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

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.