Rare radiative-and-leptonic $B_s$-meson decay within and beyond the Standard Model

The rare-and-radiative $B_s$-meson decay is a promising channel to test hypothetical New Physics effects in $b \to s$ quark transitions besides semileptonic rare $B_{(s)}$-meson transitions. In this proceedings, we review the state-of-the-art of theoretical computations of the branching ratio of the decay $B_s \to \mu^+\mu^-\gamma$ and the existing experimental bounds on this physical quantity. In particular, we will describe a peculiar parametrization of the hadronic form factors, namely a HQET-based procedure to infer the behaviour of these quantities in the $B_s$-sector starting from lattice QCD data available in the $D_s$-sector at high momentum transfer. We argue that such an approach will be particularly relevant in the near future to develop global fits of all the available lattice data on the hadronic form factors. Finally, we will review the results of the first sensitivity study of $B_s \to \mu^+\mu^-\gamma$ beyond the Standard Model.