(B)over-bars → φρ0 and (B)over-bars → φπ0 as a handle on isospin-violating New Physics

The 2.5 sigma discrepancy between theory and experiment observed in the difference ACP(B- -> pi K-0(-)) - A(CP)((B) over bar (0) -> pi K-+(-)) can be explained by a new electroweak penguin amplitude. Motivated by this result, we analyse the purely isospin-violating decays (B) over bar (s) -> phi rho(0) and (B) over bar (s) -> phi pi(0), 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 B-s- (B) over bar (s) mixing, which impose stringent constraints on the enhancement of the two B-s decays. In particular we find that, contrary to claims in the literature, electroweak penguins in the MSSM can reduce the discrepancy in the B -> pi K modes only marginally. As byproducts we update the SM predictions to Br((B) over bar (s) -> phi pi(0)) = 1.6(-0.3)(+1.1) . 10(-7) and Br((B) over bar (s) -> phi rho(0)) = 4.4(-0.7)(+2.7) . 10(-7) and perform a state-of-the-art analysis of B -> pi K amplitudes in QCD factorisation.