What Thy Right Hand Doeth: Simulating the Effects of Physics beyond the Standard Model on Earth-Traversing Ultra-High-Energy Neutrinos

Neutrinos of ultra-high energy (UHE)—that is, with energy of EeV ( eV) order and above—originate from cosmogenic processes and transient astrophysical events, and arrive at the Earth in fluxes that will be increasingly constrained and measured by next-generation large-volume observatories such as GRAND, POEMMA, PUEO, TAMBO, TAROGE-M, and Trinity. At such energies, the Earth is effectively opaque; a UHE neutrino shallowly skimming the Earth may exit, sometimes in the form of a whose decay in the atmosphere can be detected, while at deeper angles corresponding to longer distances through the Earth's interior, a UHE neutrino cannot survive the journey with comparable energy. In this thesis, I explore the influence that physics beyond the Standard Model (BSM) may have on the exit probabilities of UHE neutrinos traversing the Earth, and the signatures that such influence may produce in the observations and measurements of detectors. In particular, I introduce to this scenario a right-handed neutrino (RHN) in the form of a Majorana fermion of GeV-scale mass that mixes with the left-handed neutrino according to a mixing parameter , and use Monte Carlo simulations adapted to include the relevant BSM interactions and decays to test this model's effects. I then simulate GRAND and POEMMA, two relevant future detectors, to predict the impact on their results. It is found that, in light of a transient astrophysical event similar to GRB 221009 occurring within a vicinity of ≲ 1 Mpc, a POEMMA-like detector in particular should be capable of probing this regime and providing complementary constraints on the BSM model, thus demonstrating that the observation of Earth-traversing UHE neutrinos at large-volume detectors has potential as an avenue for exploring and testing new physics.