Search for Extremely-High-Energy Neutrinos and First Constraints on the Ultrahigh-Energy Cosmic-Ray Proton Fraction with IceCube

Abstract

We present a search for the diffuse extremely-high-energy neutrino flux using $12.6$ years of IceCube data. The nonobservation of neutrinos with energies well above $10 \, \mathrm{PeV}$ constrains the all-flavor neutrino flux at $10^{18} \, \mathrm{eV}$ to a level of $E^2 \Phi_{\nu_e + \nu_\mu + \nu_\tau} \simeq 10^{-8} \, \mathrm{GeV} \, \mathrm{cm}^{-2} \, \mathrm{s}^{-1} \, \mathrm{sr}^{-1}$, the most stringent limit to date. Using these data, we constrain the proton fraction of ultra-high-energy cosmic rays (UHECRs) above $\simeq 30 \, \mathrm{EeV}$ to be $\lesssim 70\,$% (at $90\,$% CL) if the cosmological evolution of the sources is comparable to or stronger than the star formation rate. This is the first result to disfavor the ``proton-only" hypothesis for UHECRs in this evolution regime using neutrino data. This result complements direct air-shower measurements by being insensitive to uncertainties associated with hadronic interaction models. We also evaluate the tension between IceCube's nonobservation and the $\sim 200 \, \mathrm{PeV}$ KM3NeT neutrino candidate (KM3-230213A), finding it to be $\sim 2.9 \sigma$ based on a joint-livetime fit between neutrino datasets.