Experimental requirements to determine the neutrino mass hierarchy using reactor neutrinos

This paper presents experimental requirements to determine the neutrino mass hierarchy using reactor neutrinos. The detector shall be located at a baseline around 58 km from the reactor(s) to measure the energy spectrum of electron antineutrinos (${\overline{\nu }}_e$) precisely. By applying Fourier cosine and sine transforms to the L/E spectrum, features of the neutrino mass hierarchy can be extracted from the $|\Delta m_{31}^2|$ and $|\Delta m_{32}^2|$ oscillations. To determine the neutrino mass hierarchy above 90% probability, requirements to the baseline, the energy resolution, the energy scale uncertainty, the detector mass, and the event statistics are studied at different values of ${sin}^2(2{\theta }_{13})$.

Figure 1

FCT and FST spectra from simulation with parameters $({sin}^2(2{\theta }_{13}),{\sigma }_E)=(0.02,3\%/\sqrt{E_{\mathrm{vis}}})$, together with the analytical spectra for ${sin}^2(2{\theta }_{13})=0.02$. Solid and long-dashed lines are spectra based on simulation for NH and IH cases, while dashed and dotted lines are analytical spectra.

Figure 2

Distribution of RL and PV values from 500 simulated experiments with parameters $({sin}^2(2{\theta }_{13}),{\sigma }_E)=(0.02,2\%/\sqrt{E_{\mathrm{vis}}})$. Two clusters of points show the sensitivity to determine the mass hierarchy.

Figure 3

Distribution of $\mathrm{RL}+\mathrm{PV}$ values from 1000 experiments for parameters $({sin}^2(2{\theta }_{13}),{\sigma }_E)$ being $(0.01,2\%/\sqrt{E_{\mathrm{vis}}})$, $(0.01,3\%/\sqrt{E_{\mathrm{vis}}})$, $(0.02,2\%/\sqrt{E_{\mathrm{vis}}})$, and $(0.02,3\%/\sqrt{E_{\mathrm{vis}}})$. Two Gaussian distributions show the sensitivity to determine the mass hierarchy.

Figure 4

Impact of the baseline to the determination probability for 4 sets of parameters $({sin}^2(2{\theta }_{13}),{\sigma }_E)$.

Figure 5

Impact of the event number to the determination probability in six sets of parameters $({sin}^2(2{\theta }_{13}),{\sigma }_E)$.

Figure 6

Requirements to the number of events to determine the mass hierarchy at 90% probability as a function of ${sin}^2(2{\theta }_{13})$.

Figure 7

Impact of the energy resolution to the determination probability for ${sin}^2(2{\theta }_{13})=0.02$, 0.01, and 0.005.

Figure 8

Impact of ${sin}^2(2{\theta }_{13})$ to the determination probability in four cases of the energy resolution.

Figure 9

FCT spectra for an energy shift of 0.01 MeV and shrinking of 1%.