# Standard Model The **Standard Model** is the theory that classifies every known [[Elementary_particle|elementary particle]] and describes three of the four fundamental interactions between them — the electromagnetic, weak and strong forces, but not [[Gravity|gravity]]. It is the most precisely tested theory in the history of science and, at the same time, one that everybody working on it expects to be incomplete. In the microsim below the reader slides a single quantity across nineteen orders of magnitude: the decay width Γ, on a logarithmic axis from 10⁻¹² to 10 GeV. The curve drawn is a [[Resonance|resonance]] line shape, `sigma(E) ∝ (Gamma²/4)/((E − M)² + Gamma²/4)`, and the readout beside it is the lifetime, because the two are the same fact written twice: `Gamma·tau = hbar`.[^schiller][^manual04] At Γ = 2.4952 GeV, the measured width of the Z boson, the line is enormously broad and the lifetime reads 2.64×10⁻²⁵ s; slide down to the muon's 2.99×10⁻¹⁰ eV and the line becomes a spike while the lifetime reads 2.2 μs.[^schiller][^derived-sm] A second preset does something the first cannot: it takes the measured Γ of the Z, subtracts the widths for decays into quarks and into the three charged leptons, and divides what is left by the width the model predicts for a single [[Neutrino|neutrino]] species — `N_nu = (Gamma_Z − Gamma_had − 3·Gamma_l)/Gamma_nu = 2.98`.[^pdg][^derived-sm] The answer is a count of particles that were never detected, obtained purely from the width of a curve. Beside the plot sits the particle table itself — three generations, four force carriers and the Higgs — as the sheet the slider is read against.[^spec-p56] On the [[Physics]] flagship this article serves *The Standard Model* section of Part IV — Branches and fields. Its neighbours below are [[Atomic_nucleus]] and [[Nuclear_physics|nuclear physics]], where the same quantum field theory is applied to bound states rather than to free particles. ## Historical background The model was assembled, not designed. Quantum electrodynamics came first, completed in the late 1940s as a theory of [[Electron|electrons]] and [[Photon|photons]] that agreed with measurement to a precision nothing else in physics matched. The weak interaction resisted the same treatment for two decades because its carriers are heavy and its symmetry is broken; the electroweak unification of the 1960s solved that by introducing a scalar field whose vacuum value gives the W and Z their masses while leaving the photon massless. The strong interaction was the last piece and the strangest. Hadron spectroscopy in the 1950s and 1960s produced a bewildering catalogue of particles, and the quark model organised them as bound states of three constituents — but no quark was ever seen alone. Scattering experiments at high momentum transfer then found point-like constituents inside the [[Proton|proton]], and quantum chromodynamics explained both facts at once with a coupling that weakens at short distance and strengthens at long, so that quarks are nearly free inside a hadron and permanently confined outside it. By the mid-1970s the three theories were a single framework; the discovery of the W and Z in the early 1980s, of the top quark in 1995 and of the [[Higgs_boson|Higgs boson]] in 2012 closed it.[^cern-higgs][^os-particle] ## Particle content The inventory is startlingly short. Twelve matter particles arranged in three generations, four kinds of force carrier, and one scalar — and from those the whole of chemistry, nuclear physics and astrophysics follows, with gravity added by hand. ### Fermions Matter particles are [[Fermion|fermions]]: they carry half-integer [[Spin_(physics)|spin]] and obey the exclusion principle, which is why matter occupies volume at all. They come in two families. [[Quark|Quarks]] — up, down, charm, strange, top, bottom — feel the strong force and carry fractional [[Electric_charge|electric charge]]; leptons — electron, muon, tau and their three neutrinos — do not. Each family has three generations of identical structure and wildly different mass, and nothing in the model explains either the number three or the masses. The mass hierarchy is worth one concrete number. A [[Proton|proton]] is made of two up quarks and a down quark, whose masses sum to about 2.2 + 2.2 + 4.7 = 9.1 MeV; the proton's rest energy is 938 MeV.[^raven] The constituents account for roughly one percent of the object they constitute, and the rest is the energy of the gluon field binding them. The composite rule also decides statistics: a bound object made of an odd number of fermions is itself a fermion and one made of an even number is a boson, which is why [[Helium-3|helium-3]], with two protons, one [[Neutron|neutron]] and two electrons, is a fermion while [[Helium-4|helium-4]] is a boson.[^schiller] ### Gauge bosons Forces are carried by integer-spin [[Boson|bosons]], one for each symmetry the theory is built on. The photon carries electromagnetism and is massless, giving the force infinite range. Eight gluons carry the strong force; they are massless too, but because gluons themselves carry colour charge they interact with one another, and the force does not fall off with distance the way electromagnetism does. The [[W_and_Z_bosons|W and Z bosons]] carry the weak force and are heavy — heavy enough that the weak interaction is feeble at low energy purely because of the mass in the propagator, not because its intrinsic coupling is small. That mass is directly visible in the sim. A particle's decay width is its mass times a coupling factor, and the W and Z are so unstable that their widths are a measurable fraction of their masses: Γ_Z = 2.4952 GeV against M_Z = 91.19 GeV, a line 2.7 % as wide as it is tall in energy.[^schiller][^pdg][^derived-sm] Nothing else in the particle table is remotely that broad. ### Higgs boson The Higgs is the one spin-zero particle in the model and the only one whose job is to break a symmetry rather than to enforce one. Its field has a non-zero value everywhere, including in vacuum, and the masses of the W, the Z and every charged fermion are the strength with which each couples to that value. Without it the electroweak theory predicts four massless carriers and no massive fermions at all. It was the last piece to be found because it is heavy and rare, and because its signature is a small excess in channels with large backgrounds. The ATLAS and CMS collaborations announced the observation of a new boson consistent with the Standard Model Higgs on 4 July 2012, at a mass near 125 GeV.[^cern-higgs] The discovery closed the model's particle content, and it also sharpened its central problem: nothing protects a scalar's mass from quantum corrections, and the observed value is very much smaller than the scale at which the theory is expected to fail. ## Theoretical aspects The Standard Model is a relativistic quantum field theory. Its objects are fields filling space, its particles are quantised excitations of those fields, and its predictions are computed as a perturbation series in the couplings — a series whose individual terms are infinite and whose infinities cancel systematically against a finite number of measured inputs.[^peskin] That property, renormalisability, is what makes the model predictive rather than merely descriptive: about nineteen numbers are measured once, and everything else follows. ### Construction of the Standard Model Lagrangian The construction is almost mechanical. Choose a symmetry group — for the Standard Model, the product of a colour group, a weak-isospin group and a hypercharge group. Write down every term in the fields that is invariant under it and has dimension low enough to be renormalisable. That short list is the Lagrangian, and the force carriers are not added by hand but appear as the fields required to make the symmetry hold independently at each point in spacetime.[^halzen] The constraint is severe enough to be the theory's chief evidence: the gauge structure fixes the couplings' relative sizes, and those relations have been tested rather than assumed. The one piece that is not forced is the scalar sector. The Higgs potential's shape is chosen so that the field's lowest-energy state is not zero, which breaks the electroweak symmetry while leaving the colour symmetry intact and gives the W and Z mass without spoiling renormalisability.[^halzen][^peskin] ## Fundamental interactions Three of the four known interactions are inside the model and one is not. The three inside differ in the mass and self-coupling of their carriers, and almost every qualitative difference between them follows from those two properties. ### Gravity Gravity is absent. [[General_relativity|General relativity]] describes it superbly at every scale where it has been tested, but it is not a renormalisable quantum field theory, and attempts to quantise it in the same way produce a series that cannot be tamed with finitely many measured inputs. At the energies of any laboratory the omission does not matter — gravity between two protons is about 10³⁶ times weaker than their electrostatic repulsion — but it means the model cannot be complete. [[Quantum_gravity|Quantum gravity]] remains open. ### Electromagnetism Quantum electrodynamics is the model's most precisely verified sector and its template. Its carrier is massless, so the force has infinite range; its coupling is small, so the perturbation series converges quickly; and its predictions for quantities such as the electron's magnetic moment agree with measurement to more than ten significant figures.[^peskin][^os-particle] The energy scale separation from nuclear physics is itself instructive: a nuclear transition in ¹⁶O releases 6.05 MeV while a 450 nm visible [[Photon|photon]] carries 2.75 eV, a ratio above two million, which is why chemistry and nuclear physics look like different subjects.[^raven] ### Weak interaction The weak interaction is the only one that changes a quark's or lepton's type, and therefore the only one responsible for [[Beta_decay|beta decay]] and for the hydrogen burning that powers the [[Sun|Sun]]. It is also the only one that distinguishes left from right: it couples only to left-handed fermions, a violation of parity that has no analogue elsewhere in the model. Its apparent weakness is an illusion of scale. Because the W and Z are heavy, low-energy weak processes are suppressed by the carrier mass, which is why a muon lives 2.2 μs — an eternity by particle standards — while the Z itself lives 2.6×10⁻²⁵ s.[^schiller][^derived-sm] The sim makes the point directly: the muon and the Z sit at opposite ends of the Γ slider, nineteen decades apart, and the ratio of their widths is exactly the inverse ratio of their lifetimes because `Gamma·tau = hbar` holds for both.[^derived-sm] ### Strong interaction Quantum chromodynamics binds quarks into hadrons and, as a residual effect, hadrons into [[Atomic_nucleus|nuclei]] — the [[Nuclear_force|nuclear force]] of the previous page is a leftover of this one. Its distinguishing feature is that the coupling runs the wrong way: it becomes weak at short distance, so quarks probed at high momentum transfer behave almost as free particles, and strong at long distance, so no isolated quark has ever been observed. Because the coupling is large at low energy, perturbation theory fails exactly where ordinary matter lives, and hadron masses have to be computed numerically on a spacetime lattice — one of the largest standing problems in [[Computational_physics|computational physics]].[^halzen] ## Tests and predictions The model's authority rests on predictions made before the measurements existed: the W and Z masses, the top quark's mass from precision fits, the existence of the charm quark, and the Higgs. The sim reproduces the cleanest of these arguments, the LEP neutrino count, and it is worth doing the arithmetic in full because it is short. A Z boson can decay into any particle–antiparticle pair light enough to produce, and its total width is the sum of the partial widths for every channel. The measured total is Γ_Z = 2.4952 GeV. The hadronic channels contribute 1.7444 GeV and each charged lepton channel 83.98 MeV, so the width unaccounted for by anything visible is 2495.2 − 1744.4 − 3 × 83.98 = 498.9 MeV.[^pdg][^derived-sm] The model predicts 167.16 MeV per light neutrino species, and 498.9 ÷ 167.16 = 2.98.[^pdg][^derived-sm] There are three light neutrinos and no more. A fourth would have widened the Z by 167 MeV, or 6.7 %, which is far outside the measurement.[^derived-sm] That is a complete census of a particle sector performed without detecting a single member of it, and it is the reason the Z line shape is the standard illustration of what a width means. The same relation, `Gamma·tau = hbar`, is the energy–time uncertainty relation written as an equality rather than an inequality: with Δt = τ and ΔE = ħΓ the product is exactly ħ, which does not contradict `ΔE·Δt ≥ ħ/2` but specifies one particular case of it.[^raven][^manual04] Half-lives follow as `t½ = tau·ln 2`, not as τ itself.[^schiller] The other pillar is energy reach. The Tevatron collided beams of 980 GeV for 1.96 TeV in the centre of mass; the [[Large_Hadron_Collider|Large Hadron Collider]] collides 7 TeV beams for 14 TeV, and it was that factor of seven that put the Higgs within reach.[^raven] ## Challenges The model is not wrong so much as unfinished, and its gaps are specific. It contains no [[Dark_matter|dark matter]] candidate, although the astronomical evidence for one is strong; it says nothing about [[Dark_energy|dark energy]]; it does not include gravity; and in its original form it gives neutrinos no mass at all, though neutrino oscillation shows they have some. It offers no explanation for why there are three generations, for the pattern of fermion masses spanning eleven orders of magnitude, or for the matter–antimatter asymmetry of the universe, whose observed size the model's own sources of asymmetry fall far short of producing.[^os-particle] There is also an aesthetic complaint that has driven a great deal of experiment. The Higgs mass receives quantum corrections proportional to the highest energy scale at which the theory still applies, so keeping it near 125 GeV requires either a cancellation of extraordinary precision or some new physics not far above the electroweak scale. Searches for that new physics at the LHC have so far found nothing, which is itself a result: whatever completes the Standard Model is either heavier or more weakly coupled than the simplest expectations allowed.[^os-particle][^peskin] ## See also - [[W_and_Z_bosons]] — the resonance whose width the sim measures - [[Neutrino]] - [[Elementary_particle]] - [[Higgs_boson]] - [[Boson]] - [[Fermion]] - [[Quark]] - [[Large_Hadron_Collider]] ## Notes - The sim's line shape is the non-relativistic Breit–Wigner form. The relativistic form used in fits to real collider data differs in the placement of the mass term and shifts the peak position slightly; the distinction does not change anything on this page and the two agree closely when Γ is much smaller than M. - The relation `Gamma·tau = hbar` treats Γ as an energy width. The same symbol is often used for a rate in inverse seconds, and the two differ by a factor of ħ; mixing them is the most common arithmetic error in this subject. - Partial widths quoted here are the Particle Data Group's combined values from the four LEP experiments, and Γ_ν is the model's prediction for one species rather than a measurement, since the neutrino channels are invisible by construction. The neutrino count is therefore a test of the model against itself as well as against the data. - Sources for every figure on this page are collected under *References* below. ## References [^schiller]: Schiller, Christoph. *The Adventure of Physics, Vol. IV: The Quantum of Change*, pp. 125–142: the particle data used here — Z width 2.4952 GeV, W width 2.124 GeV, muon lifetime 2.19703 μs and tau lifetime 290.6 fs, pp. 128–129; the relation `Gamma·tau = hbar` with Γ as an energy width and the half-life `t½ = tau·ln 2`, p. 129; and the composite spin–statistics rule by which an object of an odd number of fermions is a fermion, so that helium-3 with five fermions is a fermion and helium-4 with six is a boson, p. 140. Licensed CC BY-NC-ND: cited, not adapted. [^raven]: Raven, Will (2025). *Atomic Physics for Everyone*, Chapter 11 *Standard Model*, pp. 227–245 (page to pin for statements drawn from the chapter as a whole): the quark-mass analogy, 2.2 + 2.2 + 4.7 MeV summing to 9.1 MeV against the proton's 938 MeV, p. 229; the energy–time relation `(dE)(dt) ≥ hbar/2` and the demonstration that with Δt = τ and ΔE = ħΓ the product is exactly ħ, pp. 230–231; the proton rest energy of 938.27 MeV from m = 1.6726219×10⁻²⁷ kg, p. 231; the ¹⁶O nuclear state at 6.05 MeV against a 450 nm photon at 2.75 eV, a ratio above 2×10⁶, p. 232; the conversion 1 MeV = 1.602176×10⁻¹³ J, p. 244; and the collider energies, Tevatron at 980 GeV per beam for 1.96 TeV and the LHC at 7 TeV per beam for 14 TeV, p. 245. [^pdg]: Particle Data Group, *Review of Particle Physics*, Z boson data listings and the electroweak review (pages to pin): the combined LEP values Γ_Z = 2.4952 GeV, Γ_had = 1.7444 GeV and Γ_ℓ = 83.98 MeV per charged lepton species, together with the Standard Model partial width Γ_ν = 167.16 MeV per light neutrino species from which the neutrino count is obtained. No Portal Book carries the partial widths; only the total Z width appears in [^schiller]. [^cern-higgs]: CERN, announcement and subsequent documentation of the observation of a new boson consistent with the Standard Model Higgs by the ATLAS and CMS collaborations, 4 July 2012, at a mass near 125 GeV (page to pin). No Portal Book covers the discovery. [^os-particle]: OpenStax (Sanny, Jeff; Ling, Samuel, eds.) (2016). *University Physics Volume 3*, Chapter 11 *Particle Physics and Cosmology*, pp. 493–540 (pages to pin): the particle inventory and generation structure, the quark model and confinement, the discovery sequence for the W, Z and top quark, and the standing problems — dark matter, dark energy, neutrino mass, the generation puzzle and the matter–antimatter asymmetry. https://openstax.org/details/books/university-physics-volume-3 [^halzen]: Halzen, Francis; Martin, Alan D. (1984). *Quarks and Leptons: An Introductory Course in Modern Particle Physics*, Wiley (pages to pin): the gauge principle by which requiring a symmetry to hold independently at each spacetime point generates the force carriers; the construction of the Standard Model Lagrangian from the colour, weak-isospin and hypercharge groups; the Higgs mechanism giving the W and Z mass while leaving the photon and gluons massless; and the running of the strong coupling that produces asymptotic freedom at short distance and confinement at long. No Portal Book in this cluster treats gauge theory. [^peskin]: Peskin, Michael E.; Schroeder, Daniel V. (1995). *An Introduction to Quantum Field Theory*, Addison-Wesley (pages to pin): renormalisation and the cancellation of divergences against a finite set of measured inputs; the precision of quantum electrodynamics; and the sensitivity of a scalar mass to the cutoff scale that constitutes the hierarchy problem. [^manual04]: Wikitube MicroSim Guide, sub-manual 04 *Atomic, Quantum, Statistical and Electromagnetic Physics*, §2.1 "Natural linewidth ↔ lifetime": the width–lifetime relation and its unit traps — that mixing γ in Hz with Γ in rad/s is a factor-2π error, that τ = 1/Γ comes out in seconds rather than seconds per radian, that the equality ΔE·Δt = ħ defines a width and does not contradict ΔE·Δt ≥ ħ/2, and that the half-life is 0.693 τ and not τ; together with the "particles" preset in which τ runs on a log axis from 10⁻²⁵ to 10⁻⁵ s with markers for the Z, W, tau lepton and muon, and the instruction that a log time axis is required because a linear one collapses twenty decades. [^spec-p56]: Matter & Energy Cluster contract, `_registry/plans/PHYSICS_SECTIONS.md` row P56: the sim concept for this page — the Z line shape `sigma(E) ∝ (Gamma²/4)/((E − M)² + Gamma²/4)` with `Gamma·tau = hbar`; Γ as the single control on a log axis from 10⁻¹² to 10 GeV, with the lifetime reading out from 2.6×10⁻²⁵ s at the Z's 2.4952 GeV to 2.2 μs at the muon; the "count the neutrinos" preset subtracting the measured hadron and charged-lepton widths from Γ_Z to leave `N_nu = 2.98`; and the particle table of three generations, four force carriers and the Higgs as the sheet beside the plot. [^derived-sm]: Computed for this article from the widths and constants cited above, using ħ = 6.579×10⁻²² MeV·s (from ħ = 1.054×10⁻³⁴ J·s and 1 MeV = 1.602176×10⁻¹³ J): τ_Z = 6.579×10⁻²² ÷ 2495.2 = 2.64×10⁻²⁵ s and τ_W = 3.10×10⁻²⁵ s; Γ_μ = 6.579×10⁻²² ÷ 2.19703×10⁻⁶ = 2.99×10⁻¹⁰ eV and Γ_τ = 2.26×10⁻³ eV; the ratio Γ_Z/Γ_μ = 8.3×10¹⁸, equal to τ_μ/τ_Z, which is the content of `Gamma·tau = hbar`; the Z's fractional width Γ_Z/M_Z = 2.4952 ÷ 91.19 = 2.74 %; the invisible width 2495.2 − 1744.4 − 3 × 83.98 = 498.9 MeV and the neutrino count 498.9 ÷ 167.16 = 2.98; and the effect of a hypothetical fourth light species, which would add 167.16 MeV to Γ_Z, a 6.7 % increase. ## Further reading ### Introductory textbooks - Raven, Will (2025). *Atomic Physics for Everyone*, Chapter 11 *Standard Model*, pp. 227–245. CC BY. Portal Book 046; the source of the quark-mass, uncertainty-relation and collider-energy figures used here. - OpenStax (2016). *University Physics Volume 3*, Chapter 11 *Particle Physics and Cosmology*, pp. 493–540. CC BY. Portal Book 079. - Schiller, Christoph. *The Adventure of Physics, Vol. IV: The Quantum of Change*, pp. 125–142. CC BY-NC-ND. Portal Book 049; the particle widths and lifetimes and the spin–statistics discussion. ### Advanced textbooks - Halzen, Francis; Martin, Alan D. (1984). *Quarks and Leptons: An Introductory Course in Modern Particle Physics*, Wiley. - Peskin, Michael E.; Schroeder, Daniel V. (1995). *An Introduction to Quantum Field Theory*, Addison-Wesley. ### Journal articles - ATLAS Collaboration (2012). Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC. *Physics Letters B* (volume and pages to pin). - CMS Collaboration (2012). Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC. *Physics Letters B* (volume and pages to pin). - Particle Data Group, *Review of Particle Physics*, current edition — the standing compilation from which every width on this page is taken. ## External links - [*University Physics Volume 3*](https://openstax.org/details/books/university-physics-volume-3) (OpenStax, 2016), Chapter 11 *Particle Physics and Cosmology* — the open-access treatment closest to this page's level - The Wikipedia pair's *External links* section lists the CERN, PDG and collaboration sites that hold the current measured values; those, not this page, are the authority for any number quoted here. <!-- MATTERSIM:BEGIN g24 — Matter & Energy Cluster microsim (framework build, specs/sims/Standard_Model.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework), pending deploy:** *Standard Model* will play here once `https://wikitube-3d-microsims.netlify.app/matter/Standard_Model.html` is live. <!-- pending: <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Standard_Model.html" data-title="Standard Model"></div> --> <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Standard_Model) : [Wikitube](https://en.wikitube.io/wiki/Standard_Model) · pinned revision [1374132911](https://en.wikipedia.org/w/index.php?oldid=1374132911) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Physics]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Physics row P56 · sim pending (matter/Standard_Model).*