33 physics. However there are some interesting deviations from the SM associated with the b → s transitions, which provide us with possible indication of new physics. For example the mixing induced CP asymmetries in many b → s ¯ qq penguin dominated modes do not seem to agree with the SM expectations. The measured values in such modes follow the trend S$_{s}$$_{¯}$ qq < sin 2 β [5, 52], whereas in the SM they are expected to be similar [113, 114]. In this context B → πK decay modes, which receive dominant contributions from b → s mediated QCD penguins in the SM, provide another testing ground to look for new physics. The first one is the difference in direct CP asymmetries in B − → π $^{0}$K − and ¯ B 0 → π $^{+}$K − modes. These two modes receive similar dominating contributions from tree and penguin diagrams and hence one would naively expect that these two channels will have the same direct CP asymmetries i.e., A π $^{0}$K − = A π $^{+}$K − . In the QCD factorization approach, the difference between these asymmetries is found to be [3] whereas the corresponding experimental value [52] is which yields nearly 4 σ deviation. The second anomaly is associated with the mixing induced CP asymmetry in B 0 → π $^{0}$K0 mode. The time dependent CP asymmetry in this mode is defined as and in the pure QCD penguin limit one expects A$_{π}$ $^{0}$K$_{s}$ ≈ 0 and S$_{π}$ $^{0}$K$_{s}$ ≈ sin(2 β ). Small non-penguin contributions do provide some corrections to these asymmetry parameters and it has been shown in Ref. [115–117] that these corrections generally tend to increase S$_{Kπ}$ 0 from its pure penguin limit of (sin 2 β ) by a modest amount i.e., S$_{π}$ $^{0}$K$_{s}$ ≈ 0 . 8. Recently, using isospin symmetry it has been shown in [118–120] that the standard model favors a large S$_{π}$ $^{0}$K$_{s}$ ≈ 0 . 99. However, the recent results from Belle [121] and Babar [122] are A$_{π}$ $^{0}$K$_{s}$ = 0 . 14 ± 0 . 13 ± 0 . 06 , S$_{π}$ $^{0}$K$_{s}$ = 0 . 67 ± 0 . 31 ± 0 . 08 (Belle) A$_{π}$ $^{0}$K$_{s}$ = − 0 . 13 ± 0 . 13 ± 0 . 03 , S$_{π}$ $^{0}$K$_{s}$ = 0 . 55 ± 0 . 20 ± 0 . 03 (Babar) (109) Γ( ¯ B $^{0}$( t ) → π $^{0}$K$_{s}$ ) − Γ( B $^{0}$( t ) → π $^{0}$K$_{s}$ ) Γ( ¯ B $^{0}$( t ) π $^{0}$K$_{s}$ ) + Γ( B $^{0}$( t ) π $^{0}$K$_{s}$ ) = A$_{π}$ $^{0}$K$_{s}$ cos(Δ M$_{d}$t ) + S$_{π}$ $^{0}$K$_{s}$ sin(Δ M$_{d}$t ) , (108) Δ A$_{CP}$ = (14 . 8 ± 2 . 8)% , (107) Δ A$_{CP}$ = A K − π 0 − A K − π + = (2 . 5 ± 1 . 5)% (106)