EW}(\mu) &=& -\frac{\kappa^{12/23}-\kappa^{-6/23}}{2}\,
    c_3^{\rm EW}(m_W) + \frac{\kappa^{12/23}+\kappa^{-6/23}}{2}\,
    c_4^{\rm EW}(m_W) \,.\end{aligned}$$ The coefficients $\widetilde c_i^q$ scale in the same way as the $c_i^q$. Since our main focus is on electroweak penguins and their generalizations beyond the SM, we will not discuss the more complicated evolution equations for the coefficients $c_i^q$ themselves, which can however readily be deduced from the literature [@Heff].

 Searching for New Physics with $B^\pm\to\pi K$ decays  {#sec:BpiK}
=======================================================

In close correspondence with the different types of operators in the effective weak Hamiltonian, one distinguishes three classes of flavor topologies relevant to $B\to\pi K$ decays, referred to as trees, QCD penguins and electroweak penguins. In the SM, the weak couplings associated with these topologies are known. From the measured branching ratios for the various $B\to\pi K$ decay modes it follows that the QCD penguins dominate the decay amplitudes [@Digh], whereas trees and electroweak penguins are subleading and of a similar strength [@oldDesh]. The theoretical description of the two charged modes $B^\pm\to\pi^\pm K^0$ and $B^\pm\to\pi^0 K^\pm$ exploits the fact that the amplitudes for these processes differ in a pure isospin amplitude $A_{3/2}$, defined as the matrix element of the isovector part of the effective Hamiltonian between a $B$ meson and 