In the pursuit of the measurement of the still-elusive ultrahigh-energy (UHE)
neutrino flux at energies of order EeV, detectors using the in-ice Askaryan
radio technique have increasingly targeted lower trigger thresholds. This has
led to improved trigger-level sensitivity to UHE neutrinos. Working with data
collected by the Askaryan Radio Array (ARA), we search for neutrino candidates
at the lowest threshold achieved to date, leading to improved analysis-level
sensitivities. A neutrino search on a data set with 208.7~days of livetime from
the reduced-threshold fifth ARA station is performed, achieving a 68\% analysis
efficiency over all energies on a simulated mixed-composition neutrino flux
with an expected background of 0.10−0.04+0.06​ events passing the
analysis. We observe one event passing our analysis and proceed to set a
neutrino flux limit using a Feldman-Cousins construction. We show that the
improved trigger-level sensitivity can be carried through an analysis,
motivating the Phased Array triggering technique for use in future
radio-detection experiments. We also include a projection using all available
data from this detector. Finally, we find that future analyses will benefit
from studies of events near the surface to fully understand the background
expected for a large-scale detector.Comment: 15 pages, 8 figure