Impact of coherent scattering on relic neutrinos boosted by cosmic rays

TL;DR

This paper investigates boosting of the cosmic relic neutrino background (CnuB) by ultra-high-energy cosmic rays (UHECR) through coherent elastic neutrino-nucleus scattering and incoherent neutrino-nucleon scattering. It derives the cross sections and computes the diffuse boosted CnuB flux by convolving UHECR fluxes with scattering rates across redshift, using PriNCe simulations and the Hillas parametrization; the boosted flux peaks at $E_ u \sim 2\times 10^2$ PeV, and the results depend sensitively on CR composition. IceCube and PAO data are used to constrain the CnuB overdensity $\eta$ as a function of the lightest neutrino mass $m_1$, with Hillas-based flux giving stronger bounds, and a KM3NeT event near the peak is discussed as a potential hint within certain $\eta$ ranges; the work points to future prospects for direct boosted CnuB detection with instruments like IceCube-Gen2 and POEMMA, aided by multimessenger observations.

Abstract

Ultra-high-energy cosmic rays (UHECR) scattering off the cosmic relic neutrino background have recently gained renewed interest in the literature. Current data suggest that (UHECR) are predominantly made of heavy nuclei. Similar to the coherent elastic neutrino-nucleus scattering (CE$ν$NS) observed at low-energy neutrino experiments, the cross section of heavy nucleus scattering off relic neutrinos will be coherently enhanced since the energy of relic neutrinos can reach $\sim O(10)$ MeV in the rest frame of the UHECR. We calculate the diffuse flux of relic neutrinos boosted by UHECR after taking into account the contributions from both coherent and incoherent scatterings. Using current data from IceCube and Pierre Auger Observatory, we place constraints on the overdensity of relic neutrinos down to $\sim 10^8$. Since the flux of boosted relic neutrinos peaks at an energy of $\sim 200\, \text{PeV}$, we also entertain the possibility to explain the recently observed KM3NeT event with boosted relic neutrinos from UHECR.

Figures (10)

• Figure 1: Schematic diagram showing the C$\nu$B boosted by UHECR. A nucleus $\mathcal{N}$ with energy $E_{\mathcal{N}}$ scatters off a relic neutrino, boosting its energy to $E_\nu$. At a small momentum transfer, the wavelength of the $Z$ boson is comparable to the nucleus, and coherent scattering (dashed line) dominates. At a large momentum transfer, the individual nucleons inside a nucleus are resolved by the $Z$ boson, and incoherent scattering (dotted line) becomes important.
• Figure 2: Upper panel: The total neutrino-nucleus scattering cross section as a function of the UHECR energy $E_{\mathcal{N}}$. Lower panel: The differential scattering cross section as a function of the boosted neutrino energy $E_\nu$ with $E_{\mathcal{N}} = 100 \, \text{EeV}$. In both panels, red, blue, and gray solid lines correspond to the C$\nu$B boosted by the iron, silicon, and proton, respectively. The dashed (dotted) lines denote the coherent (incoherent) contributions. Here, we fix $m_\nu = 0.1 \, \text{eV}$.
• Figure 3: Upper panel: The UHECR flux at Earth obtained from the PriNCe simulation with the SFR source distribution. Lower panel: The UHECR flux described by the Hillas model normalized by a factor $k_\text{best-fit} = 0.601$. Different colors represent flux contributions from different CR elements, while the black solid line shows the total flux. The data points are taken from the PAO measurement Veberic:2017hwu.
• Figure 4: The boosted C$\nu$B flux as a function of neutrino energy $E_\nu$ for $\eta = 1$ and $m_1 = 0.1\,\text{eV}$. Contributions from different CR nuclei are shown for comparison. The upper panel uses the UHECR flux simulated with PriNCe, while the lower panel uses the Hillas model to parametrize the UHECR spectrum. Different colors represent various CR nuclei, with dashed and dotted lines indicating the coherent and incoherent contributions. The gray line shows the proton ES contribution, and the black line depicts the total flux. The SFR model is used for the CR source evolution.
• Figure 5: Left panels: The all-flavor boosted C$\nu$B flux as a function of neutrino energy $E_\nu$ for different lightest neutrino masses $m_1$. Red, blue, and green solid lines represent the flux for $m_1 = 0.1 \, \text{eV}$, $0.05 \, \text{eV}$, and $0.01 \, \text{eV}$, respectively. Varying shades of blue correspond to the 1$\sigma$, 2$\sigma$, and 3$\sigma$ ranges for the KM3-230213A event KM3NeT:2025npi. Also shown are limits on the diffuse cosmogenic flux from IC (90% CL) IceCube:2025ezcMeier:2024flg, PAO (90% CL) PierreAuger:2019ens, and ANTARES (95% CL) ANTARES:2024ihw, as well as the measured astrophysical neutrino spectrum from IC HESE IceCube:2020wum, NST Abbasi:2021qfz, and DPeV IceCube:2025ary. Gray curves show representative cosmogenic neutrino flux models Ahlers:2010fwAhlers:2012rzvanVliet:2019nse. The overdensity is set to $\eta=10^8$. Right panels: Constraints on the C$\nu$B overdensity $\eta$ as a function of the lightest neutrino mass $m_1$. The green and orange curves denote the 90% CL constraints from IC and PAO, respectively. The blue shaded region indicates the parameter space compatible with the KM3-230213A event, while the gray band marks the current KATRIN exclusion at 90% CL. The upper two panels are based on the UHECR flux simulated with PriNCe, while the lower two panels are based on the UHECR flux parametrized by the Hillas model. All panels use the SFR model for the CR source distribution.