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$B\to K η^{(\prime)} γ$ decays in the standard model and in scenarios with universal extra dimensions

We study the radiative $B \to K η^{(\prime)} γ$ decays, which are important to investigate CP violation, and are also relevant to assess the role of the exclusive modes induced by the $b \to s γ$ transition to saturate the inclusive $B \to X_s γ$ decay rate. Moreover, these channels do not display the same hierarchy as $B \to K η^{(\prime)}$ modes, for which the decay into $η^\prime$ is enhanced with respect to one into $η$. The three-body radiative decays reverse the role: we find that this experimentally observed behavior (although affected by a large uncertainty in the case of the $η^\prime$) is reproduced in the theoretical analysis. We compute a $B^* \to K$ form factor, needed for this study, using light cone QCD sum rules, and discuss a relation expected to hold in the large energy limit for the light meson. Finally, we examine $B\to K ηγ$ in two extensions of the standard model with universal extra dimensions, to investigate the sensitivity of this rare mode to such a kind of new physics effects.