36 λ ’s contain the weak phase information and A$_{i}$ ’s are associated with the strong phases. Thus one can explicitly separate the strong and weak phases and write the amplitudes as where a = | λ$_{u}$/λ$_{c}$ | , b = | λ$_{t}$ ′ /λ$_{c}$ | , − γ is the weak phase of V$_{ub}$ and φ$_{s}$ is the weak phase of λ$_{t}$ ′ . r = | A$_{u}$/A$_{c}$ | , r ′ = | A$_{t}$ ′ /A$_{c}$ | , and δ$_{1}$ ( δ$_{2}$ ) is the relative strong phases between A$_{u}$ and A$_{c}$ ( A$_{t}$ ′ and A$_{c}$ ). From these amplitudes one can obtain the direct and mixing induced CP asymmetry parameters as where R = 1 + ( ra ) 2 + ( r ′ b ) 2 and To find out the new contributions due to the fourth generation effect, first we have to evaluate the new Wilson coefficients C t ′ i . The values of these coefficients at the M$_{W}$ scale can be obtained from the corresponding contributions from the t quark by replacing the mass of t quark in the Inami-Lim functions [123] by t ′ mass. These values can then be evolved to the m$_{b}$ scale using the renormalization group equation [60] where C is the 10 × 1 column vector of the Wilson coefficients and U$_{5}$ is the five flavor 10 × 10 evolution matrix. The explicit forms of ⃗ C ( M$_{W}$ ) and U$_{5}$ ( m$_{b}$, M$_{W}$ , α ) are given in [60]. The values of Δ C$_{i}$$_{=1}$ − $_{10}$( m$_{b}$ ) in the NLO approximation and the coefficients of the dipole operators C eff 7 γ and C eff 8 g in the LO for different m$_{t}$ ′ values are presented in Table VI. For numerical evaluation, we use input parameters as follows. For the form factors and decay constants we use F $^{B}$→K 0 (0) = 0 . 34 ± 0 . 05, F $^{B}$→π 0 (0) = 0 . 28 ± 0 . 05, f$_{π}$ = 0 . 131 GeV, f$_{K}$ = 0 . 16 GeV and for Gegenbauer moments we use λ$_{B}$ = 350 ± 150 MeV [38]. We varied the hard spectator and annihilation phases φ$_{A,H}$ in the entire range i.e., between [ − π, π ], ⃗ C ( m$_{b}$ ) = U$_{5}$ ( m$_{b}$, M$_{W}$ , α ) ⃗ C ( M$_{W}$ ) (119) X = sin 2 β + 2 ra cos δ$_{1}$ sin(2 β + γ ) − 2 r ′ b cos δ$_{2}$ sin(2 β − φ$_{s}$ ) + ( ra ) $^{2}$sin(2 β + 2 γ ) + ( r ′ b ) $^{2}$sin(2 β − 2 φ$_{s}$ ) − 2 rr ′ ab cos( δ$_{2}$ − δ$_{1}$ ) sin(2 β + γ − φ$_{s}$ ) . (118) A$_{πK}$ = 2 [ ra sin δ$_{1}$ sin γ + r ′ b sin δ$_{2}$ sin φ$_{s}$ + rr ′ ab sin( δ$_{2}$ − δ$_{1}$ ) sin( γ + φ$_{s}$ ) ] [ R + 2 ra cos δ$_{1}$ cos γ − 2 r ′ b cos δ$_{2}$ cos φ$_{s}$ − 2 rr ′ ab cos( δ$_{2}$ − δ$_{1}$ ) cos( γ + φ$_{s}$ ) ] , S$_{πK}$ = X R + 2 ra cos δ$_{1}$ cos γ − 2 r ′ b cos δ$_{2}$ cos φ$_{s}$ − 2 rr ′ ab cos( δ$_{2}$ − δ$_{1}$ ) cos( γ + φ$_{s}$ ) , (117) Amp = λ$_{c}$A$_{c}$ [ 1 + rae i ( δ 1 − γ ) − r ′ be i ( δ 2 + φ$_{s}$ $^{)}$] , (116)