Neutrino vertex reconstruction with in-ice radio detectors using surface reflections and implications for the neutrino energy resolution

Ultra high energy neutrinos ($E_ u > 10^{16.5}$eV$)$ are efficiently measured via radio signals following a neutrino interaction in ice. An antenna placed $mathcal{O}$(15 m) below the ice surface will measure two signals for the vast majority of events (90% at $E_ u$=$10^{18}$eV$)$: a direct pulse and a second delayed pulse from a reflection off the ice surface. This allows for a unique identification of neutrinos against backgrounds arriving from above. Furthermore, the time delay between the direct and reflected signal (DnR) correlates with the distance to the neutrino interaction vertex, a crucial quantity to determine the neutrino energy. In a simulation study, we derive the relation between time delay and distance and study the corresponding experimental uncertainties in estimating neutrino energies. We find that the resulting contribution to the energy resolution is well below the natural limit set by the unknown inelasticity in the initial neutrino interaction. We present an in-situ measurement that proves the experimental feasibility of this technique. Continuous monitoring of the local snow accumulation in the vicinity of the transmit and receive antennas using this technique provide a precision of $mathcal{O}$(1 mm) in surface elevation, which is much better than that needed to apply the DnR technique to neutrinos.