KATRIN: constrain mass at the beta-spectrum endpoint

Look where the neutrino has the least energy

In tritium beta decay, the available energy is shared between an electron, an antineutrino and the recoiling molecular system. Most decays give the neutrino enough energy that a sub-electronvolt mass makes a tiny relative difference. Near the electron endpoint, the remaining energy is small and the mass alters the accessible phase space.

The signal is therefore a subtle change in the upper end of a continuous spectrum, not a neutrino arriving at a detector. KATRIN measures electrons. The neutrino mass enters the prediction for their energy distribution after the unobserved neutrino states are summed over.

An endpoint estimate alone is insufficient. Source conditions, molecular daughter states, energy loss and the spectrometer transmission can reshape the same region. The experimental task is to distinguish a mass-dependent shape from these other influences with a calibrated response and a stated fit window.

Sources: [1] · [2] · [3] · [4]

A retarding voltage makes an integral spectrum

KATRIN uses magnetic guidance and an electrostatic retarding potential. Adiabatic motion from a stronger into a weaker magnetic field reduces transverse electron energy, making the longitudinal energy sensitive to the voltage barrier. This is the MAC-E filter principle.

At each selected voltage, transmitted electrons are counted. Changing the threshold builds an integral spectrum: electrons above the effective barrier contribute, after transmission and energy-loss effects. Differencing ideal thresholds would recover a differential spectrum, but the real analysis fits the measured integral rates.

The response includes scattering in the tritium source, the angular distribution, field and potential variations, and instrumental backgrounds. A sharp theoretical endpoint is blurred by this chain. Instrument resolution belongs inside the prediction rather than being subtracted from a final mass bound.

Sources: [2] · [3] · [1]

The effective mass is an incoherent weight

An electron-flavor neutrino is connected to several mass eigenstates. When their endpoint features are unresolved, the leading spectrum distortion is summarized by an effective electron-neutrino mass. It weights each squared mass by its electron-flavor fraction.

The final neutrino mass states are orthogonal and unobserved. Their decay rates add rather than interfering as one coherent detection amplitude. This is why the effective beta mass uses absolute-squared mixing weights and differs from the phase-sensitive mass combination in light-neutrino double-beta decay.

Oscillations constrain squared-mass differences, leaving a common absolute scale undetermined. Beta spectroscopy adds a different constraint on that scale. It is relatively direct kinematics, but interpreting a precise bound still requires the beta-decay and instrument models described in the analysis.

Sources: [5] · [3] · [2]

A limit has a data set and a confidence level

The result published in Science in 2025 used the first five measurement campaigns: 259 measurement days and about 36 million electrons. It reported an effective neutrino mass below 0.45 electronvolts at 90 percent confidence. This is a bound, not a nonzero mass measurement.

The fit allowed the squared-mass parameter to extend into negative values and obtained a slightly negative central estimate, compatible with zero within uncertainty. That mathematical continuation permits an unbiased treatment of fluctuations near a physical boundary. It does not describe a neutrino with imaginary mass.

As checked on 11 October 2026, the collaboration’s publication list still identifies this 259-day analysis as the cited precision bound; the 2026 entries describe tritium operation and a TRISTAN sterile-neutrino sensitivity study, rather than a new ordinary active-neutrino mass bound. Collected exposure, a design sensitivity target and a published interval must remain separate.

Sources: [3] · [6]

Read the nuisance parameters with the headline

Endpoint energy, normalization and background are fitted along with the mass parameter. Their correlations matter because a small energy shift or an incorrectly modeled background can change the apparent curvature. A wider fit window provides more counts while increasing dependence on source and response details.

Molecular tritium leaves a distribution of daughter excitations. Their energies reduce the energy available to the electron and neutrino in different decay branches. This final-state distribution is an input with uncertainty, not an incidental correction that disappears through more electron counting.

Comparing KATRIN with oscillation, cosmological or double-beta constraints requires preserving what each experiment measures. Cosmological bounds assume an evolution model; double-beta mass interpretations assume a decay mechanism and nuclear calculation. Agreement can be informative without making those assumptions interchangeable.

Sources: [3] · [4] · [5] · [7]

Try it in the Lab

Primary sources & revision

1. KATRIN · Neutrino mass method
2. KATRIN Collaboration · Design, construction and commissioning (2021)
3. KATRIN Collaboration · Neutrino mass from 259 days (2024 preprint; Science 2025)
4. KATRIN Collaboration · Molecular final-state uncertainties (2024)
5. Particle Data Group · Neutrino Masses, Mixing, and Oscillations (2024)
6. KATRIN Collaboration · Publications
7. Dvali, Maiezza, Senjanović & Tello · Neutrino mass versus new physics (2023)

First published 2026-10-11; 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.

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