Neutrino oscillations successfully explain the flavor transitions observed in neutrinos produced in natural sources like the center of the sun and the earth atmosphere, and also from man-made sources like reactors and accelerators. These oscillations are driven by two mass-squared differences, solar and atmospheric, at the sub-eV scale. However, longstanding anomalies at short-baselines might imply the existence of new oscillation frequencies at the eV-scale and the possibility of this sterile state(s) to mix with the three active neutrinos. One of the many future neutrino programs that are expected to provide a final word on this issue is the Short-Baseline Neutrino Program (SBN) at FERMILAB. In this letter, we consider a specific model of Large Extra Dimensions (LED) which provides interesting signatures of oscillation of extra sterile states. We started re-creating sensitivity analyses for sterile neutrinos in the 3+1 scenario, previously done by the SBN collaboration, by simulating neutrino events in the three SBN detectors from both muon neutrino disappearance and electron neutrino appearance. Then, we implemented neutrino oscillations as predicted in the LED model and also we have performed sensitivity analysis to the LED parameters. Finally, we studied the SBN power of discriminating between the two models, the 3+1 and the LED. We have found that SBN is sensitive to the oscillations predicted in the LED model and have the potential to constrain the LED parameter space better than any other oscillation experiment, for $m_{1}^D<0.1,text{eV}$. In case SBN observes a departure from the three active neutrino framework, it also has the power of discriminating between sterile oscillations predicted in the 3+1 framework and the LED ones.
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