Tritium Beta Endpoint

A beta decay is a three-body process: $(A,Z)\to (A,Z+1)+e^{-}+{\bar{\nu }}_e$ The available kinetic energy is shared between the electron and the antineutrino. At the maximum electron energy (the endpoint), the antineutrino carries zero kinetic energy — and therefore only its rest mass. A finite neutrino mass shifts the endpoint down by $m_{\nu }{c}^2$ and distorts the spectrum shape in a narrow window just below.

Why tritium

The differential decay rate near the endpoint goes as $\frac{dN}{dE}\propto F(E,Z)p_e{E}_{\text{tot}}(E_0-E)\sqrt{(E_0-E{)}^2-m_{\nu }^2{c}^4}$ where $F$ is the Fermi function and $E_0$ is the endpoint energy. The fraction of decays falling within the last few eV of the endpoint scales as $(m_{\nu }/Q{)}^3$ — where $Q$ is the total available energy. Minimizing $Q$ therefore maximizes the sensitivity per decay.

Tritium’s low $Q$-value of 18.574 keV makes it the ideal isotope. It also has a short half-life (12.3 years) for high source activity, a simple nuclear structure (no excited state contamination), and a super-allowed transition with a well-understood matrix element.

The KATRIN experiment

The Karlsruhe Tritium Neutrino experiment (KATRIN) began data-taking in 2019. Its core components are:

1. A windowless gaseous tritium source providing $10^{11}$ β-decays per second with precisely controlled column density
2. A pre-spectrometer rejecting low-energy electrons
3. A main spectrometer 10 m in diameter by 23 m long, operating as a MAC-E filter — magnetic adiabatic collimation with electrostatic filtering — that integrates electrons above a settable retarding potential
4. A focal-plane silicon detector counting the transmitted electrons

The retarding potential is scanned in small steps around the endpoint; the resulting integral spectrum is fit for $m_{\nu }^2$. Systematics below 10 meV² scale matter: high-voltage stability to 3 ppm, magnetic field uniformity, and a detailed model of the gaseous source (rotational and vibrational final states, plasma effects).

Current result

The 2024 KATRIN result, combining several campaigns, gives $m_{{\nu }_e}^{\text{eff}}<0.45\text{ eV}(90\%\text{ C.L.})$ — the world-leading direct limit. The design goal remains $m_{\nu }<0.2$ eV with a five-year data set.

The quantity measured is an incoherent sum weighted by the first-row PMNS elements: $m_{{\nu }_e}^{\text{eff}2}={\sum }_i|U_{ei}{|}^2{m}_i^2$ For quasi-degenerate neutrinos this approaches the common mass; for hierarchical spectra it is dominated by $m_1$ or $m_3$ depending on the ordering.

Beyond KATRIN

Project 8 uses cyclotron radiation emission spectroscopy: a single trapped electron radiates at a frequency proportional to its total energy, observed through a radio-frequency receiver. The technique has achieved the first differential tritium spectrum reconstructed from cyclotron radiation and aims for sub-40 meV sensitivity with atomic tritium.

HOLMES and ECHo use different nuclei — ${}^{163}$Ho electron capture — whose Q-value of 2.8 keV is even lower, with microcalorimeter detection.

PTOLEMY proposes the capture of cosmic neutrino background neutrinos on polarized tritium, though the signal is expected to be extraordinarily small (~10 events per year per 100 g of tritium for the standard relic density).

The endpoint technique is the most model-independent measurement of the neutrino mass — insensitive to whether neutrinos are Dirac or Majorana, or to cosmological assumptions. It is therefore a complementary anchor for the cosmological and $\beta \beta 0\nu$ bounds.