What Happened
Physics · Particle Physics · Standard Model · History of Science · Explainerstate of the record to 2 September 2026 · every figure read from the paper that published it
The theory, and the shape of what it leaves out
Nineteen Numbers, Three Forces of Four
The Standard Model is described two ways at once: as the most precisely tested theory in physics, and as a theory known to be incomplete. Both are true, and they are not in tension — because they are about different things. What it is tested on are predictions, and a prediction that disagrees with a measurement is an anomaly that can close from either side. What it is incomplete about are omissions, and an omission has no prediction in it to be wrong. Gravity is not something the theory got wrong. It is a force the theory does not contain.
What the Standard Model is the scope, the symmetry, and the contents
It is a quantum field theory describing three of the four known fundamental forces — electromagnetic, weak and strong — and classifying all known elementary particles. Gravity is excluded, explicitly and by construction. The theory is defined by a local SU(3) × SU(2) × U(1) gauge symmetry, whose three factors give rise to the three interactions it does describe. Its matter content is twelve elementary fermions of spin one-half, arranged in three generations: six quarks, which carry colour charge and feel the strong force, and six leptons, which do not. Writing down the most general Lagrangian consistent with that symmetry leaves nineteen parameters whose values the theory does not fix. Every one of them is put in by hand, from measurement.
- 3 / 4forces described. Gravity is the one left out
- 12elementary fermions, in three generations
- 19constants the theory cannot derive, only receive
The four numbers each read from the source that publishes it
- 19free constants, fixed only by experiment
- 26–27once neutrino mass is accommodated
- 125.20 GeVHiggs mass, with a scale factor of 1.4
- 0.60 σmuon g−2, experiment against theory
What is established, and how well standing first, and the kinds kept apart
| Standing | What | On the record |
|---|---|---|
| Confirmed | The gauge symmetry and the particle content | SU(3) × SU(2) × U(1); 12 fermions in three generations; six quarks and six leptons |
| Confirmed | The four particles the theory predicted and experiment then found | W± and Z⁰ in 1983, with the mass ratio as predicted; the top quark in 1995; the tau neutrino in 2000; the Higgs boson in 2012 |
| Confirmed | The Higgs mass | 125.20 ± 0.11 GeV, the Review of Particle Physics average. Its scale factor of 1.4 says the inputs disagree by more than their stated errors |
| Confirmed, not verifiable here | The development dates from 1928 to 1974 | Dated from a reference work rather than from the original papers, which were not read for this article |
| Attributed claim | Who named the theory | Pais and Treiman published the term in 1975. Weinberg has since claimed priority for a 1973 talk in Aix-en-Provence — a recollection of an unpublished lecture |
| Proposal, not observed | Where neutrino mass comes from | A seesaw mechanism adding heavy right-handed neutrinos would give masses of the right size if new physics appears at or below 10¹⁴ GeV. Nothing has been observed |
Timeline
Fifty years of theory, forty of confirmation dated as the reference work dates them
- 1928Dirac writes down his equation, implying antimatter
- 1954Yang and Mills extend gauge theory to non-abelian groups
- 1957Wu shows parity is not conserved in the weak interaction
- 1961Glashow combines the electromagnetic and weak interactions
- 1964Quarks introduced by Gell-Mann and Zweig; colour charge, implicitly, by Greenberg
- 1967Weinberg and Salam put the Higgs mechanism into the electroweak interaction
- 1970The GIM mechanism predicts the charm quark
- 1971’t Hooft shows gauge theories can be renormalised
- 1973Neutral weak currents are discovered at CERN
- 1973–74Asymptotic freedom is proposed; QCD takes its modern form
- 1975Pais and Treiman publish the term Standard Model
- 1976Perl discovers the tau lepton at SLAC
- 1977A team led by Lederman discovers the bottom quark at Fermilab
- 1979The Nobel Prize goes to Glashow, Salam and Weinberg for the electroweak theory
- 1983W± and Z⁰ are found, with the mass ratio the theory predicted
- 1995The top quark is confirmed
- 2000The tau neutrino is confirmed
- 2012The Higgs boson is confirmed, completing the predicted content
- 2018Planck’s final cosmological parameters put most of the universe outside the theory
- 2025The muon g−2 prediction moves, and a twenty-year anomaly closes to 0.60 σ
One thing with two dates, and six with none what the chronology cannot hold
The naming has two dates and no way to choose between them from what is on record here. Pais and Treiman put the term in print in 1975; Weinberg has since said he used it in 1973, at a talk in Aix-en-Provence, and chose it out of modesty. One is a publication, the other a recollection of an unpublished lecture. Both are given above and neither is preferred.
Six other things have no entry at all, and their absence is the point of this article rather than a gap in it. Gravity, dark matter, dark energy, the matter–antimatter asymmetry, the strong CP problem and the hierarchy problem are not events. Nothing happened on a date to put them outside the theory; they were never inside it. A timeline is the wrong instrument for an omission, which is exactly why they need a section of their own. Neutrino mass is the seventh omission and the exception: it does have a discovery date, and the theory can be stretched to hold it — at the cost of seven or eight more constants.
- 6omissions with no date, because none of them is an event
- 2dates for the theory’s name, and no way to choose
The Argument
An anomaly is a subtraction; an omission is an absence why the two are never the same kind of trouble
An anomaly is the difference between a number the theory predicts and a number an experiment measures. It is a subtraction, and a subtraction has two sides. When one closes, the honest question is which side moved. Sometimes the measurement improves; sometimes the calculation is redone and the prediction shifts under a measurement that never changed at all.
An omission has no subtraction in it. There is no Standard Model prediction for the dark matter density to disagree with Planck’s, because the theory contains no particle that could be dark matter. It is not a prediction that came out badly; there is no prediction. That distinction decides how to read everything else on this page, and it is the one most often lost: a theory whose anomalies keep closing is not thereby a theory that is nearly finished.
- 2sides to every anomaly, and either one can be the one that is wrong
- 0predictions the theory makes about dark matter
The case that shows the difference the muon’s magnetic moment, both sides read from their own papers
| Quantity | Value | What it is |
|---|---|---|
| Experiment | 1 165 920 715 ± 145 | The world average, dominated by Fermilab, at 124 ppb |
| Theory | 1 165 920 330 ± 620 | The Standard Model prediction, at 530 ppb, after the hadronic term was taken from lattice QCD |
| Difference | 385 | Against a combined uncertainty of 637 |
| Tension | 0.60 σ | Agreement. The anomaly that stood for twenty years is gone — and it went because the prediction moved |
| Who is the limit now | 4.3 × | The theory’s uncertainty is 4.3 times the experiment’s. Measurement is no longer the limiting side |
What Others Add
The six quarks, one row each masses as the Review of Particle Physics gives them, with the scheme noted below
| Quark | Gen. | Charge | Mass | What is distinctive |
|---|---|---|---|---|
| up (u) | 1 | +2/3 | 2.16 ± 0.07 MeV | With the down quark it makes every proton and neutron. Does not decay |
| down (d) | 1 | −1/3 | 4.70 ± 0.07 MeV | Heavier than the up quark, which is why a free neutron decays and a proton does not |
| charm (c) | 2 | +2/3 | 1.2730 ± 0.0046 GeV | Predicted by the GIM mechanism in 1970, before it was found |
| strange (s) | 2 | −1/3 | 93.5 ± 0.8 MeV | Named for the long lifetimes of the particles that carry it |
| top (t) | 3 | +2/3 | 172.56 ± 0.31 GeV | The heaviest known elementary particle. Decays before it can bind into a hadron |
| bottom (b) | 3 | −1/3 | 4.183 ± 0.007 GeV | The quark whose decays carry most of the surviving tests of lepton universality |
The six leptons, one row each the three neutrino masses are a single bound, not three measurements
| Lepton | Gen. | Charge | Mass | Mean life |
|---|---|---|---|---|
| electron (e) | 1 | −1 | 0.51099895000 ± 0.00000000015 MeV | > 6.6×10²⁸ yr |
| electron neutrino (ν_e) | 1 | 0 | < 0.8 eV | no limit established |
| muon (μ) | 2 | −1 | 105.6583755 ± 0.0000023 MeV | 2.1969811×10⁻⁶ s |
| muon neutrino (ν_μ) | 2 | 0 | < 0.8 eV | no limit established |
| tau (τ) | 3 | −1 | 1776.93 ± 0.09 MeV | 290.3×10⁻¹⁵ s |
| tau neutrino (ν_τ) | 3 | 0 | < 0.8 eV | no limit established |
The five bosons, and the one that carries no force the Higgs is in this table because it is a boson, not because it is a force carrier
| Boson | What it carries | Spin | Charge | Mass |
|---|---|---|---|---|
| photon (γ) | Electromagnetism, over unlimited range | 1 | 0 | < 10⁻¹⁸ eV, and zero in the theory |
| gluon (g) | The strong interaction. There are eight, and they carry colour themselves | 1 | 0 | 0 |
| W± | The weak interaction, and the only carrier that changes one fermion into another | 1 | ±1 | 80.3692 ± 0.0133 GeV |
| Z⁰ | The weak interaction without changing what the fermion is | 1 | 0 | 91.1880 ± 0.0020 GeV |
| Higgs (H) | No force. Its field is what gives the W, the Z and the fermions their masses | 0 | 0 | 125.20 ± 0.11 GeV |
Why a quark’s mass is not the same kind of number as an electron’s three different definitions appear in one column above
The electron’s mass is a property of a particle that can be isolated and weighed, and it is known to eleven digits. A quark cannot be isolated at all: colour confinement means one never appears on its own, so its mass is not something measured directly but a parameter of the theory, defined only once a convention is fixed. The column above therefore holds three different definitions. The Review of Particle Physics states them: the up, down and strange masses are quoted in one scheme at an energy scale of 2 GeV; the charm and bottom masses are quoted in that scheme at their own mass; and the top mass is extracted from the kinematics of the events it appears in, which is a different thing again.
Two consequences a reader should carry. A quark mass quoted without its scheme is incomplete rather than merely imprecise. And the top quark is the exception that makes the rule visible: it is heavy enough to decay before it can bind into anything, so it is the one quark that is observed as itself.
- 0quarks ever observed in isolation, except as the top’s decay products
- 3different mass definitions in one column of six quarks
The seven things it does not explain none of these is a failed prediction
| Omission | What is missing | What is known from outside the theory |
|---|---|---|
| Gravity | The fourth force, absent by construction | Quantum field theories of gravity break down before the Planck scale, so there is no reliable theory of the very early universe |
| Dark matter | No particle in the theory has the required properties | About 26% of the universe, and 84% of all matter, derived from Planck’s densities |
| Dark energy | Nothing in the theory drives an accelerating expansion | About 68.5% of the universe, as 1 − Ω_m from the same measurements |
| Neutrino mass | The unmodified theory sets it to zero | The sum of the masses is under 0.12 eV on cosmological grounds, assuming ΛCDM. Accommodating it is believed to need 7 or 8 more constants |
| Matter over antimatter | The theory’s CP violation is not enough to account for the imbalance | The universe is made of matter, and the theory does not say why |
| The strong CP problem | Nothing requires the strong interaction to preserve CP, yet it appears to | The neutron’s electric dipole moment is measured at 0.0 ± 1.1×10⁻²⁶ e·cm — zero, to a precision that has no explanation |
| The hierarchy problem | The Higgs mass is extraordinarily sensitive to quantum corrections | Keeping the weak scale far below the Planck scale requires severe fine tuning, unless quantum gravity avoids it |
What the numbers outside the theory look like derived here from Planck’s published densities
Planck’s final analysis gives a dark matter density of Ω_c h² = 0.120 ± 0.001, a baryon density of Ω_b h² = 0.0224 ± 0.0001 and a Hubble constant of 67.4 ± 0.5 km/s/Mpc. Dividing the first two by h² turns them into fractions: about 26% dark matter and about 5% ordinary matter, with dark energy the remaining 68.5% as 1 − Ω_m. The two routes to the matter density agree to within half a percent, which is what licenses quoting the split at all — and why it is given here to two figures and not three.
Put the other way round, the share that carries the point better: dark matter is 84% of all the matter there is. The theory that classifies all known elementary particles accounts for the other sixteen.
- 84%of all matter is dark matter, which the theory has no particle for
- 5%is ordinary matter — the part the theory does describe
- 0.12 eVcaps the sum of the neutrino masses, on cosmological grounds
Three limits, and what each one actually constrains a null result is evidence about something — but not always about this theory
Proton decay
> 2.4×10³⁴ years
- Twenty-two years of running, from 1996 to 2018, and no candidate event in the p → e⁺π⁰ channel
- This does not test the Standard Model. The theory does not predict the proton decays at all
- It constrains the grand unified theories that would explain why the model has the structure it has
Neutron dipole moment
0.0 ± 1.1×10⁻²⁶ e·cm
- Zero, to about one part in 10²⁶, of a quantity nothing requires to be small
- The strong interaction is free to violate CP and does not appear to. That is the strong CP problem
- A measurement, not a limit: the figure quoted here is the value the experiment reports, uncertainties included
Muon g−2
0.60 σ
- This one is a test of the theory, and the theory passes it
- It passed because the prediction was recalculated, not because the measurement changed
- The disagreement among the e⁺e⁻ datasets that produced the old anomaly is still unexplained, so this is not a closed question
Conclusion
What to take from it and what to hold loosely
The theory is in better shape than its reputation suggests
Its most famous discrepancy closed to 0.60 σ in 2025, and for that quantity the calculation is now four times less certain than the measurement. When a theory’s tests start being limited by the difficulty of computing its own predictions, the tests are not what is failing.
And it is unfinished in a way no test can fix
Six phenomena have no entry in it, and nineteen of its constants are put in by hand. Neither is a measurement that might come out differently next year. A better experiment cannot supply a force the theory does not contain, and no amount of precision explains why nineteen numbers have the values they do.
Hold these loosely
The count of nineteen is the theory without neutrino mass; accommodating that is believed to need 7 or 8 more. The 0.12 eV cap on the neutrino masses assumes a cosmological model. The Higgs average carries a scale factor of 1.4, meaning its inputs disagree. And the muon result rests on the lattice calculation being right, with the older data-driven route still unreconciled.