Exploring memory-burdened primordial black holes with ultra-high-energy cosmic-rays

Abstract

Quantum backreaction effects may quench Hawking evaporation through a ``memory burden'', allowing primordial black holes (PBHs) with formation masses well below $10^{15}~\mathrm{g}$ to survive to the present and contribute to the dark matter. We show that ultra-high-energy cosmic rays (UHECRs) provide a powerful and previously unexplored probe of this scenario. We compute the proton and neutron emission from memory-burdened PBHs, including the Galactic-halo contribution and the extragalactic proton component, and confront it with the Pierre Auger Observatory proton spectrum and its EeV neutron limits from the Galactic plane. This yields new constraints on the PBH dark-matter fraction as a function of the PBH formation mass and the evaporation-suppression parameter $k$. For $k\gtrsim 3$ the non-observation of ultra-high-energy protons leads to bounds competitive with those from UHE gamma rays, while neutron limits remain comparable to high-energy neutrino constraints. Our results highlights the key role of multi-messenger astronomy in constraining beyond-the-standard-model scenarios.

Figures (5)

• Figure 1: Proton/neutron (solid lines), gamma-ray (dashed lines) and neutrino (dotted lines) energy spectra from PBH evaporation, shown as functions of $x = E/T_{\rm H}$. The proton, neutron, and neutrino spectra include the sum of particle and antiparticle contributions. Results are displayed for two benchmark PBH masses: $M_{\rm PBH} = 10^2\,\mathrm{g}$ (blue curves) and $M_{\rm PBH} = 10^4\,\mathrm{g}$ (orange curves).
• Figure 2: The angle-integrated J-factor as a function of the energy for the neutrons from the galactic plane (blue line), defined as the region $0^{\circ}<l<360^{\circ}$ and $-1.7^{\circ}<b<{1.7^{\circ}}$ in galactic coordinates, and for the protons from the full sky (dashed red line).
• Figure 3: The Auger All-particle PierreAuger:2021hun and proton AbdulHalim:2023YdAbdulHalim:20239/ spectra compared with the proton and neutron fluxes from PBHs fixing $f_{\rm PBH}$ at the 95% CL upper limit with protons. Left: memory-burden scenario with $k=2$, for $M_{\rm PBH} = 10^4\, \rm g$ and $M_{\rm PBH} = 4 \times 10^{4}\, \rm g$. Right: memory-burden scenario with $k=3$, for $M_{\rm PBH} = 100\, \rm g$ and $M_{\rm PBH} = 500\, \rm g$.
• Figure 4: Constraints at 95% CL on the fraction $f_{\rm PBH}$ as a function of the PBH mass at formation, in case of two scenarios for the memory-burden effect with $k = 2$ (left panel), $k = 3$ (middle panel) and $k = 4$ (right panel). The solid blue and dashed red lines represent the bounds derived in the present work from UHE neutrons and protons, respectively. The dot-dashed orange and long-dashed green lines corresponds to the previous upper limits placed by UHE gamma-rays Chianese:2025wrk and neutrinos Chianese:2024rsn, respectively (see also Refs. Alexandre:2024nuoThoss:2024hsrZantedeschi:2024ramBoccia:2025hpmDondarini:2025ktz). hatched region indicates PBHs that have fully evaporated over cosmological times.
• Figure 5: Constraints on memory-burdened PBHs as viable DM candidates. Left: the different lines refer to limits placed at 95% CL in the $k$--$M_{\rm PBH}$ plane with $f_{\rm PBH} = 1$ according to UHE protons (solid blue line), UHE neutrons (dashed red line), UHE gamma-rays (dot-dashed orange line) Chianese:2025wrk and neutrinos (long-dashed green line) Chianese:2024rsn (see also Refs. Alexandre:2024nuoThoss:2024hsrZantedeschi:2024ramBoccia:2025hpmDondarini:2025ktz). The white area represents the parameter space where memory-burdened PBHs can account for the total DM component of the Universe ($f_{\rm PBH} = 1$), whereas the hatched region indicates PBHs that have fully evaporated over cosmological times. Right: ratio of the limits on $M_{\rm PBH}$ placed by the different data samples over the global bound in order to highlight the most constraining measurement.