Searches for Non-Standard Neutrino Oscillations with the IceCube Neutrino Observatory
The short-baseline neutrino anomalies observed by LSND, MiniBooNE, and the gallium experiments can be explained by additional neutrino states beyond the three established by solar, atmospheric, and reactor oscillation measurements. The minimal 3+1 sterile neutrino model that parameterizes these anomalies is in significant tension with null results from other oscillation experiments and with cosmological constraints, motivating the exploration of non-minimal extensions in which the additional mass eigenstate is unstable. This thesis presents a search for an unstable sterile neutrino model, in which the heavy mass eigenstate $ν_4$ decays to two invisible particles, using 10.67 years of high-energy atmospheric neutrino data from the IceCube Neutrino Observatory. The analysis finds no preference for sterile decay over the no-decay 3+1 hypothesis and excludes most of the parameter space preferred by global fits to short-baseline data at 90% confidence level, providing a strong constraint on this non-minimal explanation of the anomalies. The thesis additionally develops the foundation for a future sterile neutrino search at IceCube targeting the resonant disappearance of antineutrinos. Three contributions are presented: a comprehensive calculation of neutrino-nucleon and neutrino-nucleus deep-inelastic scattering cross sections, new machine-learning reconstruction techniques, and an improved event selection with twice the signal efficiency of the previous iteration. Together, these tools enable statistical separation of neutrinos and antineutrinos and establish the infrastructure for the next generation of sterile neutrino searches with IceCube.