Neutrino Mass — A Ninety-Year Question

1. 1

   paper

   pauli 1930

   Pauli postulates the neutrino with mass 'not greater than the electron mass' — already leaving room for any value from zero to keV.

2. 2

   paper

   fermi 1934

   Fermi's beta-decay theory predicts that the shape of the electron spectrum near the endpoint is modified by a finite neutrino mass. The basis of every subsequent endpoint experiment.

3. 3

   paper

   super kamiokande 1998

   Discovery of oscillation establishes that at least two neutrino mass eigenstates are non-zero and non-degenerate. Masslessness of all three is excluded.

4. 4

   paper

   sno 2002

   Confirms oscillation independently in the solar sector, fixing Δm²₂₁ and making the oscillation framework complete.

5. 5

   concept

   tritium beta endpoint

   The theoretical framework for direct kinematic mass measurement, refined from Fermi's 1934 original and applied at progressively lower mass scales through the twentieth century.

6. 6

   experiment

   katrin

   Current world-leading direct limit, m(νe) < 0.45 eV. Design sensitivity 0.2 eV over the full dataset.

7. 7

   paper

   katrin 2024

   The 2024 combined analysis. The most precise model-independent bound on the absolute neutrino mass scale.

8. 8

   concept

   neutrinos and dark matter

   Cosmological complement: the sum of neutrino masses affects structure formation, yielding constraints Σmν ≲ 0.12 eV from CMB + galaxy surveys.

Three orthogonal routes to absolute mass

The oscillation framework tells us the differences of squared masses. Three independent experimental strategies address the absolute mass scale:

1. Kinematic endpoint measurements (KATRIN and successors) — model-independent, directly measuring the quantity $m_{{\nu }_e}^{2\text{eff}}={\sum }_i|U_{ei}{|}^2{m}_i^2$. Current bound: $m<0.45$ eV.

2. Cosmological observations — constrain ${\sum }_i{m}_i$ through the imprint on structure formation and the CMB. Current bound in $\Lambda$CDM: $\sum m_{\nu }\lesssim 0.12$ eV. Tighter but model-dependent.

3. Neutrinoless double beta decay — constrains the Majorana effective mass $⟨m_{\beta \beta }⟩=|{\sum }_i{U}_{ei}^2{m}_i|$, non-zero only if neutrinos are Majorana. Current bound ~40 meV. Cannot determine absolute scale alone, but combined with the other two can distinguish Dirac/Majorana nature.

Why the three routes differ

Each route has different systematic foundations:

• Kinematic measurement is purely quantum mechanics — no cosmological or particle-physics assumptions
• Cosmological measurement depends on the $\Lambda$CDM model and on the modeling of galaxy surveys
• Double-beta-decay measurement depends on whether neutrinos are Majorana and on nuclear matrix elements

Agreement among the three would fully determine the mass scale and the Dirac/Majorana question. Current tensions are not yet at a level that force a definitive conclusion, but the window is closing: next-generation experiments in each channel are expected to probe the full range allowed by oscillation data within the coming decade.

The minimum allowed mass

The smallest possible value for $\sum m_i$, given the measured squared-mass differences:

• Normal ordering, $m_1\to 0$: $\sum m_i\approx 0.06$ eV
• Inverted ordering, $m_3\to 0$: $\sum m_i\approx 0.10$ eV

Cosmological bounds at $\sim 0.1$ eV are already in tension with inverted ordering, and a firm determination would strongly disfavor that possibility.