We investigate the ability of the short baseline neutrino (SBN) experimental program at Fermilab to test the globally-allowed (3+N) sterile neutrino oscillation parameter space. We explicitly consider the globally-allowed parameter space for the (3+1), (3+2), and (3+3) sterile neutrino oscillation scenarios. We find that SBN can probe with 5σ sensitivity more than 85%, 95% and 55% of the parameter space currently allowed at 99% confidence level for the (3+1), (3+2) and (3+3) scenarios, respectively, with the (3+N) allowed space used in these studies closely resembling that of previous studies [J. M. Conrad, C. M. Ignarra, G. Karagiorgi, M. H. Shaevitz, and J. Spitz, Adv. High Energy Phys. 2013, 1 (2013).1687-735710.1155/2013/163897], calculated using the same methodology. In the case of the (3+2) and (3+3) scenarios, CP-violating phases appear in the oscillation probability terms, leading to observable differences in the appearance probabilities of neutrinos and antineutrinos. We explore SBN's sensitivity to those phases for the (3+2) scenario through the currently planned neutrino beam running, and investigate potential improvements through additional antineutrino beam running. We show that, if antineutrino exposure is considered, for maximal values of the (3+2) CP-violating phase φ54, SBN could be the first experiment to directly observe ∼2σ hints of CP violation associated with an extended lepton sector.
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The authors would like to thank M. Shaevitz, L. Camilleri, B. Louis and S. Pascoli for valuable discussions. This work has been supported in part by a 2014 Institute for Particle Physics Phenomenology (IPPP) Associateship to G. K. We also acknowledge support by the Science and Technology Facilities Council (UK). M. R. L acknowledges partial support from the European Union FP7 ITN INVISIBLES (Marie Curie Actions, PITN-GA-2011-289442).