${\bar{B}_s} \to \phi {\rho^0}$ and ${\bar{B}_s} \to \phi {\pi^0}$ as a handle on isospin-violating New Physics

Abstract

The 2.5σ discrepancy between theory and experiment observed in the difference ${A_{\text{CP}}}\left( {{B^{-} } \to {\pi^0}{K^{-} }} \right) - {A_{\text{CP}}}\left( {{{\bar{B}}^0} \to {\pi^{+} }{K^{-} }} \right)$ can be explained by a new electroweak penguin amplitude. Motivated by this result, we analyse the purely isospin-violating decays ${\bar{B}_s} \to \phi {\rho^0}$ and ${\bar{B}_s} \to \phi {\pi^0}$, 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 ${B_s} - {\bar{B}_s}$ 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 ${\text{Br}}\left( {{{\bar{B}}_s} \to \phi {\pi^0}} \right) = 1.6_{ - 0.3}^{ + 1.1} \cdot {10^{ - 7}}$ and ${\text{Br}}\left( {{{\bar{B}}_s} \to \phi {\rho^0}} \right) = 4.4_{ - 0.7}^{ + 2.7} \cdot {10^{ - 7}}$ and perform a state-of-the-art analysis of B → πK amplitudes in QCD factorisation.