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

Abstract

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 $B^{\ast }\to K$ 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.

Comments: RevTeX, 17 pages, 7 figures. High resolution figures available upon request. Matches the published version