Measuring the supernova unknowns at the next-generation neutrino telescopes through the diffuse neutrino background

The detection of the diffuse supernova neutrino background (DSNB) will preciously contribute to gauge the properties of the core-collapse supernova population. We estimate the DSNB event rate in the next-generation neutrino detectors, Hyper-Kamiokande enriched with Gadolinium, JUNO, and DUNE. The determination of the supernova unknowns through the DSNB will be heavily driven by Hyper-Kamiokande, given its higher expected event rate, and complemented by DUNE that will help in reducing the parameters uncertainties. Meanwhile, JUNO will be sensitive to the DSNB signal over the largest energy range. A joint statistical analysis of the expected rates in 20 years of data taking from the above detectors suggests that we will be sensitive to the local supernova rate at most at a 20 - 33% level. A non-zero fraction of supernovae forming black holes will be confirmed at a 90% CL, if the true value of that fraction is greater than or similar to 20%. On the other hand, the DSNB events show extremely poor statistical sensitivity to the nuclear equation of state and mass accretion rate of the progenitors forming black holes.