KATRIN: Weighing the Neutrino at the Tritium Endpoint

On a quiet afternoon in July 2018, a train of stainless-steel vacuum chambers at the Karlsruhe Institute of Technology hummed into operation for the first time. Inside its 23-metre main spectrometer, electrons from the beta decay of molecular tritium were being filtered to within a fraction of an electron-volt of their endpoint energy — the kinematic boundary at which a neutrino would be produced at rest, if only neutrinos were heavy enough to have a rest.

The experiment is KATRIN, the Karlsruhe Tritium Neutrino experiment. Its scientific goal is more precise than dramatic: to measure the shape of the electron energy spectrum near the 18.574 keV endpoint of tritium beta decay, and from that shape extract the effective mass of the electron antineutrino. Seven years of operation have pushed that measurement from the historical “few eV” range down to below half an electron-volt, the most stringent direct kinematic bound on the neutrino mass ever achieved.

This is the story of how the instrument got there, what exactly it measures, and why the next five years of KATRIN data will remain the gold-standard laboratory constraint on the neutrino’s rest mass.

The kinematic principle

Any single beta decay produces a continuous spectrum of electron kinetic energies bounded above by the Q-value of the reaction minus the rest mass of the coincident neutrino. For tritium, ${}^3\text{H}\to {}^3\text{He}+e^{-}+{\bar{\nu }}_e$ the Q-value is 18.574 keV. In the limit of a massless neutrino, the electron endpoint coincides with Q. With a finite neutrino mass $m_{\nu }$, the maximum electron energy is instead $Q-m_{\nu }$, and the spectrum near the endpoint is distorted in a specific, calculable way.

The distortion is tiny. For a 200-meV neutrino mass, the endpoint is depressed by 200 meV — roughly one part in $10^5$ of the endpoint energy itself. The corresponding spectral distortion affects only the last few electron-volts of a 18.6-keV spectrum. Measuring it requires not just high-resolution spectroscopy but near-perfect understanding of every systematic effect that could distort the observed spectrum on that scale: the molecular final-state distribution, the source properties, scattering inside the source, electromagnetic fields in the spectrometer, and backgrounds from cosmic rays, radon, and radiogenic decay chains in the apparatus itself.

The experiment that can do this measurement has been, for the past four decades, the principal technological frontier of direct neutrino mass determination.

A history of endpoint experiments

The first tritium endpoint measurement dates to 1949, when Samuel Curran and A. L. Hughes used a proportional counter to set a loose upper limit of roughly 1 keV. Through the 1970s, successively better electrostatic spectrometers at Zurich, Moscow, and Los Alamos brought the bound into the tens of electron-volts.

The ITEP group under Valentin Lubimov, working at the Institute of Theoretical and Experimental Physics in Moscow, made a dramatic announcement in 1980: a positive detection of neutrino mass at $30$ eV. The claim was based on careful analysis of tritium valine spectra using a magnetic spectrometer. It ran contrary to the general expectation that neutrinos were massless (or nearly so) and sparked a decade of intensive follow-up.

By 1995, the Mainz and Troitsk experiments — both using the MAC-E (Magnetic Adiabatic Collimation with Electrostatic Filter) architecture — had definitively excluded the ITEP result. Their combined upper bound of approximately 2 eV, published in the early 2000s, remained the world-leading direct limit for nearly two decades. The KATRIN proposal, approved at Karlsruhe in 2001, was designed from the outset to push that bound by an order of magnitude, to 200 meV.

The instrument

KATRIN consists of five primary systems arranged along a 70-metre beamline:

Windowless gaseous tritium source (WGTS). A 16-metre pipe held at 30 K in which molecular T₂ flows continuously, providing 10¹¹ decays per second. The source is cold enough to minimize thermal broadening, rarefied enough to prevent multiple scattering, and chemically pure to a level that required a dedicated tritium purification loop.

Transport and pumping sections. A series of differential pumping stages reduce the tritium gas flow by 14 orders of magnitude between the source and the main spectrometer, where even trace tritium contamination would compromise the vacuum and produce unwanted background.

Pre-spectrometer. A compact electrostatic filter that rejects electrons more than 300 eV below the endpoint, reducing the flux entering the main spectrometer and therefore the background.

Main spectrometer. The 23-metre, 10-metre-diameter vacuum tank that gives KATRIN its iconic silhouette. Electrons entering at one end are decelerated by a retarding electrostatic potential; only those with enough kinetic energy to climb the potential reach the detector at the far end. The MAC-E filter principle — varying magnetic field along the electron trajectory to align the momentum with the field direction — gives the spectrometer sub-eV energy resolution.

Focal plane detector. A segmented silicon pixel array counting transmitted electrons with spatial resolution fine enough to correct for residual field inhomogeneities.

The instrument’s guiding design principle is systematic control at the sub-per-cent level. Energy scale, magnetic field uniformity, source column density, retarding voltage stability, and background rate are all characterized independently and to precisions that translate into negligible contribution to the final mass bound.

From count rates to a neutrino mass

The raw observable is the counting rate as a function of the retarding potential. By varying the potential in small steps and counting electrons at each step, KATRIN reconstructs the integrated spectrum. The differential spectrum — the quantity that carries the neutrino-mass information — is obtained by differentiation.

The theoretical fit to this spectrum has three categories of inputs:

• The Kurie function, which gives the vacuum differential decay rate as a function of electron energy and $m_{\nu }^2$
• The molecular final-state distribution of ³He⁺ ions, quantifying the spread of excitation energies the daughter nucleus inherits (a crucial effect at the meV scale)
• Instrumental response functions for source scattering, transmission, and detector efficiency

The fit parameter of interest is $m_{\nu }^2$, which for small values can be negative in the best-fit sense (representing a statistical fluctuation below the true value of zero). KATRIN’s analysis procedure quotes a best-fit $m_{\nu }^2$ with a two-sided confidence interval, from which an upper limit on $m_{\nu }$ is extracted.

The 2024 result

In 2024 KATRIN published the analysis of 259 measurement days accumulated between 2019 and 2022. The best-fit effective electron antineutrino mass squared was $m_{\nu }^2=0.14\pm 0.14(\text{stat})\pm 0.12(\text{syst}){\text{ eV}}^2$ consistent with zero within uncertainty. The corresponding 90% confidence-level upper bound is $m_{\nu }<0.45\text{ eV}$ the world-leading direct kinematic constraint.

The design target remains 0.2 eV, which the collaboration expects to reach after an additional 1000 days of operation and improvements to systematic subtractions. The experiment will then approach the reach of cosmological bounds on the same quantity — though, crucially, with entirely independent methodology and no cosmological model assumptions.

What KATRIN actually constrains

The quantity probed by beta-decay endpoint experiments is not a single mass but an incoherent weighted sum of the three mass eigenstates: $m_{{\nu }_e}^{\text{eff}}=\sqrt{{\sum }_i|U_{ei}{|}^2{m}_i^2}$ where $U_{ei}$ are the first-row elements of the PMNS mixing matrix. In the limit of quasi-degenerate masses, $m_{{\nu }_e}^{\text{eff}}\to m$. In the hierarchical limit, it is dominated by $m_3$ through the small coefficient $|U_{e3}{|}^2\approx 0.022$, giving $m_{{\nu }_e}^{\text{eff}}{|}_{\text{NO},m_1=0}\approx 9\text{ meV}$ Thus KATRIN’s 0.45 eV bound is about 50 times above the hierarchical minimum. A positive signal at KATRIN’s target sensitivity would require the quasi-degenerate regime — all three masses close to 200 meV.

The independent cosmological bound, which measures the sum of masses via structure formation, gives $\sum m_{\nu }\lesssim 0.12$ eV under standard ΛCDM. The two bounds are complementary: KATRIN is model-independent but less sensitive; cosmology is more sensitive but model-dependent. A disagreement between them would itself be a scientific discovery.

Beyond KATRIN — Project 8

KATRIN’s final sensitivity of 200 meV will be the culmination of the MAC-E-filter technology. To reach below 100 meV, a fundamentally different approach is needed. Project 8, now in its demonstrator phase, uses cyclotron radiation emission spectroscopy: tritium electrons are magnetically trapped, and their cyclotron radiation is measured directly. The technique has already been demonstrated for ⁸³mKr calibration sources and is being scaled up for atomic (as opposed to molecular) tritium — the only way to eliminate the molecular final-state systematic that currently dominates KATRIN’s error budget.

A full Project 8 experiment aiming at 40 meV sensitivity is planned for the early 2030s. If built and operated at specification, it would reach into the inverted-ordering parameter space, making beta-decay endpoint measurements competitive with $0\nu \beta \beta$ and cosmology.

Legacy

KATRIN’s contribution to the neutrino-mass story is not primarily the absolute value it sets — the cosmological bound is tighter, and the $0\nu \beta \beta$ programme will probe smaller effective masses. Its contribution is the independence of its measurement from any model beyond the Standard Model: no assumptions about whether neutrinos are Majorana, no assumptions about the late-time evolution of the universe, no assumptions about the nuclear matrix elements of an unmeasured decay. KATRIN is what remains when every other approach is stripped down to its foundational assumptions.

For that reason, KATRIN’s final number — whatever it is — will be the laboratory reference against which all other neutrino-mass claims are measured for the next decade. If a tension emerges between KATRIN, cosmology, and $0\nu \beta \beta$, the community will know that new physics is at play somewhere. If all three agree, the absolute neutrino mass will be, for the first time in the particle’s 96-year history, a measured rather than estimated quantity.