Can the Earth help tell which neutrino mass comes first?

Knowing the gaps does not fix the order

Solar measurements reveal a closely spaced pair of mass states, labeled one and two by convention, with the second heavier than the first. The third state lies across the larger splitting. The open question is whether it sits above or below that pair.

In the normal ordering the third state is above the solar pair; in the inverted ordering it is below. The labels refer to mass states and do not rank the electron, muon and tau flavors. Each flavor is a mixture of mass states, so “the heaviest flavor” mixes up two different descriptions.

The ordering is a separate question from the absolute masses. Knowing which arrangement fits does not give the lightest mass. Oscillation phases mainly reveal mass-squared differences, and adding the same amount to every squared mass leaves the vacuum oscillation pattern unchanged.

Sources: [1] · [2] · [3]

Electrons in rock change how neutrinos travel

Electrons in ordinary matter give electron-flavor neutrinos an extra term from coherent forward scattering; for antineutrinos the term has the opposite sign. Added to the vacuum mass term, it changes the states that propagate locally, and with them the flavor probabilities.

For atmospheric neutrinos crossing the Earth, the key enhancement at higher energy involves the larger mass splitting and the smaller mixing angle tied to the third state. Under the standard assumptions, the enhancement appears for neutrinos in the normal ordering and for antineutrinos in the inverted ordering.

The effect is related to the MSW mechanism in the Sun, but the density profile and the dominant splitting are different. Paths through the mantle and the core differ, and changes between layers can add interference features beyond a single constant-density resonance.

Sources: [4] · [1] · [3] · [5]

The detector sees a pattern of interactions

The arrival direction gives an estimate of how much Earth a neutrino crossed, and the reconstructed energy shows where the flavor changes should appear. Analyses therefore compare event distributions in energy, zenith angle and electron-like or muon-like classes.

They must also tell neutrinos from antineutrinos, either statistically or from suitable event information. In a water detector without a magnetic field, an electron-like event does not by itself show whether a neutrino or an antineutrino produced it. The two have different fluxes and cross sections, so they do not enter a combined sample with equal weight.

The prediction combines production in the atmosphere, Earth’s density, flavor evolution, nuclear interactions and the detector response. Misreconstructed energies, neutral-current backgrounds and flavor selection all affect how clearly the ordering pattern survives in the observed sample.

Sources: [3] · [6] · [1] · [7]

Other parameters can imitate part of the change

Mixing angles, the CP phase and uncertainties in interaction models can shift some of the same event distributions. An ordering analysis has to fit or constrain them. It cannot simply compare two fixed pictures with every other parameter treated as exactly known.

Reactor and accelerator measurements add outside constraints, and independent atmospheric detectors bring different responses. Combining them can sharpen the distinction, but it can also expose tension: samples that each look favorable on their own need not prefer the same parameter values.

NuFIT 6.0, based on data available in September 2024, shows this. Its ordering preference changed noticeably when the published Super-K atmospheric likelihood was included. That is why a quoted preference must come with its dataset and statistical treatment. It is a dated result, not the final world average for 2026.

Sources: [2] · [3] · [7] · [1]

Current status: an indication, not yet a discovery

Another route to the ordering uses fine structure in a reactor spectrum measured at medium distance, which comes mainly from vacuum interference. JUNO therefore complements Earth-matter measurements: it relies on a different effect from the Earth resonance.

The JUNO Collaboration’s preprint of 29 September 2026 used 207.2 live days of data. With a Daya Bay constraint in the oscillation fit, plus long-baseline accelerator constraints in the ordering comparison, it reported a preference for normal ordering of at least 2.1 standard deviations across the CP phases tested.

This is an indication that depends on combined constraints; JUNO alone has not discovered the ordering. That is what the cited result supported when this article was checked on 9 October 2026. A stronger claim will need the spectral and matter signatures compared side by side, with their uncertainties shown.

Sources: [8] · [2] · [1]

Try it in the Lab

Primary sources & revision

1. Particle Data Group · Neutrino Masses, Mixing, and Oscillations (2024)
2. Esteban et al. · NuFIT 6.0 global analysis (2024)
3. Super-Kamiokande Collaboration · Atmospheric analysis with external constraints (2018)
4. Lincoln Wolfenstein · Neutrino oscillations in matter (1978)
5. Dziewonski & Anderson · Preliminary reference Earth model (1981)
6. Honda et al. · Atmospheric flux with a model calibrated to muon data (2007)
7. IceCube Collaboration · DeepCore mass-ordering analysis development (2020)
8. JUNO Collaboration · Oscillation parameters and indication of mass ordering (29 September 2026)

First published 2026-10-09; last revised 2026-10-11. Original explanatory text and diagrams by Sandbox Physics. Illustrations are schematic; no experimental event records are reproduced here. This is an independent educational publication, not an official Nobel or experiment collaboration publication.