Rare Radiative decays at LHCb

Radiative rare $b$-hadron decays are sensitive probes of New Physics through the study of branching fractions, angular observables, $\mathcal{CP}$ asymmetries and measurements of the polarisation of the photon emitted in the decay. The recent LHCb results on the first direct measurement of the photon polarisation using $\Lambda_b^0\to\Lambda\gamma$ decays and on the search for the rare $\Xi_b^-\to\Xi^-\gamma$ decay are reported.