Measurement of neutrino and antineutrino neutral-current quasielastic-like interactions on oxygen by detecting nuclear de-excitation $\gamma$-rays

Neutrino- and antineutrino-oxygen neutral-current quasielastic-like interactions are measured at Super-Kamiokande using nuclear de-excitation $\gamma$-rays to identify signal-like interactions in data from a $14.94 \ (16.35)\times 10^{20}$ protons-on-target exposure of the T2K neutrino (antineutrino) beam. The measured flux-averaged cross sections on oxygen nuclei are $\langle \sigma_{\nu {\rm -NCQE}} \rangle = 1.70 \pm 0.17 ({\rm stat.}) ^{+ {\rm 0.51}}_{- {\rm 0.38}} ({\rm syst.}) \times 10^{-38} \ {\rm cm^2/oxygen}$ with a flux-averaged energy of 0.82 GeV and $\langle \sigma_{\bar{\nu} {\rm -NCQE}} \rangle = 0.98 \pm 0.16 ({\rm stat.}) ^{+ {\rm 0.26}}_{- {\rm 0.19}} ({\rm syst.}) \times 10^{-38} \ {\rm cm^2/oxygen}$ with a flux-averaged energy of 0.68 GeV, for neutrinos and antineutrinos, respectively. These results are the most precise to date, and the antineutrino result is the first cross section measurement of this channel. They are compared with various theoretical predictions. The impact on evaluation of backgrounds to searches for supernova relic neutrinos at present and future water Cherenkov detectors is also discussed.