Rare $B_s$ decays to $\eta$ and $\eta^\prime$ final states

We study exclusive $B_s$ decays to final states with $\eta$ and $\eta^\prime$, induced by the rare $b \to s \ell^+ \ell^-$ and $b \to s \nu \bar \nu$ transitions. Differential decay rates and total branching fractions are predicted in the Standard Model, adopting the flavour scheme for the description of the $\eta$-$\eta^\prime$ mixing. We discuss the theoretical uncertainty related to the hadronic matrix elements. We also consider these decay modes in a new Physics scenario with a single universal extra dimension, studying the dependence of branching ratios and decay distributions on the compactification scale $R^{-1}$ of the extra dimension.