Neutrino mass hierarchy and precision physics with medium-baseline reactors: Impact of energy-scale and flux-shape uncertainties

Nuclear reactors provide intense sources of electron antineutrinos, characterized by few-MeV energy $E$ and unoscillated spectral shape $\mathrm{\Phi }(E)$. High-statistics observations of reactor neutrino oscillations over medium-baseline distances $L\sim O(50)\mathrm{km}$ would provide unprecedented opportunities to probe both the long-wavelength mass-mixing parameters ($\delta m^2$ and ${\theta }_{12}$) and the short-wavelength ones ($\mathrm{\Delta }{m}_{ee}^2$ and ${\theta }_{13}$), 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, $E\to E^{\prime }(E)$, and of the reactor flux shape, $\mathrm{\Phi }(E)\to {\mathrm{\Phi }}^{\prime }(E)$, 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.

Figure 1

Default $\pm 1\sigma$ error bands assumed for energy-scale deviations $E^{\prime }/E$ (top panel) and flux-shape variations ${\mathrm{\Phi }}^{\prime }/\mathrm{\Phi }$ (bottom panel), in terms of the neutrino energy $E$. Bands with halved errors are also shown (dot-dashed lines in both panels).

Figure 2

Comparison of event spectra in NH and IH, as obtained for fixed oscillation parameters and no systematic errors. Top: Absolute spectra for $T=5\mathrm{yr}$. Bottom: Spectral ratio.

Figure 3

Comparison of event spectra in NH (true, $S^{*}$) and IH (fitted, $S$), including oscillation and normalization uncertainties.

Figure 4

As in Fig. 3, but including energy-scale systematics.

Figure 5

As in Fig. 4, but including flux-shape systematics.

Figure 6

Energy profile of best-fit deviations $E^{\prime }/E$ (top panels) and ${\mathrm{\Phi }}^{\prime }/\mathrm{\Phi }$ (bottom panels), for different sets of systematic uncertainties.

Figure 7

Case of true NH: Statistical significance of the IH rejection as a function of the detector live time $T$, as derived from fits including different sets of systematics. Note that the abscissa scales as $\sqrt{T}$. The horizontal $3\sigma$ line is shown to guide the eye.

Figure 8

As in Fig. 7, but for true IH and rejection of NH.

Figure 9

Mass-mixing parameters $(\delta m^2,s_{12}^2)$: $1\sigma$ contours for true NH and $T=5\mathrm{yr}$, as derived from fits including different systematic uncertainties. The arrows indicate the best-fit displacement in the cases of wrong hierarchy (green arrow) and no matter effects (magenta arrow).

Figure 10

As in Fig. 9, but for the $(\mathrm{\Delta }{m}_{ee}^2,s_{13}^2)$ parameters.

Figure 11

As in Fig. 9, but for (Th, U) geo-$\nu$ normalizations.

Figure 12

As in Fig. 5, but with halved energy-scale and flux-shape errors.

Figure 13

As in Fig. 6, but with halved energy-scale and flux-shape uncertainties.

Figure 14

As in Fig. 7 (true NH), but with halved energy-scale and flux-shape uncertainties.

Figure 15

As in Fig. 14, but for true IH.

Figure 16

As in Fig. 9, but with halved energy-scale and flux-shape uncertainties.

Figure 17

As in Fig. 10, but with halved energy-scale and flux-shape uncertainties.