Search for <i>hep</i> solar neutrinos and the diffuse supernova neutrino background using all three phases of the Sudbury Neutrino Observatory

A search has been performed for neutrinos from two sources, the hep reaction in the solar $pp$ fusion chain and the ${\ensuremath{\nu}}_{e}$ component of the diffuse supernova neutrino background (DSNB), using the full dataset of the Sudbury Neutrino Observatory with a total exposure of $2.47\text{ }\text{ }\mathrm{kton}\text{\ensuremath{-}}\mathrm{years}$ after fiducialization. The hep search is performed using both a single-bin counting analysis and a likelihood fit. We find a best-fit flux that is compatible with solar model predictions while remaining consistent with zero flux, and set a one-sided upper limit of ${\mathrm{\ensuremath{\Phi}}}_{hep}&lt;30\ifmmode\times\else\texttimes\fi{}{10}^{3}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}2}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ [90% credible interval (CI)]. No events are observed in the DSNB search region, and we set an improved upper bound on the ${\ensuremath{\nu}}_{e}$ component of the DSNB flux of ${\mathrm{\ensuremath{\Phi}}}_{{\ensuremath{\nu}}_{e}}^{\mathrm{DSNB}}&lt;19\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}2}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ (90% CI) in the energy range $22.9&lt;{E}_{\ensuremath{\nu}}&lt;36.9\text{ }\text{ }\mathrm{MeV}$.