Direct Neutrino-Mass Measurement Based on 259 Days of KATRIN Data

The measurement

KATRIN — the Karlsruhe Tritium Neutrino experiment — measures the endpoint of the tritium beta-decay spectrum, ${}^3\text{H}\to {}^3{\text{He}}^{+}+e^{-}+{\bar{\nu }}_e$ with $Q=18.574$ keV. The shape of the electron spectrum in the last few eV below the endpoint is modified by a finite neutrino mass; the modification is proportional to $(m_{\nu }/Q{)}^3$ in the event fraction.

The experimental infrastructure includes a windowless gaseous tritium source producing ~$10^{11}$ decays per second, a differential pumping and cryogenic trapping section, and a large main spectrometer operating as a MAC-E filter (Magnetic Adiabatic Collimation with Electrostatic filtering). The retarding potential is scanned in small steps near the endpoint; transmitted electrons are counted by a segmented silicon detector. The integral spectrum is fit for $m_{\nu }^2$ as the free parameter.

The 2024 result

The paper combines data from five campaigns (KNM1 through KNM5) taken between 2019 and 2021. The combined best fit gives $m_{{\nu }_e}^2=(0.007\pm 0.097\pm 0.090){\text{ eV}}^2$ consistent with zero. The 90% confidence upper limit from a unified frequentist analysis is $m_{{\nu }_e}<0.45\text{ eV}(90\%\text{ C.L.})$

The quantity measured is an incoherent, mixing-matrix-weighted sum over the three mass eigenstates: $m_{{\nu }_e}^{2\text{eff}}={\sum }_i|U_{ei}{|}^2{m}_i^2$ so the limit applies uniformly regardless of the mass ordering.

Systematics

KATRIN’s precision is limited by systematics at the $10^{-2}$ eV² level:

• Tritium-source plasma effects on electron energy (dominant)
• Column-density fluctuations and isotopologue composition
• Magnetic field stability and alignment
• Electronic and rotational-vibrational final states of the ${}^3$HeT⁺ daughter ion
• Detector backgrounds from Rydberg-state tritium recoils

A dedicated calibration program using a ${}^{83m}$Kr source with a sharp monoenergetic line at 17.8 keV calibrates the retarding-potential scale.

Looking ahead

KATRIN is designed to continue through 2025, targeting the design sensitivity of 0.2 eV with the full dataset. Beyond KATRIN, Project 8 uses cyclotron-radiation emission spectroscopy to measure single-electron energies in a magnetic trap; with atomic tritium, its design sensitivity extends below 40 meV — crossing into the inverted-ordering-guaranteed regime.

The HOLMES and ECHo experiments take a different approach, using ${}^{163}$Ho electron capture ($Q=2.8$ keV) with microcalorimeter detection. Lower $Q$ enhances endpoint sensitivity per event but introduces new systematic concerns.

Complementarity

The direct kinematic mass measurement is complementary to two other constraints:

• Cosmological bounds on $\sum m_{\nu }$, currently approaching 0.1 eV in $\Lambda$CDM analyses of CMB and large-scale structure
• Neutrinoless double beta decay searches, which constrain the Majorana effective mass $⟨m_{\beta \beta }⟩$ if neutrinos are Majorana

Each route has different systematic foundations. The direct measurement is model-independent; the cosmological bound depends on cosmological assumptions; the double-beta bound depends on Majorana nature. Agreement (or disagreement) among the three can in principle resolve both the mass ordering and the Dirac/Majorana question.