtual exchange of the t ′ -quark and can be written as 

<img src='content_image/350946.jpg'>

The values of C t ′ 7 , 8 can be calculated from the expression of C$_{7}$$_{,}$$_{8}$ by replacing the mass of t -quark by m$_{t}$ ′ . 

In order to reduce the uncertainties arising from b –quark mass, we consider the following ratio 

In leading logarithmic approximation this ratio can be written as [56] 

<img src='content_image/350945.jpg'>

<img src='content_image/350944.jpg'>

Here the Wilson coefficient C$_{7}$ is evaluated at the scale µ = m$_{b}$ . The phase space factor f ( ˆ m$_{c}$ ) in Br ( B → X$_{c}$e ¯ ν ) is given by [57] 

κ ( ˆ m$_{c}$ ) is the 1-loop QCD correction factor [57] 

<img src='content_image/350943.jpg'>

<img src='content_image/350942.jpg'>

Here ˆ m$_{c}$ = m$_{c}$/m$_{b}$ . 

The quark level transition b → s l $^{+}$l − is responsible for the inclusive decay B → X$_{s}$ l $^{+}$l − . We apply the same approach introduced for b → sγ . The effective Hamiltonian for the decay b → s l $^{+}$l − is given by 10 

<img src='content_image/350941.jpg'>

<img src='content_image/350939.jpg'>

