  In the Standard Model (SM) charmless hadronic decays $B_s^0 \rightarrow
\eta^\prime \eta$ proceed via tree-level $b\to u$ and penguin $b\to s$
transitions. Penguin transitions are sensitive to Beyond-the-Standard-Model
(BSM) physics scenarios and could affect the branching fractions and {\it CP}
asymmetries in such decays. Once branching fractions for two-body decays $B_s
\to \eta\eta, \eta\eta^{\prime}, \eta^{\prime}\eta^{\prime} $ are measured, and
the theoretical uncertainties are reduced, it would be possible to extract {\it
CP} violating parameters from the data using the formalism based on SU(3)/U(3)
symmetry. To achieve this goal, at least four of these six branching fractions
need to be measured. Only the branching fraction for $B_s^0 \to
\eta^{\prime}\eta^{\prime}$ has been measured so far.
