Neutral-Current Atmospheric Neutrino Flux Measurement Using Neutrino-Proton Elastic Scattering in Super-Kamiokande

Recent results show that atmospheric $\nu_\mu$ oscillate with $\delta m^2 \simeq 3 \times 10^{-3}$ eV$^2$ and $\sin^2{2\theta_{atm}} \simeq 1$, and that conversion into $\nu_e$ is strongly disfavored. The Super-Kamiokande (SK) collaboration, using a combination of three techniques, reports that their data favor $\nu_\mu \to \nu_\tau$ over $\nu_\mu \to \nu_{sterile}$. This distinction is extremely important for both four-neutrino models and cosmology. We propose that neutrino-proton elastic scattering ($\nu + p \to \nu + p$) in water \v{C}erenkov detectors can also distinguish between active and sterile oscillations. This was not previously recognized as a useful channel since only about 2% of struck protons are above the \v{C}erenkov threshold. Nevertheless, in the present SK data there should be about 40 identifiable events. We show that these events have unique particle identification characteristics, point in the direction of the incoming neutrinos, and correspond to a narrow range of neutrino energies (1-3 GeV, oscillating near the horizon). This channel will be particularly important in Hyper-Kamiokande, with $\sim 40$ times higher rate. Our results have other important applications. First, for a similarly small fraction of atmospheric neutrino quasielastic events, the proton is relativistic. This uniquely selects $\nu_\mu$ (not $\bar{\nu}_\mu$) events, useful for understanding matter effects, and allows determination of the neutrino energy and direction, useful for the $L/E$ dependence of oscillations. Second, using accelerator neutrinos, both elastic and quasielastic events with relativistic protons can be seen in the K2K 1-kton near detector and MiniBooNE.