During the past decade there have been several attempts to detect cosmogenic ultra high energy (UHE) neutrinos by searching for radio Cerenkov bursts resulting from charged impact showers in terrestrial ice or the lunar regolith. So far these radio searches have yielded no detections, but the inferred flux upper limits have started to constrain physical models for UHE neutrino generation. For searches which use the Moon as a target, we summarize the physics of the interaction, properties of the resulting Cerenkov radio pulse, detection statistics, effective aperture scaling laws, and derivation of upper limits for isotropic and point source models. We report on initial results from the RESUN search, which uses the Expanded Very Large Array configured in multiple sub-arrays of four antennas at 1.45 GHz pointing along the lunar limb. We detected no pulses of lunar origin during 45 observing hours. This implies upper limits to the differential neutrino flux E^2 dN/dE < 0.003 EeV km^{-2} s^{-1} sr^{-1} and < 0.0003 EeV km$^{-2} s^{-1} at 90% confidence level for isotropic and sampled point sources respectively, in the neutrino energy range 10^{21.6} < E(eV) < 10^{22.6}. The isotropic flux limit is comparable to the lowest published upper limits for lunar searches. The full RESUN search, with an additional 200 hours observing time and an improved data acquisition scheme, will be be an order of magnitude more sensitive in the energy range 10^{21} < E(eV) < 10^{22} than previous lunar-target searches, and will test Z burst models of neutrino generation.
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