The Standard Model of particle physics: fermions (quarks, leptons), gauge bosons (photon, W, Z, gluon), the Higgs boson, electroweak unification, and quantum chromodynamics.
standard-model
Quarks
Six flavors (u, d, s, c, b, t) of spin-½ fermions carrying color charge; confined into hadrons by the strong force.
Leptons
Six flavors (e, μ, τ and their neutrinos) of spin-½ fermions without color charge; only the charged ones couple to EM.
Gauge bosons
Force-carrier particles (photon, W±, Z, gluon) that mediate the three gauge interactions of the Standard Model.
Higgs boson
Scalar particle associated with the Higgs field whose vacuum expectation value breaks electroweak symmetry and endows W/Z and fermions with…
Electroweak unification
At high energies, electromagnetic and weak interactions merge into a single SU(2)×U(1) gauge theory; the Higgs mechanism breaks the…
Physics beyond the Standard Model
Generative placeholder for all empirically motivated extensions not yet confirmed: SUSY, extra dimensions, new gauge sectors, dark-matter…
Elementary particle
A particle that (as far as current experiment can resolve) has no internal substructure — the irreducible constituents of the Standard…
Fermion
A particle with half-integer spin (½, 3/2, …) obeying Fermi-Dirac statistics and the Pauli exclusion principle. All matter particles in the…
Boson
A particle with integer spin (0, 1, 2, …) obeying Bose-Einstein statistics. Multiple bosons can occupy the same quantum state — the basis…
Antiparticle
For every particle species there exists a corresponding antiparticle with identical mass and spin but opposite additive quantum numbers…
Up quark
Lightest up-type quark; along with the down quark, a constituent of nucleons (proton = uud, neutron = udd). Spin-½, colour-charged fermion;…
Down quark
Lightest down-type quark; constituent of nucleons (neutron = udd, proton = uud). Spin-½, colour-charged fermion; confined inside hadrons by…
Charm quark
Second-generation up-type quark; discovered via the J/ψ meson (November Revolution, 1974). Spin-½, colour-charged fermion; confined inside…
Strange quark
Second-generation down-type quark; carrier of strangeness quantum number, constituent of kaons and hyperons. Spin-½, colour-charged…
Top quark
Heaviest known fundamental particle (~173 GeV, mass of a gold atom); discovered at Fermilab 1995. Decays before hadronizing. Spin-½,…
Bottom quark
Third-generation down-type quark; key to B-meson physics and CP-violation studies at LHCb / Belle II. Spin-½, colour-charged fermion;…
Electron (lepton)
First-generation charged lepton: spin-½, charge −e, mass 0.511 MeV/c². Stable. Constituent of atoms (orbital electrons); discovered by J.J.…
Muon
Second-generation charged lepton: spin-½, charge −e, mass 105.66 MeV/c². Unstable, mean lifetime 2.20 μs, decays via weak interaction to e⁻…
Tau lepton
Third-generation charged lepton: spin-½, charge −e, mass 1777 MeV/c². Heaviest charged lepton, lifetime 2.9×10⁻¹³ s. Massive enough to…
Electron neutrino
First-generation neutrino: spin-½, electrically neutral, nearly massless (m < 0.8 eV). Couples to the electron via the charged-current weak…
Muon neutrino
Second-generation neutrino: spin-½, electrically neutral, nearly massless. Couples to the muon via charged-current weak interaction.…
Tau neutrino
Third-generation neutrino: spin-½, electrically neutral, nearly massless. Couples to the tau via charged-current weak interaction. Directly…
Photon
Massless, electrically neutral spin-1 gauge boson; quantum of the electromagnetic field and mediator of the electromagnetic force.…
W boson (W±)
Massive charged spin-1 gauge boson mediating the charged-current weak interaction (e.g. β-decay: n → p + e⁻ + ν̄_e proceeds via virtual…
Z boson
Massive neutral spin-1 gauge boson mediating the neutral-current weak interaction. Mass ≈ 91.1876 GeV/c². Discovered at CERN UA1/UA2…
Gluon
Massless, electrically neutral, colour-charged spin-1 gauge boson mediating the strong interaction (QCD) between quarks. Eight independent…
Positron (e⁺)
The antiparticle of the electron: spin-½, charge +e, mass 0.511 MeV/c². Predicted by Dirac (1928) from the negative-energy solutions of his…
Hadron
A composite particle bound by the strong interaction from quarks, antiquarks, and gluons. Divides into two families: baryons (three-quark…
Baryon
A three-quark bound state (qqq); always a fermion. Baryon number B = +1 (antibaryons have B = −1); conserved in all known Standard-Model…
Meson
A quark-antiquark bound state (q q̄); always a boson. Zero baryon number. Lightest meson is the pion (π), the carrier of the residual…
Pion (π±, π⁰)
Lightest meson (m ≈ 140 MeV). Three charge states: π⁺ (ud̄), π⁻ (ūd), π⁰ (uū / dd̄ mixture). Mediator of the residual strong nuclear force…
Kaon (K±, K⁰, K̄⁰)
Strangeness-carrying meson (m ≈ 494 MeV for K±, 498 for K⁰). Quark content: K⁺ (us̄), K⁻ (ūs), K⁰ (ds̄), K̄⁰ (d̄s). First particle for…
Higgs mechanism
Spontaneous breaking of electroweak SU(2)×U(1) by a scalar doublet vacuum expectation value; gives mass to W± and Z while leaving the…
CKM quark-mixing matrix
Unitary 3×3 matrix relating weak-interaction eigenstates to mass eigenstates of down-type quarks; sources CP violation via a single…
PMNS neutrino-mixing matrix
Unitary matrix between neutrino flavour eigenstates (ν_e, ν_μ, ν_τ) and mass eigenstates (ν_1, ν_2, ν_3); responsible for neutrino…
CP violation
Breaking of combined charge-conjugation and parity symmetry; observed in kaon (1964) and B-meson systems. Source of matter–antimatter…
Neutrino oscillations & mass ordering
P(ν_α → ν_β) = sin²(2θ) sin²(Δm² L/4E); Δm²_21 ≈ 7.5×10⁻⁵ eV², |Δm²_32| ≈ 2.5×10⁻³ eV². SNO, Super-K, KamLAND, T2K, NOvA.
CP violation in K⁰–K̄⁰
K_L → 2π at 2×10⁻³ branching (Cronin–Fitch 1964); direct CPV Re(ε'/ε); CKM-driven via box and penguin diagrams.
CP violation in B mesons (BaBar/Belle)
sin 2β from J/ψ K_S; β, α, γ angles of unitarity triangle; CKM mechanism confirmed to few-percent; 2008 Nobel (Kobayashi–Maskawa).
Deep inelastic scattering
e⁻p → e⁻X at large Q²; Bjorken scaling F(x); parton model (Feynman); QCD scaling violations via DGLAP.
DGLAP evolution equations
Q²∂f_i/∂Q² = (α_s/2π) P_ij⊗f_j; evolves PDFs with factorization scale; needed for collider predictions.
QCD factorization theorem
Hadronic cross sections factorize into process-dependent partonic cross sections and universal PDFs σ = Σ∫f_i f_j σ̂_ij + O(Λ/Q).
Electroweak precision observables
Z-pole measurements (LEP/SLC): Γ_Z, sin²θ_W, A_LR; S,T,U parameters constrain new physics; top mass from global fit before Tevatron.
Muon anomalous moment g-2
a_μ = (g-2)/2 measured to 0.2 ppm (BNL + Fermilab E989); SM hadronic-VP tension of ~4σ (lattice vs e⁺e⁻ data unresolved).
Strong CP problem and θ̄
θ̄ (G G̃) term allowed by QCD; experimental |d_n| < 10⁻²⁶ e·cm forces θ̄ < 10⁻¹⁰; Peccei–Quinn axion solution.
Peccei–Quinn axion
Anomalous U(1)_PQ broken spontaneously → pseudoscalar Goldstone (axion) dynamically cancels θ̄. Dark matter candidate; ADMX search.
Custodial SU(2) symmetry
Higgs potential has accidental SU(2)_L×SU(2)_R broken to diagonal; protects ρ = M_W²/(M_Z² cos²θ_W) ≈ 1 against large EW corrections.
Peskin–Takeuchi S, T, U parameters
Oblique EW corrections from new physics; global fit constrains many BSM models. Current: S ≈ 0.00±0.07, T ≈ 0.05±0.06.
Seesaw mechanism for neutrino mass
Heavy right-handed Majorana N_R + Dirac mass m_D → light m_ν ≈ m_D²/M_R; explains eV-scale neutrinos if M_R ≈ 10¹⁴ GeV.
Lepton-flavor universality tests
SM gauge couplings equal for e/μ/τ; tested in π, K, B decays; LHCb R_K, R_K* anomalies (now consistent with SM per 2022 measurement).
Electroweak sphaleron & B+L violation
Classical saddle of SU(2) Higgs gauge theory violates B+L by 3 units; active at T ≳ 100 GeV; role in baryogenesis.
GIM mechanism
Flavor-changing neutral currents suppressed by unitarity of CKM; predicted charm quark to cancel K→μμ loop. Glashow–Iliopoulos–Maiani 1970.
Higgs boson discovery (ATLAS/CMS 2012)
125-GeV scalar observed in γγ, ZZ→4ℓ, WW channels at LHC; couplings proportional to mass; CP-even, J=0; Nobel 2013 (Englert, Higgs).
LHC high-luminosity physics
HL-LHC (3000 fb⁻¹) target 2029+; precision Higgs couplings, di-Higgs HH → bb̄γγ, vector-boson scattering probes of EW sector.
PMNS / CKM unitarity as a Lie-group constraint (standard-model)
Standard-model application of L0 Lie-group and group-homomorphism theory. The Pontecorvo–Maki–Nakagawa–Sakata matrix U_PMNS (and its quark…
SU(3) flavor decomposition 3 ⊗ 3̄ = 1 ⊕ 8 (standard-model)
Standard-model application of L0 representation-theory and simple-group theory. SU(3)_flavor is a simple compact Lie group, and its…