A direct limit, not a detection

The Weight Missing at the Edge

Move an effective electron antineutrino mass across the last few electronvolts of a tritium beta spectrum, pass that spectrum through a live response proxy, inspect KATRIN's published fit and confidence belts, then map the different mass quantities used by oscillation experiments and cosmology.

There is almost no room left at the endpoint. Give the escaping antineutrino mass and the final electrons lose access to that room. Drag first. The curve is evaluated again for every movement.

Layer one: endpoint phase space

calculating

The published KATRIN value shown later is an upper limit. This control is a hypothetical mass.

Energy is plotted as deficit below the zero-mass endpoint.

last electron retreats by calculating
phase space removed calculating
integral response ratio calculating
phase(epsilon, m) = epsilon * sqrt(epsilon^2 - m^2) * Theta(epsilon - m)

The canvas keeps only the load-bearing phase-space term from the published beta-spectrum equation. Electron momentum and the Fermi function vary little across this tiny energy window, so they cancel in the normalized comparison. The molecular button adds three deliberately chosen teaching states. It is not KATRIN's ab initio final-state distribution. The filter button integrates the curve through a deliberately simplified transmission ramp. It is not the collaboration response model.

Layer twoA limit is not a slider position

KATRIN did not look at a bare differential curve. It recorded an integral spectrum at retarding voltages, with a molecular final-state distribution, scattering, transmission, detector response, source-potential effects, backgrounds, campaign correlations, and constrained nuisance parameters. The peer-reviewed analysis states that there were 144 constrained systematic parameters.

Published campaign totals

calculating

Approximate counts reported in the peer-reviewed KNM1 to KNM5 dataset description

This is a campaign-level ledger, not the official retarding-potential JSON. The verified Zenodo record contains the two files named in The Check, but their payloads could not be retrieved in this build environment. No point-by-point refit is claimed.

Published fit, live Gaussian profile proxy

mbeta2 = calculating

The curve uses the published central value and asymmetric total errors as a split Gaussian. It does not reproduce the collaboration likelihood.

Selected published belt

calculating

calculating

proxy delta chi squared calculating
proxy 90 percent crossing calculating
difference from selected belt calculating

The mismatch is the point. A confidence belt is not obtained by drawing one horizontal line across a Gaussianized profile. KATRIN generated frequentist acceptance regions with constrained systematics. Because the unconstrained best-fit squared mass fluctuated below zero, the Lokhov-Tkachov construction returned the experiment's sensitivity as the upper limit, while Feldman-Cousins returned a smaller number from the same data.

Three lanesDo not exchange these masses

Oscillations, beta decay, and cosmology do not report the same observable. Choose a lightest mass and an ordering. The page derives all three eigenvalues from the displayed NuFit 6.0 inputs, then computes KATRIN's flavor-weighted root-mean-square and the cosmological sum.

Setting this to zero finds the ordering-dependent floor. Oscillation data allow that choice.

The NuFit parameter convention changes with ordering.

Lightest eigenvalue calculating

A free absolute offset. Oscillations measure squared differences, not this value.

KATRIN mbeta calculating

sqrt(sum |Uei|2 mi2), an incoherent electron-flavor weighting.

Cosmology sum(mi) calculating

calculating

calculating

The Check

Every green value below is recomputed in this browser. Published comparison values are labeled as published. The page does not tune a proxy until it lands on the collaboration result.

Ideal missing fraction calculating
Molecular-proxy missing fraction calculating
Published campaign count sum calculating
Proxy versus published limit calculating
Normal-ordering floor calculating
Inverted-ordering floor calculating

Published result: KATRIN reports mbeta2 = -0.14+0.13-0.15 eV2, with statistical uncertainty 0.108 eV2 and systematic uncertainty 0.072 eV2. Its Lokhov-Tkachov construction gives mbeta < 0.45 eV at 90 percent confidence. Feldman-Cousins gives 0.31 eV from the same likelihood. These are published comparisons, not page outputs.

Uncertainties, free choices, approximations, and conventions
  • Units: energies and masses use eV with c = 1, matching the paper's natural-unit convention. Squared masses use eV2.
  • Normalization: endpoint curves are normalized to the largest massless value in the selected plotting window. Absolute decay rates are not claimed.
  • Endpoint coordinate: epsilon is E0 - E. A larger epsilon lies farther below the zero-mass endpoint.
  • Ideal spectrum: the plotted comparison retains the endpoint phase-space factor. Electron momentum, the Fermi function, radiative terms, and recoil terms are omitted from the normalized teaching view.
  • Molecular proxy: its three excitation energies and weights are free teaching choices. They are not the KNM5 ab initio molecular final-state distribution.
  • Filter proxy: its transmission width and ramp form are free teaching choices. It omits scattering energy loss, pitch-angle integration, magnetic-field maps, source-potential broadening, detector efficiency, and the full MAC-E response.
  • Campaign ledger: campaign counts are approximate peer-reviewed totals. The five displayed values sum to a rounded total that need not equal the separately published rounded 36 million.
  • Profile proxy: a split Gaussian uses the published central value and asymmetric total errors. It does not include endpoint, signal-normalization, detector-background, source-potential, final-state, response, or campaign-correlation nuisance parameters.
  • Confidence construction: the 0.45 eV and 0.31 eV marks are published belt results, not crossings calculated by this page. The visible proxy crossing is intentionally separate.
  • Oscillation inputs: the map fixes the displayed NuFit 6.0 best-fit values and ignores their uncertainties and correlations. It uses the IC19-without-Super-K atmospheric table to match the cited 2024 fit choice.
  • Mass ordering: normal and inverted ordering use different definitions of the atmospheric splitting. The lightest eigenvalue is a free input and may be zero.
  • Cosmology: the 0.0642 eV and 0.163 eV marks are 95 percent upper limits from different cosmological models and assumptions. They constrain sum(mi), not mbeta.
  • Raw release boundary: the Zenodo filenames, sizes, DOI, and MD5 checksums were verified. The JSON payloads could not be retrieved in this sandbox, so retarding-potential points and an exact collaboration likelihood are not embedded or claimed.
What remains open

The 259-day result does not detect a nonzero absolute mass, determine the lightest mass eigenvalue, establish the mass ordering, or decide whether neutrinos are Dirac or Majorana particles. Oscillations fix mass-squared differences, not the common absolute offset. Later KATRIN exposure is outside this published 259-day result.

Primary sources and review status
  1. KATRIN Collaboration, "Direct neutrino-mass measurement based on 259 days of KATRIN data," Science 388, 180-185 (2025), DOI 10.1126/science.adq9592. Peer-reviewed. Online 10 April 2025. The author manuscript and supplement are arXiv:2406.13516. Used for the spectrum equations, response equation, nuisance count, best fit, uncertainties, and both confidence limits.
  2. A. Lokhov and C. Wiesinger, official KNM1-5 data and inputs release, DOI 10.5281/zenodo.13644900. Research dataset, not peer-reviewed. Created 27 January 2025. Verified files: KATRIN_data_KNM1-5.json, MD5 7c9e30c35c394d87917cc56c7bf7ff53; KATRIN_inputs_KNM1-5.json, MD5 6fcb3fbd3059190caa95f37243a9593a.
  3. KATRIN Collaboration, "Direct neutrino-mass measurement with sub-electronvolt sensitivity," Nature Physics 18, 160-166 (2022), DOI 10.1038/s41567-021-01463-1. Peer-reviewed. Published 14 February 2022. Used for the previous combined 0.8 eV limit.
  4. I. Esteban et al., "NuFit-6.0: updated global analysis of three-flavor neutrino oscillations," JHEP 12, 216 (2024), DOI 10.1007/JHEP12(2024)216, arXiv:2410.05380. Peer-reviewed. Published 30 December 2024. Used for mixing angles and mass-squared splittings.
  5. DESI Collaboration, "Constraints on neutrino physics from DESI DR2 BAO and DR1 full shape," Physical Review D 112, 083513 (2025), DOI 10.1103/w9pk-xsk7, arXiv:2503.14744. Peer-reviewed. Published 6 October 2025. Used for the model-dependent 0.0642 eV and 0.163 eV limits on the mass sum.
  6. KATRIN Collaboration, "Sterile-neutrino search based on 259 days of KATRIN data," Nature 648, 70-75 (2025), DOI 10.1038/s41586-025-09739-9. Peer-reviewed. Published 3 December 2025. Used only for the approximate KNM1 through KNM5 campaign count totals and the 68,237 recorded scan-step total, not for a sterile-neutrino claim here.