KATRIN: limiting neutrino mass at the end of the beta spectrum

Follow electrons from tritium decay through a magnetic and electrostatic filter to a fit of the spectrum’s end. See how a limit on the effective absolute mass differs from the mass differences found by oscillations and from the design sensitivity.

Sandbox Physics · 2026-10-11 · Updated 2026-10-13 · Interpreting evidence

Look where the neutrino has the least energy

In tritium beta decay, the released energy is shared among an electron, an antineutrino and the recoiling molecule. In most decays the neutrino gets so much energy that a sub-electronvolt mass hardly matters. Near the end of the electron spectrum, little energy is left for the neutrino, and its mass reshapes the available phase space.

So the signal is a subtle change at the top end of a continuous electron spectrum. KATRIN measures only electrons. The neutrino mass enters the predicted electron energy distribution once the unobserved neutrino states are summed over.

Locating the endpoint is not enough. Conditions in the source, the states of the daughter molecule, energy loss and the spectrometer’s transmission can all reshape the same region. The experiment must separate the mass-dependent shape from these effects, using a calibrated response and a clearly defined fit window.

Sources: [1] · [2] · [3] · [4]

A retarding voltage builds an integral spectrum

KATRIN guides electrons with magnetic fields and slows them with an electrostatic retarding potential. As an electron moves adiabatically from a strong magnetic field into a weak one, its sideways energy shrinks, so the voltage barrier acts on its motion along the field. This is the MAC-E filter principle.

At each voltage setting, the electrons that get through are counted. Stepping the threshold builds an integral spectrum: every electron with enough energy to cross the effective barrier counts, after transmission and energy losses. With ideal thresholds, the difference between adjacent settings would give the differential spectrum, but the real analysis fits the measured integral rates directly.

The response includes scattering in the tritium source, the spread of electron angles, variations in the fields and potentials, and instrumental background. Together they blur the sharp theoretical endpoint. The instrument’s resolution therefore goes into the predicted spectrum; it cannot be subtracted from the final mass limit afterwards.

Sources: [2] · [3] · [1]

01Tritium decay
Electron energies show the energy that went missing
02Voltage scan
Build an integral spectrum, voltage by voltage
03Endpoint fit
Fit the mass together with correlated uncertainties

KATRIN measures electrons; it never detects the neutrino. A published mass limit is a different number from the design sensitivity.

The effective mass adds mass states without interference

An electron-flavor neutrino is a mixture of several mass states. When their separate endpoints cannot be resolved, the main distortion of the spectrum is described by one effective electron-neutrino mass, which weights each squared mass by that state’s electron-flavor share.

The outgoing mass states are orthogonal and never observed, so their decay rates simply add; there is no single amplitude in which they could interfere. That is why the effective beta mass uses the squared magnitudes of the mixing elements. It differs from the phase-sensitive mass combination in double-beta decay mediated by light neutrinos.

Oscillations measure differences between squared masses and leave the overall scale open. Beta spectroscopy constrains that scale in another way. It relies on fairly direct kinematics, but a precise limit still depends on the beta-decay and instrument models described in the analysis.

m_{\beta}^{2}=\sum_{i}|U_{ei}|^{2}m_{i}^{2}

Assumes standard active-neutrino mixing and mass-state endpoints too close to resolve. The masses are absolute masses, so this is neither a difference of squared masses nor the coherent Majorana effective mass.

Sources: [5] · [3] · [2]

A limit comes with its data set and confidence level

The result published in Science in 2025 used the first five measurement campaigns: 259 measurement days and about 36 million electrons. It put the effective neutrino mass below 0.45 electronvolts at 90 percent confidence. That is an upper limit; no nonzero mass was measured.

The fit let the squared-mass parameter take negative values, and its best estimate came out slightly negative, consistent with zero within the uncertainty. Allowing negative values avoids biasing the treatment of fluctuations near the physical boundary. It does not mean the neutrino has an imaginary mass.

When we checked on 11 October 2026, the collaboration’s publication list still pointed to this 259-day analysis as the precision limit cited here. The 2026 entries cover tritium operation and a TRISTAN sensitivity study for sterile neutrinos, not a new mass limit for ordinary active neutrinos. Data collected so far, a design sensitivity target and a published interval are three different things.

Sources: [3] · [6]

Read the other fit parameters, not just the headline

The endpoint energy, the overall normalization and the background are fitted together with the mass. Their correlations matter: a small energy shift or a badly modeled background can change the apparent curvature of the spectrum. A wider fit window gives more counts but makes the result depend more on details of the source and response.

Because the tritium is molecular, the daughter molecule can be left in a range of excited states. Each excitation takes energy that would otherwise go to the electron and neutrino. This final-state distribution is an input with its own uncertainty, and counting more electrons does not make it go away.

To compare KATRIN with oscillation, cosmological or double-beta limits, keep track of what each one measures. Cosmological limits assume a model of how the universe evolved; double-beta mass values assume a decay mechanism and a nuclear calculation. Agreement among them is informative, but it does not make those assumptions interchangeable.

Sources: [3] · [4] · [5] · [7]

Try it in the Lab

Beta Endpoint Mass Observatory Neutrino flavor propagation

Primary sources & revision

First published 2026-10-11; last revised 2026-10-13. 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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