Interactive neutrino physics · Absolute masses

What do β decay, 0νββ and cosmology each measure?

m_β, m_ββ and Σ as functions of the lightest mass, the ordering and the Majorana phases, set against the current bounds.

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Interactive figure

Neutrino mass observables

The three absolute-mass observables — the beta-decay mass m_β, the effective Majorana mass m_ββ and the cosmological sum Σ — as functions of the lightest mass, the ordering and the two Majorana phases, set against the current bounds. Move the phases to see how m_ββ can cancel in normal ordering but not in inverted ordering.

About this figure

Neutrino mass observables

Level. Advanced undergraduate to graduate.

Move the lightest mass and the two Majorana phases, switch the ordering, and watch the three observables against their bounds; the phasor sum shows why m_ββ can cancel in normal ordering but not in inverted ordering.

Assumptions

Central oscillation values only; their uncertainties are not propagated.
δm² = 7.48×10⁻⁵ eV² and sin²θ₁₂ = 0.3085 (with first JUNO data), sin²θ₁₃ = 0.0223, |Δm²| = 2.495 (NO) / 2.465 (IO) ×10⁻³ eV².
Bounds: m_β < 0.45 eV (KATRIN, 90% C.L.); m_ββ < 86 meV (2σ, with nuclear-matrix-element covariances); Σ < 64 meV (DESI DR2 + CMB, ΛCDM, 95%). Next generation: the LEGEND-1000 goal, 9–21 meV.

References

Where it fits

Cite and reuse

A. Marrone, Neutrino mass observables, interactive figure (2026), https://home.ba.infn.it/~marrone/interactive-mass-observables.html.

@misc{Marrone:massobservables,
  author       = {Marrone, Antonio},
  title        = {Neutrino mass observables},
  howpublished = {Interactive figure, \url{https://home.ba.infn.it/~marrone/interactive-mass-observables.html}},
  year         = {2026}
}

Text and figures: CC BY 4.0. Code (assets/js/nu-mass.js): MIT licence. Use it in lectures and talks, adapt it, redistribute it — with attribution.