Determination of mass hierarchy with medium baseline reactor neutrino experiments

Abstract

We study the sensitivity of future medium baseline reactor antineutrino experiments on the neutrino mass hierarchy. By using the standard χ ² analysis, we find that the sensitivity depends strongly on the baseline length L and the energy resolution ${{\left( {{{{\delta E}} \left/ {E} \right.}} \right)}^2}={{\left( {{a \left/ {{\sqrt{{{E \left/ {\mathrm{MeV}} \right.}}}}} \right.}} \right)}^2}+{b^2}$, where a and b parameterize the statistical and systematic uncertainties, respectively. The optimal length is found to be L ~ 40 − 55 km, where a slightly shorter L in the range is preferred for poorer energy resolution. The running time needed to determine the mass hierarchy also depends strongly on the energy resolution; for a 5 kton detector (with 12% weight fraction of free proton) placed at L ~ 50 km away from a 20 GW_th reactor, an experiment would determine the mass hierarchy with (Δχ ²)_min ~ 9 on average after 5 (15) or more years of running if the energy resolution (a, b) = (2, 0.5)% ((3, 0.5)%) is achieved. The probability that an experiment with the expectation of $\overline{{{{{\left( {\varDelta {\chi^2}} \right)}}_{\min }}}}=9$ resolves the mass hierarchy is estimated to be ~ 90% by taking into account statistical fluctuation in the data. On the other hand, the experiment can measure the mixing parameters accurately, achieving δ sin² 2θ ₁₂ ~ 4 × 10⁻³, $\delta \left( {m_2^2-m_1^2} \right)$ ~ 0.03 × 10⁻⁵eV² , and $\delta \left| {m_3^2-m_1^2} \right|$ ~ 0.007 × 10⁻³eV², in 5 years, almost independently of the energy resolution for a < 3% and b < 1%. In order to compare our simple (Δχ ²)_min results with those obtained by simulating many experiments, we develop an efficient method to estimate the uncertainty of (Δχ ²)_min, and the probability for determining the right mass hierarchy by an experiment is presented as a function of the mean (Δχ ²)_min.