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Physics › Particle Physics

Supersymmetry Basics

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supersymmetry susy sparticles naturalness

Core Idea

Supersymmetry (SUSY) is a symmetry relating bosons and fermions: every Standard Model particle has a superpartner with spin differing by 1/2. SUSY solves the hierarchy problem by cancelling the quadratic divergences in the Higgs mass, provides a dark matter candidate (the lightest supersymmetric particle), and enables gauge coupling unification. The minimal supersymmetric Standard Model (MSSM) doubles the particle content and introduces over 100 new parameters, making it a rich but complex framework.

Explainer

Supersymmetry is the unique extension of the Poincare spacetime symmetry that relates particles of different spin. In a SUSY theory, every boson has a fermionic partner and vice versa: the electron (spin 1/2) has a scalar selectron (spin 0), the photon (spin 1) has a fermionic photino (spin 1/2), and the Higgs boson (spin 0) has a fermionic higgsino (spin 1/2). This doubling of the particle spectrum is the price of the symmetry, but the payoff is substantial: the quadratic divergences in the Higgs mass cancel exactly if SUSY is unbroken.

The MSSM (Minimal Supersymmetric Standard Model) is the simplest phenomenologically viable SUSY model. It contains superpartners for all SM particles: squarks and sleptons (spin-0 partners of quarks and leptons), gluinos (spin-1/2 partner of the gluon), charginos and neutralinos (spin-1/2 mixtures of wino, bino, and higgsino states), and two Higgs doublets (required by the structure of SUSY and holomorphy of the superpotential), giving five physical Higgs bosons (h, H, A, H+, H-). The 105 new parameters are the soft SUSY-breaking masses, mixing angles, and phases.

A key feature of the MSSM is R-parity, a discrete symmetry under which SM particles have R = +1 and superpartners have R = -1. If R-parity is conserved, superpartners are always produced in pairs and the lightest superpartner (LSP) is stable. A neutral LSP (typically the lightest neutralino) is an excellent dark matter candidate. R-parity also implies that SUSY events at the LHC always contain two LSPs escaping the detector, producing the characteristic missing transverse energy signature. SUSY searches at the LHC typically look for jets and/or leptons plus large missing energy.

The experimental status of SUSY is that no superpartners have been found. LHC searches have excluded gluinos below ~2.3 TeV and first/second generation squarks below ~1.8 TeV in simplified models. Light stops (below ~1.2 TeV in most scenarios) are excluded except in compressed spectra where the stop-LSP mass difference is small. These limits have pushed the MSSM into regions of parameter space where the hierarchy problem solution requires some fine-tuning (~1% level or worse), leading to debate about whether naturalness remains a reliable guide. SUSY remains theoretically attractive for its other virtues -- gauge coupling unification, dark matter, and its role in string theory -- and the search continues at the LHC, the HL-LHC, and future colliders.

Practice Questions 3 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 → Collider Physics Methods → Cross Section Measurements → Higgs Boson Discovery and Properties → Beyond Standard Model (BSM) Overview → Supersymmetry Basics

Longest path: 191 steps · 1271 total prerequisite topics

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Beyond Standard Model (BSM) Overviewhard Standard Model Overviewhard

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