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 $\ensuremath{\Delta}{m}_{31}^{2}$ and $\ensuremath{\Delta}{m}_{32}^{2}$ oscillations enables a relative measurement independent of the knowledge of the absolute mass-squared difference. With a 20 kton liquid scintillator detector of the $3%/\sqrt{E\text{ }\text{ }(\mathrm{MeV})}$ energy resolution, the Daya Bay II experiment at a baseline of $\ensuremath{\sim}50\text{ }\text{ }\mathrm{km}$ from reactors of total thermal power 36 GW can determine the mass hierarchy at a confidence level of $\ensuremath{\Delta}{\ensuremath{\chi}}_{\mathrm{MH}}^{2}\ensuremath{\sim}(10\textdiv{}12)$ ($3\textdiv{}3.5\ensuremath{\sigma}$) 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 $\ensuremath{\Delta}{\ensuremath{\chi}}_{\mathrm{MH}}^{2}\ensuremath{\simeq}4(9)$ can be obtained, by including the precise measurement of the effective mass-squared difference $\ensuremath{\Delta}{m}_{\ensuremath{\mu}\ensuremath{\mu}}^{2}$ 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 $\ensuremath{\Delta}{\ensuremath{\chi}}_{\mathrm{MH}}^{2}\ensuremath{\sim}(15\textdiv{}20)$ ($4\ensuremath{\sigma}$) in six years.