Limits on the transient ultra-high energy neutrino flux from gamma-ray bursts (GRB) derived from RICE data

We present limits on ultra-high energy (UHE; E_ν > 10¹⁵ eV) neutrino fluxes from gamma-ray bursts (GRBs), based on recently presented data, limits, and simulations from the RICE experiment. We use data from five recorded transients with sufficient photon spectral shape and redshift information to derive an expected neutrino flux, assuming that the observed photons are linked to neutrino production through pion decay via the well-known "Waxman-Bahcall" prescription. Knowing the declination of the observed burst, as well as the RICE sensitivity as a function of polar angle and the previously published non-observation of any neutrino events allows an estimate of the sensitivity to a given neutrino flux. Although several orders of magnitude weaker than the expected fluxes, our GRB neutrino flux limits are nevertheless the first in the PeV-EeV energy regime. For completeness, we also provide a listing of other bursts, recorded at times when the RICE experiment was active, but requiring some assumptions regarding luminosity and redshift to permit estimates of the neutrino flux.