What Happened
Physics · Particle Physics · Standard Model · Metrology · Explainerstate of the record to 1 September 2026 · every figure read from the paper that published it
Three of them are gone, and they went in three different ways
Four Lepton Anomalies, One Survivor
Between 1998 and 2025, four measurements involving leptons disagreed with the Standard Model at a level the field took seriously. One of them was right, and it is why neutrinos are known to have mass. The other three ended — excluded, superseded, dissolved — and those three endings are not one event told three times.
The four numbers One from each anomaly, each read from the paper that published it.
- 5.3σby which SNO’s non-electron solar neutrino flux exceeds zero — the measurement that settled the one real anomaly
- 95%the confidence at which MicroBooNE excludes a single light sterile neutrino as the explanation of LSND and MiniBooNE
- 0.846 → 0.949R(K) in 2021 and in 2022: same observable, same range, same collaboration, more data
- 38(63)muon g-2, experiment minus theory, in units of 10⁻¹¹ — a difference consistent with zero
What is established, and how well Sorted by standing, and the bands are not interleaved. A value read out of an abstract and a date checked in a database are not the same kind of fact.
| Standing | What |
|---|---|
| Read from the paper | Super-Kamiokande (1998) reports a zenith-angle-dependent deficit of muon neutrinos that flux and cross-section uncertainties cannot explain, and which is consistent with two-flavour oscillation. |
| Read from the paper | SNO (2002) finds the non-electron component of the solar flux 5.3 standard deviations greater than zero, and the total flux across all three flavours consistent with solar models. The missing neutrinos had changed, not gone. |
| Read from the paper | MicroBooNE (December 2025) excludes the single light sterile neutrino interpretation of the LSND and MiniBooNE anomalies at 95% confidence, using two accelerator beams to break a degeneracy between appearance and disappearance. |
| Read from the paper | LHCb (March 2021) measures R(K) = 0.846, with combined uncertainties of about +0.044 and −0.041, against a Standard Model expectation of 1.00 ± 0.01 — a 3.1 standard deviation difference. |
| Read from the paper | LHCb (December 2022), on the full 9 fb⁻¹ dataset, returns four values: R(K) = 0.949 and R(K*) = 1.027 in the central range, R(K) = 0.994 and R(K*) = 0.927 in the low range. The paper’s own summary is that all four agree with the Standard Model. |
| Read from the paper | Fermilab’s Muon g-2 (June 2025) gives a combined magnetic anomaly of 116 592 070.5(14.8) × 10⁻¹¹, a precision of 127 parts per billion, and a world average of 116 592 071.5(14.5) × 10⁻¹¹ — improving that average’s precision by more than a factor of four. |
| Read from the paper | The Muon g-2 Theory Initiative (May 2025) gives a Standard Model prediction of 116 592 033(62) × 10⁻¹¹ and states that experiment minus theory is 38(63) × 10⁻¹¹, “which implies that there is no tension”. It uses lattice QCD as its primary input after new CMD-3 data broke the agreement among data-driven evaluations. |
| Read from the paper | KamLAND-Zen sets the half-life of neutrinoless double-beta decay above 3.8 × 10²⁶ years at 90% confidence, from 2.1 tonne-years of enriched xenon-136, with effective Majorana mass limits spanning 28 to 122 meV. |
| Read from the paper | LEGEND-200 sets a limit above 1.9 × 10²⁶ years at 90% confidence, combining GERDA, the MAJORANA Demonstrator and LEGEND-200’s own 61 kilogram-year exposure, with no evidence for a signal. |
| Citation checked | Majorana’s 1937 paper, and the theorem tying an observation of neutrinoless double-beta decay to a Majorana mass: Schechter and Valle, submitted December 1981 and published 1982. It is routinely dated 1980. |
| Citation checked | The four seesaw papers and their earliest dates: Minkowski (February 1977), Gell-Mann, Ramond and Slansky (September 1979), Mohapatra and Senjanovic (November 1979), Yanagida (June 1980). |
| Not established here | That R(K) moved because a background of hadrons mistaken for electrons had been underestimated; that the pre-2025 muon g-2 difference stood at 4.2 standard deviations; the three-way split of the 2025 g-2 uncertainty. |
| Not established here | The Homestake rate and the thirty-year solar neutrino argument that preceded 1998; the GERDA final limit; the 2001 Heidelberg-Moscow signal claim and its later exclusion. |
Timeline
Two theory papers, and then twenty-seven years of results Dated by submission where the record gives one, and by publication otherwise.
- Apr 1937Majorana’s symmetric theory of the electron and the positron: a neutral fermion may be its own antiparticle.
- 1977–1980The seesaw papers: Minkowski, then Gell-Mann with Ramond and Slansky, then Mohapatra and Senjanovic, then Yanagida.
- Dec 1981Schechter and Valle submit the theorem tying an observed neutrinoless double-beta decay to a Majorana mass. Usually dated 1980.
- Jan 1986Fukugita and Yanagida link heavy Majorana neutrinos to the matter-antimatter asymmetry.
- Jul 1998Super-Kamiokande publishes the atmospheric muon-neutrino deficit.
- Apr 2001LSND publishes an excess that does not fit a three-neutrino picture.
- Apr 2002SNO measures the total three-flavour solar flux and closes the solar neutrino problem.
- 2002Nobel Prize to Raymond Davis Jr. and Masatoshi Koshiba for the detection of cosmic neutrinos.
- 2015Nobel Prize to Takaaki Kajita and Arthur B. McDonald “for the discovery of neutrino oscillations, which shows that neutrinos have mass”.
- Mar 2021LHCb reports R(K) = 0.846, a 3.1 standard deviation departure from lepton universality.
- 2022MicroBooNE publishes its first combined appearance-and-disappearance constraint on a sterile state.
- Dec 2022LHCb reanalyses the full dataset. R(K) becomes 0.949 and all four ratios agree with the Standard Model.
- Jun 2024KamLAND-Zen publishes the complete-dataset limit on neutrinoless double-beta decay.
- May 2025The Theory Initiative publishes a Standard Model prediction built on lattice QCD, and reports no tension with experiment.
- Jun 2025Fermilab’s Muon g-2 publishes its 127 parts-per-billion result, four times sharper than the previous world average.
- Aug 2025LEGEND-200 publishes its first results and a three-experiment combination in germanium-76.
- Dec 2025MicroBooNE excludes the single light sterile neutrino explanation at 95% confidence, using two beams.
Old theory, new results The record is thin at the start and thick at the end, and that is a fact about publishing.
Everything old in this subject is weakly sourced here and everything recent is strongly sourced. The 1937 and 1977 to 1981 entries are citations checked in a bibliographic database; every entry from 1998 onwards is a value read out of the paper’s own abstract or text. That is a property of the record rather than of the science, and it is why this page does not narrate the thirty years of argument about the solar neutrino deficit before Super-Kamiokande — the deficit is famous, and none of the measurements behind it was opened here. What the page does carry is the two results that ended the argument.
- 1937the oldest entry, and a citation only
- 1998where the record starts carrying numbers
The Argument
An anomaly is a subtraction, and either side of it can move The muon g-2 case makes this visible, because only one side moved and it was not the measurement.
A reported tension is the difference between a measured number and a predicted one. Between the era when the muon’s magnetic anomaly was the field’s most-watched discrepancy and the 2025 comparison, the experiment got more than four times more precise and its central value stayed where it was. What changed was the number it is subtracted from: new CMD-3 hadron-production data broke the agreement among the data-driven evaluations of the hadronic contribution, and the Theory Initiative moved its primary input to lattice QCD, reaching about 0.9 per cent. The 2025 statement is that experiment minus theory is 38(63) in units of 10⁻¹¹, “which implies that there is no tension”. Nothing about the muon was found to be different. One consequence follows immediately: a significance quoted from one year cannot be compared with one quoted from another, because the value being subtracted is not the same value. The familiar arc from four-point-something sigma down to nothing is a comparison between two subtractions, not between two measurements.
- 4×sharper measurement, same central value
- 38(63)experiment minus theory, in units of 10⁻¹¹
Four endings, four different things that were wrong Only one of the three that died died because the measurement was wrong.
| Anomaly | Ended by | What turned out to be wrong |
|---|---|---|
| The neutrino deficits | Nothing. It was real. | The theory. Neutrinos have mass and change flavour, and the Standard Model said they could not. |
| LSND and MiniBooNE | A different experiment, with a technique the earlier ones did not have. | The interpretation. The excess was there; a single light sterile neutrino was not what explained it. |
| R(K) | The same collaboration, more data, a changed analysis. | The measurement. This is the only one of the three where the number itself did not hold up. |
| Muon g-2 | The theory prediction moving, while the measurement got sharper and stayed put. | The comparison. Neither the muon nor the experiment turned out to be different from what was reported. |
What Others Add
Six ideas the results turn on Read in the order they were proposed, which is also the order in which each depends on the one before it.
| Idea | What it says | Why it is in this story |
|---|---|---|
| The symmetric theory of the electron and positron | Majorana's 1937 result: the Dirac equation also has solutions in which one field describes the particle and its antiparticle together, rather than two fields describing them separately. The condition is that the particle equals its own conjugate. It can only hold for a fermion with no electric charge. | Of every matter particle known, the neutrino is the only candidate. Every question below descends from this one, and it was asked eighty-nine years ago. |
| Majorana mass | A mass term that couples the neutrino field to itself, instead of coupling a left-handed field to a distinct right-handed partner as every charged fermion's mass does. Because it turns a neutrino into an antineutrino, it changes total lepton number by two. The Particle Data Group notes the consequence: such a neutrino needs a two-component spinor, where a charged fermion — a Dirac particle — needs four. | It is the alternative to the ordinary way of having mass, and the Standard Model conserves the quantity it breaks. |
| The seesaw mechanism | Add heavy neutrino states whose mass sits far above the electroweak scale. Diagonalising the combined mass matrix then splits the spectrum in two: the heavy states come out proportional to that large mass and the light ones proportional to its inverse. One end goes down as the other goes up, which is where the name comes from. In the one-generation shorthand the light mass is the Dirac mass squared, divided by the heavy one. | It is the standing answer to why neutrino masses are minute rather than merely small — and it delivers Majorana neutrinos at both ends, which is what makes the next row a test of it. |
| Neutrinoless double-beta decay | Ordinary double-beta decay emits two electrons and two antineutrinos. In the neutrinoless version the two antineutrinos never leave: the one emitted at the first vertex is absorbed at the second, which it can only do if it is its own antiparticle. Lepton number changes by two, and the two electrons carry away the full decay energy. It has never been seen: the complete KamLAND-Zen dataset puts the half-life above 3.8 × 10²⁶ years at 90% confidence. | It is the only practical experiment that can settle the three rows above, and after decades of running it has returned a limit rather than an answer. |
| Neutrino oscillation | The flavour a neutrino is produced with — electron, muon or tau — is not a state of definite mass, but a mixture of three states that are. The components of that mixture accumulate phase at slightly different rates as it travels, so the flavour measured at a distance need not be the flavour produced. Two conditions are required and both are now measured: the masses must differ, and the mixing must not vanish. | It is the one anomaly on this page that was real. It is also why the four rows above stay open: the Majorana phases cancel out of the oscillation probability, so no oscillation experiment can tell a Majorana neutrino from a Dirac one. |
| A single light sterile neutrino | A fourth neutrino state that takes no part in the weak interaction — which is what sterile means — and so does not couple to the Z boson. It stays invisible to the LEP count of 2.996 ± 0.007 neutrino types, and shows itself only by mixing with the three active ones, adding a fourth mass splitting to the pattern. | It was the standard reading of the short-baseline excesses. MicroBooNE excluded it at 95% confidence — that one model, of one state, and not sterile neutrinos in general. |
What is still open, and what the limits actually say Three questions the four endings above do not settle.
1937 → 2025 · the null search
Whether a neutrino is its own antiparticle
- If it is, neutrinoless double-beta decay happens and total lepton number is not conserved. KamLAND-Zen puts the half-life above 3.8 × 10²⁶ years at 90 per cent confidence, from 2.1 tonne-years of xenon-136.
- The germanium line agrees and is a little behind: above 1.9 × 10²⁶ years, combining GERDA, the MAJORANA Demonstrator and LEGEND-200 itself.
- The mass limits that follow span 28 to 122 meV — a factor of more than four, set by disagreement between nuclear matrix element calculations rather than by the data.
1977–1980 · the mass question
Why neutrino masses are so small is a separate, older problem
- Minkowski in February 1977, Gell-Mann with Ramond and Slansky in September 1979, Mohapatra and Senjanovic in November 1979, Yanagida in June 1980 — the four papers that between them proposed the seesaw mechanism set out in the table above.
- Yanagida’s contribution is usually dated 1979, to a workshop; the published paper is dated 1980. Both may be right.
- Fukugita and Yanagida, January 1986, connect heavy Majorana neutrinos to the matter-antimatter asymmetry, which is why the null search above is watched outside particle physics.
December 2025 · what was excluded
The sterile exclusion is narrower than it is usually reported
- The published statement is that the single light sterile neutrino interpretation of the LSND and MiniBooNE anomalies is excluded at 95 per cent confidence. It is not a statement that sterile neutrinos do not exist.
- What made it possible was two beams rather than more data: running two accelerator beams breaks a degeneracy between electron-neutrino appearance and disappearance that a single beam cannot separate.
- This supersedes MicroBooNE’s own 2022 constraint, which is the result most secondary accounts still stop at.
Conclusion
How to read the next one There will be a next one, and these four are the range of things it can turn out to be.
What holds
Neutrinos have mass and change flavour: that anomaly was real, and the two results that established it are the best-evidenced things on this page. The single light sterile neutrino explanation of the short-baseline excess is excluded at 95 per cent confidence. R(K) agrees with the Standard Model on the full dataset. Experiment and theory for the muon’s magnetic anomaly differ by 38(63) in units of 10⁻¹¹.
The question worth asking first
Not “how many sigma” but “which side of the subtraction is being claimed”. Three of these four disagreements are gone and only one of the three went because a measurement was wrong. One went because the interpretation was wrong and the excess was real; one went because the predicted number moved while the measured one stood still. A report that says only that a tension vanished has left out the part that tells you anything.
What to hold loosely
“No tension” is a statement about today’s precision, not a verdict: 38(63) is equally consistent with zero and with a real effect half its size. The g-2 theory disagreement was routed around rather than resolved, and it can move again. The sterile exclusion covers one specific model. And a limit is not an answer — neutrinoless double-beta decay has been looked for and not found, which settles nothing about whether it happens.