[Paper Review] Confidence in the neutrino mass hierarchy

Jarah Evslin|arXiv (Cornell University)|Oct 15, 2013

Neutrino Physics Research5 references3 citations

TL;DR

This paper develops a Bayesian framework to translate the expected $\overline{\Delta\chi^{2}}$ from neutrino oscillation experiments into a meaningful significance level for determining the neutrino mass hierarchy. It shows that $\overline{\Delta\chi^{2}} = 11$ ($20$) from 6 years of JUNO data combined with MINOS (NOvA) yields $2.6\sigma$ ($3.9\sigma$) sensitivity in median experiments, but this degrades significantly when nonlinear energy response uncertainties are included—restored by a two-detector setup with a near-far configuration and a $\pi^+$ decay-at-rest source for CP-phase measurement.

ABSTRACT

The number of sigma of confidence in a determination of the neutrino mass hierarchy may be obtained from the statistic Delta chi squared. However, as the hierarchy is a discrete variable, this number is not given by the usual square root formula. We review a simple Bayesian formula for the sensitivity to the hierarchy that can be obtained from the median experiment as a function of Delta chi squared. We compare this analytical formula to 6 years of simulated data from JUNO together with a 4% (1%) determination of the effective atmospheric mass splitting from the disappearance channel at MINOS (NOvA). We find a Delta chi squared of 11 (20) yielding 2.6 sigma (3.9 sigma). However when the unknown nonlinear energy response of the detector is included in our analysis this significance degrades considerably. This degradation can be eliminated by dividing the single detector into a near and far detector of the same total target mass. A further advantage of a second detector is that, even while the reactor neutrino experiment runs, the decay at rest of a single, high intensity, continuously running pion source close to one of the detectors, such as that described by the DAEdALUS project, may determine the leptonic CP-violating phase delta.

Motivation & Objective

• To establish a Bayesian method for translating $\overline{\Delta\chi^{2}}$ into a meaningful significance level for neutrino mass hierarchy determination.
• To assess how uncertainties in the detector's nonlinear energy response degrade hierarchy sensitivity in reactor experiments like JUNO.
• To evaluate the benefits of a two-detector configuration in mitigating energy response uncertainties and enabling additional physics, such as CP-violation phase measurement.
• To explore the synergy between reactor and accelerator experiments in improving mass hierarchy sensitivity through combined constraints on $\Delta m^2_{32}$.

Proposed method

• Uses a Bayesian approach with equal prior probabilities for normal and inverted hierarchies to compute the probability of correct hierarchy determination as a function of $\overline{\Delta\chi^{2}}$.
• Applies the formula $p_c(\overline{\Delta\chi^{2}}) = \frac{1}{2}\left(1 + \mathrm{erf}\left(\sqrt{\overline{\Delta\chi^{2}}/8}\right)\right)$ to estimate the mean success probability of hierarchy determination.
• Derives the median experiment significance via $s(\overline{\Delta\chi^{2}}) = \sqrt{2}\ \mathrm{erf}^{-1}\left(\frac{1 - e^{-\overline{\Delta\chi^{2}}/2}}{1 + e^{-\overline{\Delta\chi^{2}}/2}}\right)$, linking $\overline{\Delta\chi^{2}}$ to $\sigma$-level sensitivity.
• Performs 100,000 Monte Carlo simulations combining JUNO's 6-year reactor data with MINOS/NOvA constraints on $\Delta m^2_{32}$, including variations in $\delta$ and nonlinear energy response models.
• Evaluates the impact of nonlinear energy response by simulating different detector configurations (single vs. dual 10-kton detectors) at various sites, including DongKeng, GuemSeong, and Munmyeong.
• Proposes a dual-detector setup with a $\pi^+$ decay-at-rest source near one detector to simultaneously measure $\delta$ and improve hierarchy sensitivity.

Experimental results

Research questions

• RQ1 What is the correct way to interpret $\overline{\Delta\chi^{2}}$ as a significance level for neutrino mass hierarchy determination, given that the hierarchy is a discrete variable?
• RQ2 How does an unknown nonlinear energy response in scintillator detectors affect the sensitivity to the neutrino mass hierarchy in reactor experiments?
• RQ3 Can a two-detector configuration with different baselines restore hierarchy sensitivity degraded by energy response uncertainties?
• RQ4 What is the potential for a single $\pi^+$ decay-at-rest source to simultaneously determine the leptonic CP-violating phase $\delta$ and enhance hierarchy sensitivity?

Key findings

• With 6 years of JUNO data and a 4% determination of $\Delta m^2_{32}$ from MINOS, $\overline{\Delta\chi^{2}} = 11$ corresponds to $2.6\sigma$ significance in a median experiment.
• With a 1% determination from NOvA, $\overline{\Delta\chi^{2}} = 20$ yields $3.9\sigma$ significance, consistent with the analytical formula.
• When nonlinear energy response uncertainties are included, $\overline{\Delta\chi^{2}}$ drops significantly—e.g., from 14.1 to 8.2 at DongKeng—reducing significance from $3.2\sigma$ to $2.6\sigma$.
• A two-detector configuration with 10-kton near and far detectors at different baselines restores $\overline{\Delta\chi^{2}}$ to 13.9 (NH) and 13.5 (IH) at ZiLuoShan, eliminating the degradation from nonlinearity.
• The dual-detector setup enables a $\pi^+$ decay-at-rest experiment that can measure $\delta$ with high precision, even while the reactor experiment runs.
• At the DongKeng site, cosmic muon backgrounds (5 muons/sec) and $^9$Li backgrounds (200,000 decays in 6 years) pose a significant challenge, suggesting deeper excavation may be needed.