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

We study the radiative \(B \to K \eta^{(\prime)} \gamma\) decays, which are important to investigate CP violation, and are also relevant to assess the role of the exclusive modes induced by the \(b \to s \gamma\) transition to saturate the inclusive \(B \to X_s \gamma\) decay rate. Moreover, these channels do not display the same hierarchy as \(B \to K \eta^{(\prime)}\) modes, for which the decay into \(\eta^\prime\) is enhanced with respect to one into \(\eta\). 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 \(\eta^\prime\)) 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 \(B\to K \eta \gamma\) 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.