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Abstract

Neutrinos can be pseudo-Dirac in Nature - they can be Majorana fermions while behaving effec- tively as Dirac fermions. Such scenarios predict active-sterile neutrino oscillations driven by a tiny mass-squared difference (δm²), which is an outcome of soft lepton number violation. Oscillations due to tiny δm² can only take place over astrophysical baselines and hence are not accessible in ter- restrial neutrino oscillation experiments. This implies that high-energy neutrinos coming from large distances can be naturally used to test this scenario. We use the recent observation of high-energy neutrinos from the active galactic nuclei NGC 1068 by the IceCube collaboration to rule out δm² in the region [1.4 × 10⁻¹⁸, 10⁻¹⁷] eV² at more than 90% confidence level - one of the strongest limits to date on the values of δm². We also discuss possible uncertainties which can reduce the sensitivity of these results.