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Neutrino experiments do not all measure the same mass. Oscillation experiments prove that neutrinos have nonzero mass and measure differences between the squared masses. Tritium beta-decay experiments such as KATRIN make a direct laboratory test of an electron-flavor-weighted mass. Cosmological observations from the cosmic microwave background (CMB), baryon acoustic oscillations (BAO) and galaxy surveys constrain the sum of the three masses under an assumed model of the universe. Their results are complementary, not interchangeable.
The three measurements answer different questions
A useful first step is to identify the quantity each method actually determines. Neutrinos are produced and detected in flavor states—electron, muon or tau—but travel as quantum mixtures of mass eigenstates. Because those mass eigenstates have different masses, an experiment can be sensitive to mass differences, an electron-flavor combination, or the total mass carried through cosmic history.
| Method | What is observed | Mass quantity | Main strength | Main limitation |
|---|---|---|---|---|
| Oscillation | Flavor-transition probability versus energy and travel distance | Mass-squared differences (Δm²) and mixing parameters | Established nonzero mass and provides information sensitive to mass ordering | Cannot determine the absolute mass scale; long-baseline or reactor/solar data and matter-effect modeling are required |
| Tritium beta decay (KATRIN) | Electron-energy spectrum close to the beta endpoint | Effective electron-neutrino mass, mβ | Direct, laboratory, kinematic constraint with relatively few cosmological assumptions | The endpoint distortion is tiny, and source and instrumental backgrounds limit sensitivity |
| Cosmology (Planck, BAO and DESI analyses) | CMB anisotropies and lensing, galaxy clustering, BAO and structure growth | Sum of neutrino masses, Σmν | Very strong numerical leverage on the total mass | Results depend on the baseline cosmological model, calibration, nonlinear structure modeling and consistency of the data sets |
These distinctions explain why a limit of 0.8 eV from KATRIN and a limit of 0.12 eV from Planck plus BAO cannot be compared as though they were two measurements of one parameter.
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How oscillation experiments reveal that neutrinos have mass
Flavor states are mixtures of mass states
A neutrino created in a weak interaction has a defined flavor, but that flavor state is a combination of mass eigenstates. As the components propagate, each accumulates a quantum-mechanical phase. The phase depends on the mass-squared value, energy and distance traveled. When the components are recombined at detection, the probability of observing a particular flavor can differ from the production flavor.
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Experiments therefore measure a changing transition probability as they vary energy, baseline, or both. Reactor and solar experiments observe disappearance or appearance over comparatively short or astronomical distances; accelerator and long-baseline experiments track flavor changes over controlled distances. Matter effects in the Earth or the Sun alter the propagation and must be modeled when extracting parameters.
What the oscillation frequency determines
The measured oscillation frequencies determine differences such as Δm²21 and the larger atmospheric-scale splitting, along with mixing angles and a possible CP-violating phase. A nonzero splitting means that at least two mass eigenstates are nonzero: if all masses were zero and degenerate, no mass-dependent phase difference would develop.
This is decisive evidence for neutrino mass, but it is not an absolute weighing. If the same constant mass were added to every eigenstate, the differences between squared masses would change in a way that can be compensated only in limited circumstances; more fundamentally, oscillation patterns are controlled by splittings and mixing, not by a common lowest-mass offset. Many spectra with the same measured splittings can therefore produce the same oscillation data while having different absolute masses.
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What oscillation data can and cannot say about ordering
The signs and sizes of the splittings, together with matter effects, provide information about whether the lightest state belongs to one ordering or the other. Once an ordering is assumed, the measured splittings imply a minimum scale for the masses and a minimum possible mass sum. Oscillation alone still does not tell you how far above that minimum the entire spectrum sits. A direct absolute-mass result must come from another technique.
What KATRIN measures in tritium beta decay
The endpoint method
In tritium beta decay, a tritium nucleus transforms into helium-3, an electron and an electron antineutrino. Energy conservation fixes an endpoint: the electron cannot carry more than the available decay energy minus the energy associated with the neutrino. A massive neutrino slightly changes the shape of the electron spectrum in the final region below that endpoint.
KATRIN uses a high-resolution spectrometer to select electrons and fit the spectrum near the endpoint. It is a kinematic measurement at the point of creation, rather than a measurement of how a flavor changes after traveling a distance. The fitted parameter is the effective electron-neutrino mass, commonly written mβ, which combines the mass eigenvalues with their electron-flavor admixtures. In standard notation, it is represented by a weighted sum of squared masses, mβ2 = Σ|Uei|2mi2.
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KATRIN’s published representative limit
A 2022 KATRIN review, based on first-year data, reports mβ < 0.8 eV at 90% confidence. This is an upper limit, not a detection: the data did not require a nonzero endpoint distortion at that sensitivity. The result placed KATRIN in the sub-eV domain while remaining a direct laboratory constraint.
The experiment’s approach is comparatively model-light because it does not require a cosmological history. It does require precise knowledge of the tritium source, electron transmission, energy-loss processes, detector response and background rate. A neutrino-mass signal would appear as an extremely small spectral change in only a narrow endpoint region, so systematic uncertainties and finite statistics matter as much as the nominal spectrometer resolution.
Why beta decay is an absolute-mass test
Unlike oscillation, beta decay responds to the kinematics of the decay products themselves. It does not need a long propagation baseline or an assumed expansion history. If the endpoint shape showed a statistically significant distortion, the fitted mβ would constitute a direct absolute-scale measurement of the electron-flavor combination.
That directness does not make mβ equal to any individual mass eigenvalue or to Σmν. The electron-flavor weights depend on the mixing matrix, and several mass eigenstates contribute. A null result places an upper bound on this weighted quantity; converting it into a bound on each mass or on the total requires the oscillation splittings and an ordering scenario.
How cosmology constrains the summed mass
Massive neutrinos leave a cumulative signature
The universe contains a relic background of neutrinos produced in the early hot plasma. While relativistic, they contribute to the radiation content and influence the evolution of early-universe perturbations. After becoming nonrelativistic, their thermal motion prevents them from clustering on small scales as efficiently as cold dark matter. This free-streaming suppresses the growth of small-scale structure.
Those effects alter several observables at once. CMB temperature and polarization anisotropies probe the early-universe energy budget and distances to the last-scattering surface; CMB lensing traces the integrated matter distribution. BAO provide a standard ruler in galaxy surveys, while galaxy-clustering and full-shape measurements add information about distances and the growth of structure. The combined response is primarily sensitive to the total mass, Σmν = m1 + m2 + m3.
The Planck-plus-BAO bound
For the baseline cosmological model, Planck 2018 data combined with BAO gave Σmν < 0.12 eV, reported by the Planck Collaboration in 2020. This is a cosmological inference: the parameter value is the one that best fits the measured anisotropies, distances and structure growth when neutrino mass is included in the model.
DESI’s publication program adds dedicated neutrino-physics constraints from BAO and full-shape analyses. New survey releases can change the numerical bound as the data combination, calibration and modeling change, so a quoted DESI limit must always be tied to its particular release and analysis choices.
Why the strongest number is conditional
Cosmological bounds assume a framework such as ΛCDM and specify the neutrino sector, primordial fluctuations, dark-energy behavior, calibration parameters and nonlinear structure model. If the data are combined with supernova measurements, different BAO samples or other probes, the inferred mass can shift. Extensions to ΛCDM can weaken or alter the limit because additional parameters may mimic some effects attributed to neutrino mass.
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Consequently, a very small cosmological upper bound does not mean that a laboratory experiment has been outperformed in a direct measurement. It means that, within the selected model and data set, a larger summed mass would produce a cosmic pattern inconsistent with the observations.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.Why the KATRIN and cosmology numbers are not interchangeable
| Question | KATRIN beta decay | Cosmology |
|---|---|---|
| Parameter | mβ, an electron-flavor-weighted kinematic mass | Σmν, the sum of mass eigenvalues |
| Signal | Endpoint shape of electrons from tritium decay | Changes to CMB, distances, lensing and structure growth |
| Typical quoted result in the cited sources | mβ < 0.8 eV at 90% confidence (KATRIN review, 2022) | Σmν < 0.12 eV for Planck 2018 plus BAO in baseline ΛCDM (Planck Collaboration, 2020) |
| Dominant assumptions | Source, spectrometer, energy-loss and background models | Expansion history, primordial spectrum, gravity and nonlinear structure model, plus data-set consistency |
The quantities differ even before confidence levels are considered. A limit on mβ cannot be subtracted from or directly compared with a limit on Σmν. Oscillation measurements provide the mixing weights and splittings needed to translate between possible spectra, but they do not supply the missing common mass offset.
A simple translation example
Suppose oscillation data fix the splittings and an ordering is selected. Raising the lightest mass raises all three eigenvalues and therefore raises Σmν. It also raises mβ, but according to the electron-flavor weights rather than a simple arithmetic average. The same underlying spectrum predicts both quantities, yet each experiment constrains a different projection of it. A cosmological limit may exclude spectra that remain below KATRIN’s direct sensitivity, while a future beta-decay detection would test the mass scale without relying on ΛCDM.
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Choosing the right experiment for a specific question
“Do neutrinos have mass?”
Use oscillation evidence. Flavor transitions establish nonzero mass-squared differences and are the foundational discovery of neutrino mass.
“What are the mass splittings and mixing parameters?”
Use oscillation data from reactor, solar, accelerator and long-baseline measurements. Matter effects and baseline-dependent measurements add ordering-sensitive information.
“Can a laboratory experiment weigh an electron neutrino?”
Use tritium beta decay. KATRIN directly tests the endpoint spectrum and constrains mβ without adopting a cosmological expansion model.
“How much total neutrino mass is allowed in the universe?”
Use CMB, BAO and large-scale-structure analyses. They constrain Σmν through its accumulated effect on cosmic evolution, but the answer must be quoted with the model and data combination.
Common interpretation mistakes
- Calling an oscillation result an absolute mass. Oscillation frequencies measure Δm², not the lightest mass.
- Treating mβ as one eigenstate. It is an electron-flavor-weighted combination of all contributing eigenstates.
- Reading a cosmological limit as model-free. The bound changes when the cosmological model, calibration or data combination changes.
- Comparing confidence limits without checking their definitions. KATRIN’s cited value is a 90% confidence upper limit; cosmological analyses have their own statistical conventions and nuisance parameters.
- Assuming a tighter number means a more direct measurement. Cosmology has greater leverage but relies on more assumptions; beta decay is more direct but currently less sensitive in mass scale.
Current status and what remains unresolved
The three approaches now form a coherent measurement program. Oscillation experiments establish nonzero mass and map the splittings. KATRIN supplies a direct sub-eV laboratory constraint on mβ. Planck, BAO and DESI-style analyses provide much tighter numerical constraints on Σmν within specified cosmological models.
None of these cited results establishes which method will first make a positive absolute-mass measurement. Cosmological limits must be refreshed when new survey releases or model analyses alter the accepted constraint, and any future comparison should state the exact data combination, confidence convention and model assumptions. The scientifically useful conclusion is not that one method replaces the others: each probes a different aspect of the same mass spectrum.
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