Constraints on pseudo-Dirac neutrinos using high-energy neutrinos from NGC 1068

Neutrinos can be pseudo-Dirac in Nature - they can be Majorana fermions whilebehaving effectively as Dirac fermions. Such scenarios predict active-sterileneutrino oscillation driven by a tiny mass-squared difference $(\delta m^2)$,which is an outcome of soft-lepton number violation. Oscillations due to tiny$\delta m^2$ can take place only over astrophysical baselines and hence are notaccessible in terrestrial neutrino oscillation experiments. This implies thathigh-energy neutrinos coming from large distances can naturally be used to testthis scenario. We use the recent observation of high-energy neutrinos from theactive galactic nuclei NGC 1068 by the IceCube collaboration to constrain$\delta m^2 \leq 10^{-18}{\rm eV}^2$ at more than $90\%$ confidence level - oneof the strongest limits to date on the values of $\delta m^2$.