Experimental Conditions for Determination of the Neutrino Mass Hierarchy with Reactor Antineutrinos

This article reports the optimized experimental requirements to determine neutrino mass hierarchy using electron antineutrinos ($\bar{\nu}_e$) generated in a nuclear reactor. The features of the neutrino mass hierarchy can be extracted from the $|\Delta m^{2}_{31}|$ and $|\Delta m^{2}_{32}|$ oscillations by applying the Fourier sine and cosine transform to the $L/E$ spectrum. To determine the neutrino mass hierarchy above 90\% probability, the requirements on the energy resolution as a function of the baseline are studied at $\sin 2\theta_{13}=0.1$. If the energy resolution of the neutrino detector is less than $0.04/ \sqrt{E_{\nu}}$ and the determination probability obtained from Bayes' theorem is above 90\%, the detector needs to be located around 48--53 km from the reactor(s) to measure the energy spectrum of $\bar{\nu}_e$. These results will be helpful for setting up an experiment to determine the neutrino mass hierarchy, which is an important problem in neutrino physics.