Constraining pseudo-Dirac neutrinos from a galactic core-collapse supernova

Neutrinos can be pseudo-Dirac in nature -- Majorana fermions behaving as Dirac fermions for all practical purposes. In such a scenario, active and sterile neutrinos are quasi-degenerate in mass, and hence oscillations between the two, due to their tiny mass-squared difference $(\delta m^2)$, can develop only over very long baselines. Under this hypothesis, we analyze the neutrino data from SN1987A, and find a mild preference for a non-zero mass-squared difference. The same data can also be used to exclude values of $\delta m^2\sim 10^{-20}{\rm eV}^2$ - the smallest constrained so far. We also discuss how next-generation experiments like the DUNE and Hyper-Kamiokande can probe this scenario for a future galactic supernova.