Nuclear reactors provide intense sources of electron antineutrinos, characterized by few-MeV energy E and unoscillated spectral shape Φ(E). High-statistics observations of reactor neutrino oscillations over medium-baseline distances L∼O(50) km would provide unprecedented opportunities to probe both the long-wavelength mass-mixing parameters (δm2 and θ12) and the short-wavelength ones (Δmee2 and θ13), together with the subtle interference effects associated with the neutrino mass hierarchy (either normal or inverted). In a given experimental setting - here taken as in the JUNO project for definiteness - the achievable hierarchy sensitivity and parameter accuracy depend not only on the accumulated statistics but also on systematic uncertainties, which include (but are not limited to) the mass-mixing priors and the normalizations of signals and backgrounds. We examine, in addition, the effect of introducing smooth deformations of the detector energy scale, E→E′(E), and of the reactor flux shape, Φ(E)→Φ′(E), within reasonable error bands inspired by state-of-the-art estimates. It turns out that energy-scale and flux-shape systematics can noticeably affect the performance of a JUNO-like experiment, both on the hierarchy discrimination and on precision oscillation physics. It is shown that a significant reduction of the assumed energy-scale and flux-shape uncertainties (by, say, a factor of 2) would be highly beneficial to the physics program of medium-baseline reactor projects. Our results also shed some light on the role of the inverse-beta decay threshold, of geoneutrino backgrounds, and of matter effects in the analysis of future reactor oscillation data.
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