Complex analysis of Askaryan radiation: energy and angular reconstruction of ultra-high energy neutrinos

The detection of ultra-high-energy (UHE, >10 PeV) neutrinos via detectors designed to utilize the Askaryan effect has been a long-time goal of the astroparticle physics community. The Askaryan effect describes radio-frequency (RF) radiation from UHE cascades. When a UHE neutrino initiates a cascade, cascade properties are imprinted on the radiation. The radiation is captured by RF detection channels in Askaryan-based detectors. The observed RF waveforms may be used to reconstruct properties of the UHE neutrino interaction. Previously, we produced a fully analytic Askaryan model that correlates with Monte-Carlo based models (used in our standard simulation toolkit, NuRadioMC) at levels greater than 95%, with power differences less than 5%. In this work, we use the analytic Askaryan model to reconstruct the viewing angle and energy of UHE neutrino interactions in dense media at energies between 10 and 100 PeV. First, we derive the analytic Hilbert envelope of the Askaryan signal. Second, we produce an equation that relates the Hilbert envelopes of the Askaryan electric field, the RF detection channel response, and the observed voltage waveform from the RF detection channel. Finally, we use this relationship to match voltage envelopes from NuRadioMC to our analytic prediction. We will present our first reconstruction results of the viewing angle and UHE neutrino cascade energy from the match between simulated and analytic envelopes.