Calculating the Total Cherenkov Radiation Emitted by Low Energy Protons in Liquid Argon and Comparing with Argon Scintillation Light at 128 nm

Neutrino experiments using liquid argon (LAr) detectors estimate the amount of light produced by different types of particles, but only consider scintillation light, at 128 nm, ignoring Cherenkov light contributions. This research aims to theoretically compare these two contributions to the total amount of light produced between ~ 128 - 500 nm for a proton travelling in LAr and explores how to leverage these under-utilized observables for future detector applications. A new theoretical fit of the refractive index of LAr was performed using recent experimental data, which incorporates the physics of anomalous dispersion in the UV resonance for the first time. Using this fit, we integrate the Frank-Tamm (FT) formula to calculate the instantaneous Cherenkov angular distribution and yield of a proton with a given kinetic energy, as well as the integrated distribution and yield over its trajectory. We compare our results with those obtained using two other non-absorptive refractive index fits available in the literature. Because those fits diverge at the resonance, they significantly overestimate the yield.