Investigating DUNE oscillations sensitivity to Pseudo-Dirac Neutrinos

We explore the sensitivity of the Deep Underground Neutrino Experiment (DUNE) to sterile neutrino oscillations within a $3+$(pseudo-Dirac pair) framework. We first consider a pair of two sterile neutrinos forming a pseudo-Dirac pair, then we consider a low-scale seesaw realization, that we name ``Linear-Inverse Seesaw" model. This scenario features two nearly degenerate sterile neutrino states at the keV scale, characterized by a small mass splitting arising from a small amount of lepton number violation. In this scenario, the oscillation behavior can be described in three distinct regimes depending on the sterile-sterile mass-squared difference : low ($< 1\,\mathrm{eV}^2$), resonant ($1$--$100\,\mathrm{eV}^2$), and high ($> 100\,\mathrm{eV}^2$) regimes, recovering in both low- and high-mass regimes an effective non-unitarity of the leptonic mixing matrix. A distinctive feature of this framework is that observable effects persist even in the low-mass limit, unlike the case of standard $3+1$ scenarios, due to rapid oscillation averaging from larger keV-scale splittings. We leverage the complementarity of both near and far detectors to explore the sensitivity for $\nu_e$ and $\nu_\mu$ disappearance and $\nu_e$ and $\nu_{\tau}$ appearance oscillation probabilities.Our analysis reveals that DUNE can achieve significant improvements over current experimental constraints, especially in neutrino appearance modes. Additionally, we show that new CP-violating phases associated with the sterile sector can dramatically alter the sensitivity, with destructive interference potentially suppressing signals by orders of magnitude.