8 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 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 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] 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] Here ˆ m$_{c}$ = m$_{c}$/m$_{b}$ . H eff = 4 G$_{F}$ √$_{2}$ V ∗ $_{ts}$V$_{tb}$ 10 ∑ i =1 C$_{i}$ ( µ ) Q$_{i}$ ( µ ) . (18) 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 D. B → X$_{s}$ l $^{+}$l − decay κ ( ˆ m$_{c}$ ) = 1 − 2 α$_{s}$ ( m$_{b}$ ) 3 π [( π 2 − 31 4 ) (1 − ˆ m$_{c}$ ) 2 + 3 2 ] . (17) f ( ˆ m$_{c}$ ) = 1 − 8 ˆ m 2 c + 8 ˆ m 6 c − ˆ m 8 c − 24 ˆ m 4 c ln ˆ m$_{c}$ . (16) R = | V ∗ $_{ts}$V$_{tb}$ | 2 | V$_{cb}$ | 2 6 α | C tot 7 ( m$_{b}$ ) | 2 πf ( ˆ m$_{c}$ ) κ ( ˆ m$_{c}$ ) . (15) R = Br ( B → X$_{s}$γ ) Br ( B X$_{c}$e ¯ ν$_{e}$ ) . C tot 7 , $_{8}$( µ ) = C$_{7}$$_{,}$$_{8}$ ( µ ) + V ∗ t ′ $_{s}$V$_{t}$ ′ b V ∗ $_{ts}$V$_{tb}$ C t ′ 7 , $_{8}$( µ ) . (14) H eff = 4 G$_{F}$ √$_{2}$ V ∗ $_{ts}$V$_{tb}$ 8 ∑ i =1 C$_{i}$ ( µ ) Q$_{i}$ ( µ ) , (13)