B→Kη(′)γdecays in the standard model and in scenarios with universal extra dimensions

Abstract

We study the radiative $B\ensuremath{\rightarrow}K{\ensuremath{\eta}}^{(\ensuremath{'})}\ensuremath{\gamma}$ decays, which are important to investigate $CP$ violation, and are also relevant to assess the role of the exclusive modes induced by the $b\ensuremath{\rightarrow}s\ensuremath{\gamma}$ transition to saturate the inclusive $B\ensuremath{\rightarrow}{X}_{s}\ensuremath{\gamma}$ decay rate. Moreover, these channels do not display the same hierarchy as $B\ensuremath{\rightarrow}K{\ensuremath{\eta}}^{(\ensuremath{'})}$ modes, for which the decay into ${\ensuremath{\eta}}^{\ensuremath{'}}$ is enhanced with respect to one into $\ensuremath{\eta}$. 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 ${\ensuremath{\eta}}^{\ensuremath{'}}$) is reproduced in the theoretical analysis. We compute a ${B}^{*}\ensuremath{\rightarrow}K$ 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 $B\ensuremath{\rightarrow}K\ensuremath{\eta}\ensuremath{\gamma}$ 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.