Unambiguous determination of the neutrino mass hierarchy using reactor neutrinos

Determination of the neutrino mass hierarchy in a reactor neutrino experiment at the medium baseline is discussed. Observation of the interference effects between the $\Delta m_{31}^2$ and $\Delta m_{32}^2$ oscillations enables a relative measurement independent of the knowledge of the absolute mass-squared difference. With a 20 kton liquid scintillator detector of the $3\%/\sqrt{E(\mathrm{MeV})}$ energy resolution, the Daya Bay II experiment at a baseline of $\sim 50\mathrm{km}$ from reactors of total thermal power 36 GW can determine the mass hierarchy at a confidence level of $\Delta {\chi }_{\mathrm{MH}}^2\sim (10÷12)$ ($3÷3.5\sigma$) in six years after taking into account the real spatial distribution of reactor cores. We show that the unknown residual energy nonlinearity of the liquid scintillator detector has limited impact on the sensitivity due to the self-calibration of small oscillation peaks. Furthermore, an extra increase of $\Delta {\chi }_{\mathrm{MH}}^2\simeq 4(9)$ can be obtained, by including the precise measurement of the effective mass-squared difference $\Delta m_{\mu \mu }^2$ of expected relative error 1.5% (1%) from ongoing long-baseline muon neutrino disappearance experiments. The sensitivities from the interference and from absolute measurements can be cross-checked. When combining these two, the mass hierarchy can be determined at a confidence level of $\Delta {\chi }_{\mathrm{MH}}^2\sim (15÷20)$ ($4\sigma$) in six years.

Figure 1

The MH discrimination ability for the proposed reactor neutrino experiment as functions of the baseline (left panel) and the detector energy resolution (right panel) with the method of the least-squares function in Eq. (11).

Figure 2

The variation (left panel) of the MH sensitivity as a function of the baseline difference of two reactors and the comparison (right panel) of the MH sensitivity for the ideal and actual distributions of the reactor cores.

Figure 3

Two classes of typical examples for the residual nonlinear functions in our simulation.

Figure 4

Effects of two classes of energy nonlinearity models in the determination of the neutrino MH without the self-calibration in fitting. The normal (inverted) MH is assumed to be the true one in the upper (lower) panels. The sign and size of the nonlinear parameters in the form of $(p_0,p_1)$ are indicated in the legend.

Figure 5

Effects of two classes of energy nonlinearity models in the determination of the neutrino MH with the self-calibration in fitting. The normal (inverted) MH is assumed to be the true one in the upper (lower) panels. The sign and size of the nonlinear parameters in the form of $(p_0,p_1)$ are indicated in the legend.

Figure 6

The reactor-only (dashed) and combined (solid) distributions of the $\Delta {\chi }^2$ function in Eqs. (11, 17), where a 1% (left panel) or 1.5% (right panel) relative error of $\Delta m_{\mu \mu }^2$ is assumed and the $CP$-violating phase ($\delta$) is assigned to be $90°/270°$ ($\cos \delta =0$) for illustration. The black and red lines are for the true (normal) and false (inverted) neutrino MH, respectively. The nonlinearity in Eq. (13) is assigned with $\mathrm{\text{sign}}=+1$, ${\mathrm{\text{size}}}_0=2\%$, and ${\mathrm{\text{size}}}_1=4\%$.

Figure 7

The $\Delta {\chi }_{\mathrm{MH}}^2$ dependence on different input errors of $\Delta m_{\mu \mu }^2$ is illustrated. The blue dashed, black solid, and red dotted lines stands for different $CP$ values ($\delta =0°$, $\delta =90°/270°$, and $\delta =180°$, respectively).