Standard Model Overview

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standard-model particle-physics gauge-theory

Core Idea

The Standard Model is the quantum field theory of all known fundamental interactions except gravity. It is based on the gauge group SU(3)_C x SU(2)_L x U(1)_Y, with matter content consisting of three generations of quarks and leptons, and the Higgs doublet. Its 19 free parameters are determined by experiment. Every prediction has been confirmed, including the Higgs boson discovery in 2012.

Explainer

The Standard Model of particle physics is a quantum field theory based on the gauge group SU(3)_C x SU(2)_L x U(1)_Y. SU(3)_C is the color gauge group of QCD, mediating the strong interaction via 8 gluons. SU(2)_L x U(1)_Y is the electroweak gauge group, mediating the weak and electromagnetic interactions via the W+, W-, Z, and photon. The Higgs doublet breaks the electroweak symmetry to U(1)_EM, giving mass to the W, Z, and all charged fermions.

The matter content consists of three generations of quarks and leptons. Each generation contains an up-type quark, a down-type quark, a charged lepton, and a neutrino: (u, d, e, nu_e), (c, s, mu, nu_mu), (t, b, tau, nu_tau). Left-handed fermions form SU(2)_L doublets; right-handed fermions are singlets. Quarks carry color charge (SU(3) triplets); leptons do not (SU(3) singlets). The three generations are identical in their gauge quantum numbers but differ in their Yukawa couplings (and hence masses) -- why three generations exist, and why their masses span five orders of magnitude, is unexplained.

The Standard Model has 19 free parameters (in its minimal form): 3 gauge couplings (g_s, g, g'), 6 quark masses, 3 lepton masses, 3 CKM mixing angles and 1 CP-violating phase, the Higgs vacuum expectation value v, the Higgs self-coupling lambda, and the QCD vacuum angle theta. Including neutrino masses and mixing adds 7 more (3 masses, 3 angles, 1 or 2 CP phases). All are measured experimentally; the theory does not predict their values.

The experimental success of the Standard Model is extraordinary. QED predictions agree with experiment to 12 significant figures (electron g-2). Electroweak precision measurements at LEP predicted the top quark mass before its discovery. The Higgs boson, predicted by the theory, was discovered at the LHC in 2012. QCD describes jet production, scaling violations, and the running of alpha_s with percent-level accuracy. Despite this, the Standard Model is known to be incomplete: neutrino oscillations require physics beyond the minimal model, dark matter and dark energy have no Standard Model explanation, and gravity is not included. The Standard Model is best understood as an extraordinarily successful effective field theory valid up to some energy scale, beyond which new physics must appear.

Practice Questions 4 questions

Prerequisite Chain

Counting to 10Counting to 20Understanding ZeroThe Number ZeroCounting to FiveOne-to-One CorrespondenceCombining Small Groups Within 5Addition Within 10Addition Within 20Two-Digit Addition Without RegroupingTwo-Digit Addition with RegroupingAddition Within 100Repeated Addition as MultiplicationMultiplication Facts Within 100Division as Equal SharingDivision as Grouping (Measurement Division)Division: Grouping (Repeated Subtraction) ModelDivision: Fair Sharing ModelDivision as Equal SharingDivision as GroupingBasic Division FactsDivision Facts Within 100Two-Digit by One-Digit DivisionDivision with RemaindersRemainders and Quotients in DivisionDivision Word ProblemsIntroduction to Long DivisionFactors and MultiplesPrime and Composite NumbersEquivalent FractionsRelating Fractions and DecimalsDecimal Place ValueReading and Writing DecimalsComparing and Ordering DecimalsAdding and Subtracting DecimalsMultiplying DecimalsDividing DecimalsDividing FractionsMixed Number ArithmeticOrder of OperationsInteger Order of OperationsVariable ExpressionsCombining Like TermsOne-Step EquationsTwo-Step EquationsSolving Multi-Step EquationsEquations with Variables on Both SidesAngle Pairs: Complementary, Supplementary, and VerticalParallel Lines and TransversalsCorresponding AnglesAlternate Interior AnglesTriangle Angle Sum TheoremExterior Angle TheoremTriangle Inequality TheoremSimilar Triangles: AA SimilaritySimilar Triangles: SSS and SAS SimilarityProportions in Similar TrianglesRight Triangle Trigonometry IntroductionTrigonometric Ratios ReviewRadian MeasureConverting Between Degrees and RadiansThe Unit CircleGraphing Sine and CosineGraphing Tangent and Reciprocal Trigonometric FunctionsDerivatives of Trigonometric FunctionsAntiderivativesIterated Integrals and Fubini's TheoremDouble Integrals in Cartesian CoordinatesDouble Integrals over Rectangular RegionsDouble Integrals in Polar CoordinatesDouble Integrals: Definition and SetupIterated Integrals and Fubini's TheoremDouble Integrals over Rectangular RegionsDouble Integrals over General RegionsApplications of Double Integrals: Area, Mass, and MomentsTriple Integrals in Cartesian CoordinatesTriple Integrals in Cylindrical and Spherical CoordinatesChange of Variables and the Jacobian DeterminantApplications of Triple Integrals: Volume and MassVector Fields and Their RepresentationsLine Integrals of Vector FieldsGreen's TheoremSurface Integrals and Flux of Vector FieldsSurface Integrals and Flux of Vector FieldsDivergence Theorem: Flux and OutflowDivergence TheoremElectric FluxGauss's LawConductors in Electrostatic EquilibriumCapacitance and CapacitorsDielectricsDielectric Constant and Relative PermittivityElectric Field Inside Dielectric MaterialsDielectric Materials and PolarizationDielectric Susceptibility and PermittivityEnergy Density in Electric FieldsElectric Current and Current DensityElectrical Resistance and ResistivityOhm's Law and Circuit ElementsElectromotive Force (EMF) and BatteriesKirchhoff's Circuit Laws: Voltage and CurrentDC Circuit Network Analysis MethodsTransient Response in RC CircuitsRC CircuitsLC and RLC CircuitsAC Circuits: FundamentalsImpedance and ReactanceAC Power and ResonanceElectromagnetic WavesThe Electromagnetic SpectrumBlackbody Radiation and Planck's LawPhotoelectric EffectThe Photon: Light as QuantaCompton ScatteringWave-Particle Dualityde Broglie WavelengthHeisenberg Uncertainty PrincipleWavefunction and the Born RuleThe Schrödinger EquationState Vectors and WavefunctionsQuantum SuperpositionQuantum EntanglementBell Theorem and Bell InequalitiesPostulates of Quantum MechanicsScattering TheoryIntroduction to Scattering TheoryPartial Wave Analysis in ScatteringSpin Angular MomentumElectron Spin and Intrinsic Magnetic MomentStern-Gerlach Experiment: Spin Quantization and MeasurementElectron Diffraction and Matter Wave PropertiesDavisson-Germer Experiment: Crystal Diffraction of ElectronsElectron Diffraction and Matter Wave InterferenceWavefunctions and Probability Density InterpretationQuantum Superposition and Linear Combinations of StatesQuantum Operators and ObservablesCanonical Commutation Relations and UncertaintyThe Quantum Harmonic OscillatorLadder Operators for the Harmonic OscillatorCreation and Annihilation OperatorsKlein-Gordon Field (Canonical Quantization)Propagators and Green's FunctionsWick's TheoremFeynman Diagrams (Systematic Rules)QED Vertex and Basic ProcessesLoop Diagrams and DivergencesRegularization (Dimensional, Cutoff)Renormalization of QEDNon-Abelian Gauge Theories (Yang-Mills)Quantum Chromodynamics (QCD) BasicsStandard Model Overview

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