Hunting for Neutral Leptons with Ultra-High-Energy Cosmic Rays

Next-generation large-volume detectors, such as GRAND, POEMMA, Trinity, TAROGE-M, TAMBO, or PUEO, have been designed to search for ultra-high-energy cosmic rays (UHECRs) with unprecedented sensitivity. We propose to use these detectors to search for new physics beyond the Standard Model (BSM). By considering the simple case of a right-handed neutrino that mixes exclusively with the active $\tau$ neutrino, we demonstrate that the existence of new physics can increase the probability for UHECRs to propagate through the Earth and produce extensive air showers that will be measurable soon. We compare the fluxes of such showers that would arise from various diffuse and transient sources of high-energy neutrinos, both in the Standard Model and in the presence of a right-handed neutrino. We show that detecting events with emergence angles $\gtrsim 10$ deg is promising to probe the existence of BSM physics, and we study the sensitivity of GRAND and POEMMA to do so. In particular, we show that the hypothesis of a right-handed neutrino with a mass of $\mathcal O(1-16)$ GeV may be probed in the future for mixing angles as small as $|U_{\tau N}|^2 \gtrsim 10^{-7}$, thus competing with existing and projected experimental limits.