The next galactic supernova can uncover mass and couplings of particles decaying to neutrinos

Many particles predicted by extensions of the Standard Model feature interactions with neutrinos, e.g., Majoron-like bosons $\phi$. If the mass of $\phi$ is larger than about 10 keV, they can be produced abundantly in the core of the next galactic core-collapse supernova through neutrino coalescence, and leave it with energies of around 100 MeV. Their subsequent decay to high-energy neutrinos and anti-neutrinos provides a distinctive signature at Earth. Ongoing and planned neutrino and dark matter experiments allow us to reconstruct the energy, flavor, and time of arrival of these high-energy neutrinos. For the first time, we show that these measurements can help pinpointing the mass of $\phi$ and its couplings to neutrinos of different flavor. Our results can be generalized in a straightforward manner to other hypothetical feebly interacting particles, like novel gauge bosons or heavy neutral leptons, that decay into neutrinos.