and as a handle on isospin-violating New Physics

The 2.5 σ discrepancy between theory and experiment observed in the difference can be explained by a new electroweak penguin amplitude. Motivated by this result, we analyse the purely isospin-violating decays and , which are dominated by electroweak penguins, and show that in presence of a new electroweak penguin amplitude their branching ratio can be enhanced by up to an order of magnitude, without violating any constraints from other hadronic B decays. This makes them very interesting modes for LHCb and future B factories. We perform both a model-independent analysis and a study within realistic New Physics models such as a modified- Z 0 -penguin scenario, a model with an additional Z ′ boson and the MSSM. In the latter cases the new amplitude can be correlated with other flavour phenomena, such as semileptonic B decays and mixing, which impose stringent constraints on the enhancement of the two B sdecays. In particular we find that, contrary to claims in the literature, electroweak penguins in the MSSM can reduce the discrepancy in the B → πK modes only marginally. As byproducts we update the SM predictions to and and perform a state-of-the-art analysis of B → πK amplitudes in QCD factorisation.