Complex Analysis of Askaryan Radiation: A Fully Analytic Model in the Time-Domain

Hanson, Jordan C.; Hartig, Raymond

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 high-energy cascades. When a UHE neutrino initiates a cascade, cascade properties are imprinted on the radiation. Thus, observed radiation properties must be used to reconstruct the UHE neutrino event. Analytic Askaryan models have three advantages when used for UHE neutrino reconstruction. First, when analytic models are matched to observed data, cascade properties may be calculated directly from single RF waveforms. Second, fully analytic models require no Monte Carlo simulation of cascade particle trajectories, minimizing computational intensity. Third, fully analytic models can be embedded in firmware to enhance the real-time sensitivity of detectors. We derive a fully analytic Askaryan model in the time-domain given the energy and geometry of the UHE neutrino-induced cascade. We compare the fully analytic model to a semi-analytic parameterization used commonly in NuRadioMC, a simulation being used to design the radio component of IceCube-Gen2. We find correlation coefficients greater than 0.95 between the fully analytic and semi-analytic cases, and we find the total power in the signals agree to within 5\%.