The diffuse neutrino flux from supernovae: upper limit on the electron neutrino component from the non-observation of antineutrinos at SuperKamiokande

I derive an upper bound on the electron neutrino component of the diffuse supernova neutrino flux from the constraint on the antineutrino component at SuperKamiokande. The connection between antineutrino and neutrino channels is due to the similarity of the muon and tau neutrino and antineutrino fluxes produced in a supernova, and to the conversion of these species into electron neutrinos and antineutrinos inside the star. The limit on the electron neutrino flux is 5.5 cm^-2 s^-1 above 19.3 MeV of neutrino energy, and is stronger than the direct limit from Mont Blanc by three orders of magnitude. It represents the minimal sensitivity required at future direct searches, and is intriguingly close to the reach of the Sudbury Neutrino Observatory (SNO) and of the ICARUS experiment. The electron neutrino flux will have a lower bound if the electron antineutrino flux is measured. Indicatively, the first can be smaller than the second at most by a factor of 2-3 depending on the details of the neutrino spectra at production.