decays $B^\pm\to\pi K$ is discussed in Section \[sec:BpiK\], where we indicate how various observables in these decays can be used to test for physics beyond the SM. We derive model-independent bounds on a ratio $R_*$ of CP-averaged $B^\pm\to\pi K$ branching ratios in the presence of New Physics, and show that the value $\gamma_{\pi K}$ of the weak phase extracted in $B\to\pi K$ decays is extremely sensitive to isospin-violating New Physics contributions. Because the theoretical analysis has only small hadronic uncertainties, potential New Physics effects can be detected even if they are 50% smaller than the isospin-violating contributions present in the SM. In Sections \[sec:tree\] and \[sec:loop\], we calculate the Wilson coefficients of the $\bar b\to\bar s q\bar q$ penguin operators in a large class of extensions of the SM, including models with tree-level FCNC couplings of the $Z$ boson, extended gauge models, multi-Higgs models, and SUSY models with and without R-parity conservation. In each case, we explore which region of parameter space can be probed by measuring certain $B^\pm\to\pi K$ observables, and how big a departure from the SM predictions one can expect under realistic circumstances. Section \[sec:concl\] contains a summary of our results and the conclusions.

Effective Hamiltonian for 