Exploring Sterile Neutrinos at High and Low Energy Scales

The inability of the Standard Model (SM) to explain certain observations, such as neutrino masses, hints at new physics Beyond the SM (BSM). Sterile neutrinos – hypothetical right-handed neutral leptons appearing in numerous BSM theories – are compelling extensions of the SM as they can remedy several of these issues. This thesis offers a phenomenological study of light and massive sterile neutrinos in future experiments. Without model predictions, the neutrino mass needs to be determined experimentally. Single beta-decay is the only available direct probe, thus we explore whether these experiments can search for new physics beyond the SM, such as keV-mass sterile neutrinos, which manifest as distortions in the energy and angular spectra of the emitted beta-electron. Studying these distributions, we conclude that the next generation of tritium beta-decay experiments utilising Cyclotron Radiation Emission Spectroscopy can improve existing bounds by an order of magnitude. Furthermore, we find that such experiments will also be sensitive to BSM couplings parameterising exotic interactions differing from the usual V-A structure of the weak Lagrangian. In Effective Field Theory (EFT) frameworks, the SM can be extended with Dirac and Majorana sterile neutrino states. In the EFT formalism, the interactions are approximated by operators, and their relative coupling strength is parameterised by Wilson Coefficients (WC). Considering the Future e⁺e⁻ Circular Collider (FCC-ee), we study monophoton final states originating from active-sterile mixing by performing and analysing computer simulations of the process using MadGraph and derive projected sensitivities to the mixing angle. Additionally, we study monophoton final states from four-fermion processes, displaced di-electron final states, and effective Z and W⁺⁻ mediated processes. We estimate the sensitivity of the FCC to the WCs and conclude that the FCC will place stringent limits on the operator scales of the relevant WCs associated with GeV-mass sterile states.