Search for $hep$ 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 $\nu_e$ component of the diffuse supernova neutrino background (DSNB), using the full dataset of the Sudbury Neutrino Observatory with a total exposure of 2.47 kton-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 $\Phi_{hep} < 30\times10^{3}~\mathrm{cm}^{-2}~\mathrm{s}^{-1}$ [90% credible interval (CI)]. No events are observed in the DSNB search region, and we set an improved upper bound on the $\nu_e$ component of the DSNB flux of $\Phi^\mathrm{DSNB}_{\nu_e} < 19~\textrm{cm}^{-2}~\textrm{s}^{-1}$ (90% CI) in the energy range $22.9 < E_\nu < 36.9$~MeV.