Determining Neutrino Mass Ordering with NOvA and Upcoming JUNO Measurements

This paper demonstrates that combining NOvA's ten-year data with anticipated precise measurements of $|\Delta m^2_{32}|$ from the upcoming JUNO experiment could enable the determination of the neutrino mass ordering with $3\sigma$ significance within the next five years.

The Gist

The Big Mystery: Which Way is "Up"?

Imagine neutrinos as tiny, ghost-like messengers that zip through the universe. Scientists know these messengers come in three different "flavors" (like different types of ice cream), and they can change from one flavor to another as they travel. This is called "oscillation."

However, there is a massive mystery hanging over this field: What is the "Mass Ordering"?

Think of the three neutrino flavors as three siblings with different weights. We know the two lighter siblings are close in weight, but we don't know if the third, heaviest sibling is:

1. Normal Ordering: The heaviest sibling is actually the heaviest (a clear hierarchy).
2. Inverted Ordering: The heaviest sibling is actually the lightest (a flipped hierarchy).

Knowing which one it is is crucial. It helps scientists understand how the universe was built, how stars explode, and what the future of the cosmos looks like. But right now, the answer is still a toss-up.

The Two Detectives: NOvA and JUNO

To solve this mystery, the paper looks at two different "detectives" (experiments) trying to weigh these siblings.

1. NOvA (The Long-Distance Runner)
NOvA is an experiment in the US that shoots a beam of neutrinos 500 miles (810 km) through the Earth.

• How it works: It's like throwing a ball through a foggy field. As the neutrinos travel through the Earth (the "fog"), they interact with matter, which changes how they oscillate. This interaction depends on whether the mass ordering is "Normal" or "Inverted."
• The Problem: NOvA is good at this, but it has a blind spot. Its results are heavily influenced by another unknown variable (called $\delta_{CP}$), which acts like a "twist" in the neutrino's path. Because of this twist, NOvA alone is only about 70% sure which ordering is correct. It's like a detective who has a strong hunch but lacks the final piece of evidence.

2. JUNO (The Precision Scale)
JUNO is a new experiment in China that is just starting to take data. It watches neutrinos coming from nuclear power plants (reactors).

• How it works: Instead of shooting a beam, JUNO sits still and counts neutrinos disappearing. Because it's so close to the source and has a massive detector, it can measure the "weight difference" between the neutrino siblings with incredible precision.
• The Goal: JUNO is expected to measure the mass difference so precisely that it acts like a super-accurate scale.

The Strategy: Teamwork Makes the Dream Work

The paper asks a simple question: What happens if NOvA and JUNO combine their notes?

The authors ran a simulation to see how JUNO's future, ultra-precise measurements would help NOvA solve the mystery.

• The Analogy: Imagine NOvA is trying to guess the exact weight of a mystery box, but its scale is a bit wobbly. JUNO is a lab with a perfect, high-tech scale. If JUNO tells NOvA, "The box weighs exactly 10.00 kg," NOvA can use that number to fix its own wobbly scale and finally figure out the mystery.

What They Found

The paper concludes that if JUNO measures the mass difference with high precision (better than 1% error) and the result falls within a specific range, NOvA could solve the mystery in the next five years.

• The "3 Sigma" Goal: In science, "3 sigma" is a high bar for confidence. It means there is a 99.7% chance the result isn't just a fluke. The paper says that with JUNO's help, NOvA could reach this level of confidence for the Normal Ordering.
• The Catch: This only works if JUNO's measurement lands in a specific "sweet spot." If JUNO's measurement is slightly off or not precise enough, NOvA might still be stuck in the middle, unable to declare a winner.

The Bottom Line

This paper is a roadmap for the next few years. It tells us that:

1. We are close to solving the neutrino mass mystery.
2. NOvA needs a little help from JUNO's new, precise data to get there.
3. If everything goes according to plan, we could have a definitive answer on whether neutrinos are "Normal" or "Inverted" very soon, without waiting for the next generation of experiments.

It's a story of two experiments working together: one providing the long-distance view and the other providing the microscopic precision, combining forces to finally weigh the ghostly neutrinos.

Technical Summary

Technical Summary: Determining Neutrino Mass Ordering with NOvA and Upcoming JUNO Measurements

Problem Statement
The fundamental nature of neutrino mass remains incomplete, specifically regarding the "mass ordering" (or hierarchy). While the solar mass-squared difference $\Delta m^2_{21}$ is known to be positive, the sign of the atmospheric mass-squared difference $\Delta m^2_{32}$ (or $\Delta m^2_{31}$) is unknown. A positive sign corresponds to the normal ordering (NO), and a negative sign to the inverted ordering (IO). Determining this ordering is critical for understanding neutrino mass generation mechanisms, interpreting supernova neutrino fluxes, analyzing neutrinoless double beta decay, and refining cosmological models.

Current experimental status is inconclusive. Previous analyses by NOvA, T2K, and Super-Kamiokande show mild preferences for normal ordering, while cosmological data disfavors inverted ordering. However, joint NOvA-T2K oscillation analyses suggest that good agreement with the CP-violating phase ($\delta_{CP}$) is achieved only under the inverted ordering hypothesis. NOvA's standalone 10-year dataset yields a 70% posterior probability for normal ordering, which rises to 87% (a $1.6\sigma$ preference) when constrained by external measurements of $\Delta m^2_{32}$ and $\sin^2\theta_{13}$ from the Daya Bay reactor experiment. The authors posit that the upcoming JUNO reactor experiment, with its anticipated sub-percent precision on $|\Delta m^2_{32}|$, could significantly enhance the sensitivity of NOvA to resolve the mass ordering.

Methodology
The authors perform a Bayesian inference analysis to assess the potential impact of a precise JUNO measurement on NOvA's mass ordering determination. The methodology involves:

1. Data and Framework: The analysis utilizes NOvA's 10-year dataset of $\nu_\mu$ disappearance and $\nu_e$ appearance (neutrinos and antineutrinos). The statistical framework follows the Bayesian approach detailed in Ref. [10], employing Hamiltonian Markov chain Monte Carlo (via Stan) to sample posteriors.
2. Constraints and Priors:
   • The external constraint on $\sin^2(2\theta_{13})$ from Daya Bay is retained.
   • The existing Daya Bay constraint on $\Delta m^2_{32}$ is removed and replaced with a series of hypothetical reactor constraints modeled as one-dimensional bi-Gaussian priors. These priors represent potential future measurements with varying central values and fractional uncertainties (up to 2%).
   • The analysis assumes a specific offset $\lambda \equiv \delta(|\Delta m^2_{32}|)_{NO-IO} \approx 0.12 \times 10^{-3} \text{ eV}^2$ between the NO and IO hypotheses, derived from JUNO's expected performance.
3. Sensitivity Analysis: The authors scan a range of central values for $\Delta m^2_{32}$ and associated uncertainties. They calculate the Bayes Factor (BF), defined as the ratio of posterior probabilities for normal versus inverted ordering. The significance in terms of sigma ($\sigma$) is derived by mapping the posterior probability to a two-sided Gaussian tail probability.
4. Offset Adjustment: Recognizing that the actual offset $\lambda$ measured by JUNO may differ from the assumed nominal value, the authors provide a derivative function $d[\log_{10}(\text{BF})]/d\lambda$ (Fig. 3) to allow adjustment of the results based on JUNO's actual observed offset.

Key Contributions and Results
The paper quantifies the conditions under which NOvA, aided by a JUNO-like measurement, could achieve a $3\sigma$ evidence level for the mass ordering:

• Complementarity: The analysis confirms that the combination of long-baseline (NOvA) and reactor (JUNO) measurements is powerful because the extracted values of $\Delta m^2_{32}$ should agree if the correct ordering is assumed but disagree if the incorrect ordering is assumed.
• Significance Thresholds:
  • If a reactor experiment measures $\Delta m^2_{32} > 2.490 \times 10^{-3} \text{ eV}^2$ (under the normal ordering hypothesis) with a precision of 0.3% or better, NOvA combined with this data would achieve $>3\sigma$ evidence for normal ordering.
  • As the central value of the reactor measurement increases, the required precision to maintain $3\sigma$ significance relaxes slightly (as shown by the iso-contours in Fig. 2).
  • Conversely, achieving $3\sigma$ evidence for inverted ordering would require a reactor measurement of $\Delta m^2_{32} < 2.25 \times 10^{-3} \text{ eV}^2$ (under the normal ordering hypothesis), a value the authors note is far outside the range of current experimental measurements.
• Limitations and Tension:
  • If the reactor central value exceeds $2.55 \times 10^{-3} \text{ eV}^2$, the NOvA and reactor measurements would be in strong tension under both ordering hypotheses, rendering the combined inference unreliable.
  • For reactor measurements with precision better than $\sim0.3\%$, the sensitivity is limited by the current precision of NOvA's data (approximately 1.5% uncertainty on the mass splitting). Further improvements in NOvA's sensitivity would require additional muon neutrino disappearance data and tighter systematic control.

Significance and Claims
The paper concludes that a precise reactor measurement of $\Delta m^2_{32}$ from JUNO has the potential to enhance NOvA's current $1.6\sigma$ preference for normal ordering, potentially providing $3\sigma$ evidence for the normal mass ordering within the next five years, provided JUNO's central value falls within a plausible range (specifically $>2.490 \times 10^{-3} \text{ eV}^2$).

However, the authors maintain a modest tone regarding the certainty of this outcome. They state that if the reactor central value remains near the current global average, the precision anticipated from JUNO alone may be insufficient to enable an early determination of the mass ordering through this specific complementarity. In such a scenario, a definitive result would still require either improved precision from long-baseline measurements or the accumulation of sufficient exposure for experiments to establish the ordering independently. The work serves as a projection of potential sensitivity rather than a guarantee of a specific discovery, contingent on the actual future data from JUNO.