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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. 

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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 

<img src='content_image/335756.jpg'>

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 

<img src='content_image/335755.jpg'>

