Relic Neutrino Background from Cosmic-Ray Reservoirs

We compute the flux of relic neutrino background (RνB) up-scattered by ultra-high-energy (UHE) cosmic rays (CRs) in clusters that act as CR-reservoirs. The long trapping times of UHECRs make this flux larger than that of RνB up-scattered by UHECRs on their way to Earth, which we also compute. We find that IceCube excludes RνB weighted overdensities larger than 10¹⁰ in clusters, and that PUEO, RNO-G, GRAND and IceCube-Gen2 will test values down to 10⁸. Our treatment incorporates the momentum transfer dependence of the neutrino-nucleus cross section, deep inelastic scattering, a mixed UHECR composition, and flavour information on the up-scattered RνB fluxes for both cases of neutrino mass spectrum with normal and inverted ordering, providing new handles to possibly disentangle the up-scattered RνB from cosmogenic neutrinos.