Disentangling axion-like particle couplings to nucleons via a delayed signal in Super-Kamiokande from a future supernova

Abstract: In this work, we show that, if axion-like particles (ALPs) from core-collapse supernovae (SNe) couple to protons, they would produce very characteristic signatures in neutrino water Cherenkov detectors through their scattering off free protons via $a \, p \rightarrow p \, \gamma$ interactions. Specifically, sub-MeV ALPs would generate photons with energies $\sim 30$ MeV, which could be observed by Super-Kamiokande and Hyper-Kamiokande as a delayed signal after a future detection of SN neutrinos. We apply this to a hypothetical neighbouring SN (at a maximum distance of 100 kpc) and demonstrate that the region in the parameter space with ALP masses between $10^{-4}$ MeV and $1$ MeV and ALP-proton couplings in the range $3 \times 10^{-6}-4 \times 10^{-5}$ could be probed. We argue that this new signature, combined with the one expected at $\sim 7$ MeV from oxygen de-excitation, would allow us to disentangle ALP-neutron and ALP-proton couplings.