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Standard Model Overview

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1,264prerequisites beneath it

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Electroweak Unification Higgs Mechanism +1 more→→Beyond Standard Model (BSM) Overview Collider Physics Methods +9 more

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

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → One-to-One Correspondence → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Making 10 as an Addition Strategy → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Dividing Integers → Unit Rates → Proportions → Percent Concept → Converting Between Fractions, Decimals, and Percents → Operations with Rational Numbers → Two-Step Equations → Solving Multi-Step Equations → Equations with Variables on Both Sides → Angle Pairs: Complementary, Supplementary, and Vertical → Parallel Lines and Transversals → Corresponding Angles → Alternate Interior Angles → Triangle Angle Sum Theorem → Exterior Angle Theorem → Triangle Inequality Theorem → Similar Triangles: AA Similarity → Similar Triangles: SSS and SAS Similarity → Proportions in Similar Triangles → Right Triangle Trigonometry Introduction → Sine, Cosine, and Tangent Ratios → Trigonometric Ratios Review → Radian Measure → Converting Between Degrees and Radians → The Unit Circle → Graphing Sine and Cosine → Graphing Tangent and Reciprocal Trigonometric Functions → Derivatives of Trigonometric Functions → Antiderivatives → Iterated Integrals and Fubini's Theorem → Double Integrals in Cartesian Coordinates → Double Integrals in Polar Coordinates → Double Integrals in Polar Coordinates → Double Integrals: Definition and Setup → Iterated Integrals and Fubini's Theorem → Double Integrals over Rectangular Regions → Double Integrals over General Regions → Applications of Double Integrals: Area, Mass, and Moments → Triple Integrals in Cartesian Coordinates → Triple Integrals in Cylindrical and Spherical Coordinates → Change of Variables and the Jacobian Determinant → Applications of Triple Integrals: Volume and Mass → Vector Fields and Their Representations → Line Integrals of Vector Fields → Work and Circulation → Line Integrals of Scalar and Vector Functions → Fundamental Theorem for Line Integrals → Conservative Vector Fields → Conservative Vector Fields and Potential Functions → Curl and Divergence of Vector Fields → Curl and Divergence → Divergence Theorem → Electric Flux and Divergence Theorem → Gauss's Law: Integral Form and Meaning → Solving Problems with Gauss's Law → Conductors in Electrostatic Equilibrium → Capacitance and Capacitors → Dielectrics → Dielectric Constant and Relative Permittivity → Electric Field Inside Dielectric Materials → Dielectric Materials and Polarization → Dielectric Susceptibility and Permittivity → Energy Density in Electric Fields → Electric Current and Current Density → Electrical Resistance and Resistivity → Ohm's Law and Circuit Elements → Electromotive Force (EMF) and Batteries → Kirchhoff's Circuit Laws: Voltage and Current → DC Circuit Network Analysis Methods → Transient Response in RC Circuits → RC Circuits → LC and RLC Circuits → AC Circuits: Fundamentals → Impedance and Reactance → AC Power and Resonance → Electromagnetic Waves → Postulates of Special Relativity → Time Dilation → Length Contraction → Lorentz Transformation → Relativistic Velocity Addition → Relativistic Momentum and Energy → Mass-Energy Equivalence and E=mc² → Photons as Particles with Energy and Momentum → Planck-Einstein Relation: Energy and Frequency → Photoelectric Effect → The Photon: Light as Quanta → Compton Scattering → Wave-Particle Duality → de Broglie Wavelength → The Schrödinger Equation → State Vectors and Wavefunctions → Quantum Superposition → The Measurement Problem → Interpretations of Quantum Mechanics → Postulates of Quantum Mechanics → Observables and Quantum Operators → Commutators and Commutation Relations → Quantum Angular Momentum → Quantum Mechanical Treatment of Hydrogen → Solving the Schrödinger Equation for Hydrogen Atom → Quantum Numbers → Electron Configuration → Periodic Trends → Covalent Bonding → Electronegativity and Bond Polarity → Ionic Bonding → Lewis Structures → VSEPR Theory and Molecular Geometry → Molecular Geometry and Electron Pair Geometry → Molecular Polarity and Dipole Moments → Intermolecular Forces → States of Matter and Phase Changes: Melting, Boiling, and Sublimation → Gas Laws and the Ideal Gas Equation → Gas Stoichiometry and Volume-Volume Calculations → Thermochemistry and Enthalpy → Heat Capacity and Calorimetry → Entropy and Molecular Disorder → Spontaneity and ΔG → Entropy and Gibbs Free Energy → Chemical Equilibrium → Statistical Mechanics: Ensembles and the Boltzmann Distribution → Partition Function: Definition and Properties → Helmholtz Free Energy → Gibbs Free Energy → Phase Transitions: First Order and Second Order → Critical Phenomena and Critical Exponents → Landau Theory of Phase Transitions → Symmetry Breaking and Phase Transitions → Goldstone's Theorem and Gapless Modes → Goldstone Theorem → Higgs Mechanism → Electroweak Unification → Standard Model Overview

Longest path: 186 steps · 1264 total prerequisite topics

Prerequisites (3)

Electroweak Unificationhard Quantum Chromodynamics (QCD) Basicshard Higgs Mechanismhard

Leads To (11)

Beyond Standard Model (BSM) Overviewhard Collider Physics Methodssoft Dark Matter Candidateshard Effective Field Theory in Particle Physicshard Electroweak Precision Measurementshard Extra Dimensionshard Grand Unification (GUTs)hard Higgs Boson Discovery and Propertieshard Lepton Flavorhard Neutrino Masses and Oscillationshard Supersymmetry Basicshard