$\phi^f_A$), ($\rho^i_A$, $\phi^i_A$) and ($\rho_H$, $\phi_H$), and check whether the approximation ($\rho_H$, $\phi_H$) = ($\rho^i_A$, $\phi^i_A$) is allowed or not, a fit on such six free parameters is performed.

Other input parameters used in our evaluation are summarized in Appendix \[app02\]. Our fit approach is illustrated in detail in Appendix \[app03\].

Scenario I {#sec0301}
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Comparing Eq.(\[amp2\]) with Eq.(\[amp3\]), it can be clearly seen that $\sqrt{2} {\cal A}_{ B^- \to \pi^0 K^-}$ $\simeq$ ${\cal A}_{ \bar{B}^0 \to \pi^+ K^-}$ if $\delta_{pu} \alpha_2$ $+$ $\frac{3}{2} \alpha_{3,{\rm EW}}^p$ is negligible compared with $\delta_{pu} \alpha_1$ $+$ $\alpha_4^p$. Hence it is expected $\Delta A$ $\simeq$ 0 in SM, which significantly disagrees with the current experimental data in Eq.(\[acppi\]), this is the so-called $\pi K$ puzzle. To resolve the $\pi K$ puzzle, one possible solution is that there is a large complex contributions from $\delta_{pu} \alpha_2$ $+$ $\frac{3}{2} \alpha_{3,{\rm EW}}^p$. Many proposals have been offered, such as the enhancement of color-suppressed tree amplitude $\alpha_2$ in Ref.[@Cheng1], significant new physics corrections to the electroweak penguin coefficient $\alpha_{3,{\rm EW}}^p$ in Ref.[@pipipuz], and so on. Indeed, it has been shown [@Beneke2] that the coefficients $\alpha_2$ and $\alpha_{3,{\rm EW}}^p$ are seriously affected by spectator scattering corrections within QCDF framework. 