This paper studies how very energetic cosmic rays can kick the faint sea of relic neutrinos left over from the Big Bang up to much higher energies. Those up‑scattered neutrinos could in principle be seen by high‑energy neutrino telescopes, so the process offers an indirect way to probe the cosmic neutrino background (CνB) that is otherwise extremely hard to detect.

The authors make a systematic calculation of the diffuse flux of boosted relic neutrinos produced when ultra‑high‑energy cosmic rays (UHECRs) interact with relic neutrinos via Standard Model neutral‑current interactions. They include a full set of scattering channels: elastic neutrino–nucleon scattering (ES), coherent elastic neutrino–nucleus scattering (COH), incoherent neutrino–nucleus scattering (INCOH), baryon‑resonance production (RES), and deep inelastic scattering (DIS). To represent the incoming cosmic rays, they use mixed‑composition spectra from the PriNCe propagation code and two Hillas‑model implementations called H3a and H4a. They also test three source‑evolution histories: star formation rate (SFR), quasi‑stellar objects (QSO), and gamma‑ray bursts (GRB).

At a simple, physical level, which scattering channel matters depends on how much momentum is transferred in the collision. The authors define the positive momentum transfer Q2 ≃ 2 mν Eν, where mν is the relic neutrino mass and Eν is the boosted neutrino energy. Small Q2 means the neutrino interacts with the whole nucleus at once (coherent scattering). Larger Q2 resolves individual protons and neutrons (elastic and incoherent scattering). Still larger transfers can excite baryon resonances (RES) and finally probe quarks inside nucleons, the deep inelastic scattering (DIS) regime.

Their results show a clear hierarchy. For heavy nuclear cosmic rays, coherent scattering dominates the low‑energy portion of the boosted neutrino flux. Once the collision can resolve individual nucleons, ES and INCOH become important. The RES channel gives a visible contribution at high boosted energies. DIS appears only at the very highest boosted energies and is most noticeable in the H4a cosmic‑ray model; DIS is negligible for the PriNCe and H3a models. The predictions are sensitive to the assumed cosmic‑ray composition: current data from the Pierre Auger Observatory favor a mixed composition that becomes heavier toward the highest energies, with the proton fraction dropping below roughly 10% above 10 EeV.