We study a supersymmetric phenomenon that can give spectacular signals at the LHC: oscillations of neutralinos. Such oscillations can be naturally realised in R-symmetric models, where additional fields are introduced as Dirac mass partners of gauginos and Higgsinos. Majorana masses for gauginos, necessarily generated from anomaly mediation, can create tiny mass splittings between degenerate mass eigenstates, causing states produced at the LHC to oscillate between neutralinos and their Dirac partner fields. Scenarios where such states decay with displaced vertices can lead to striking signatures at the LHC, where the oscillation can be visible directly in the distribution of displaced vertex lengths. We elaborate on the theory and LHC phenomenology of this feature within a specific scenario of a Higgsino decaying with a displaced vertex into a gravitino and a Z boson.

17 pages, 4 figures