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Sensitivity to oscillation with a sterile fourth generation neutrino from ultra-low threshold neutrino-nucleus coherent scattering

We discuss prospects for probing short-range sterile neutrino oscillation using neutrino-nucleus coherent scattering with ultra-low energy ($\sim 10$ eV - 100 eV) recoil threshold cryogenic Ge detectors. The analysis is performed in the context of a specific and contemporary reactor-based experimental proposal, developed in cooperation with the Nuclear Science Center at Texas A\&M University, and references developing technology based upon economical and scalable detector arrays. The baseline of the experiment is substantially shorter than existing measurements, as near as about 2 meters from the reactor core, and is moreover variable, extending continuously up to a range of about 10 meters. This proximity and variety combine to provide extraordinary sensitivity to a wide spectrum of oscillation scales, while facilitating the tidy cancellation of leading systematic uncertainties in the reactor source and environment. With 100~eV sensitivity, for exposures on the order of 200 kg$\cdot$y, we project an estimated sensitivity to first/fourth neutrino oscillation with a mass gap $Δm^2 \sim 1 \, {\rm eV}^2$ at an amplitude $\sin^2 2θ\sim 10^{-1}$, or $Δm^2 \sim 0.2 \, {\rm eV}^2$ at unit amplitude. Larger exposures, around 5,000 kg$\cdot$y, together with 10 eV sensitivity are capable of probing more than an additional order of magnitude in amplitude.