We have conducted a new search for the diffuse supernova neutrino background (DSNB) flux at Super-Kamiokande (SK), with a 22.5×2970-kton·day exposure from its fourth operational phase IV. With the new analysis we improve on the existing background reduction techniques and systematic uncertainties and take advantage of an improved neutron tagging algorithm to lower the energy threshold compared to the previous phases of SK. This allows for setting the world's most stringent upper limit on the extraterrestrial ν¯e flux, for neutrino energies below 31.3 MeV. The SK-IV results are combined with the ones from the first three phases of SK to perform a joint analysis using 22.5×5823 kton·days of data. This analysis has the world's best sensitivity to the DSNB ν¯e flux, comparable to the predictions from various models. For neutrino energies larger than 17.3 MeV, the new combined 90% CL upper limits on the DSNB ν¯e flux lie around 2.7 cm-2·sec-1, strongly disfavoring the most optimistic predictions. Finally, potentialities of the gadolinium phase of SK and the future Hyper-Kamiokande experiment are discussed.
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