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Particle Physics

Introduction

Particle physics studies the smallest known constituents of matter and the interactions through which they transform. At university level, the subject is not a catalogue of particles but a meeting point of special relativity, quantum mechanics, quantum field theory, symmetry, statistics, accelerator technology, and data analysis. You learn how experimental signatures are connected to theoretical models and how claims about new physics are tested quantitatively.

The modern framework is the Standard Model, a relativistic quantum field theory based on the gauge symmetry $S U (3)_{C} \times S U (2)_{L} \times U (1)_{Y}$ . It describes quarks, leptons, the electromagnetic, weak, and strong interactions, and the Higgs sector. Gravity is not part of the Standard Model, and several observations—including neutrino masses, the cosmological dark-matter problem, and the matter-antimatter asymmetry—motivate research beyond it.

The diagram above is a compact map of Standard Model particles. Treat it as a starting point rather than an endpoint: each entry represents a quantum field, each particle has measurable quantum numbers, and interactions follow from symmetries and coupling terms in the theory.

CERN's overview of the rise of the Standard Model provides useful historical context. While watching, identify which discoveries changed the particle classification scheme and which measurements tested previously predicted particles.

Learning Goals

After completing this aiMOOC, you should be able to explain the particle content and gauge structure of the Standard Model, apply conservation laws and quantum numbers to reactions, interpret simple Feynman diagrams, connect amplitudes with measurable rates, describe how accelerators and detectors produce particle-physics data, reason about decays and scattering using relativistic kinematics, explain the role of the Higgs field, describe neutrino oscillations, evaluate statistical evidence, and identify well-motivated limitations of the Standard Model.

Foundations: Relativity, Quantum Fields, and Natural Units

Particle physics is naturally relativistic. For a free particle with energy $E$ , momentum $𝐩$ , and mass $m$ ,

$E^{2} = p^{2} c^{2} + m^{2} c^{4} .$

In high-energy physics it is common to choose natural units with $c = ℏ = 1$ . Energy, mass, momentum, inverse length, and inverse time can then be expressed in related units. Particle masses are frequently quoted in MeV or GeV, implicitly meaning MeV divided by $c^{2}$ or GeV divided by $c^{2}$ when conventional units are restored.

A particularly important Lorentz-invariant quantity is the invariant mass of a system,

$m_{i n v}^{2} = {(\sum_{i} E_{i})}^{2} - {| \sum_{i} 𝐩_{i} |}^{2}$

in natural units. Peaks in reconstructed invariant-mass distributions are one of the central ways unstable particles are identified experimentally.

From Particles to Fields

Quantum field theory treats a particle as an excitation of an underlying field. Fermionic matter fields obey Fermi-Dirac statistics and have half-integer spin. Bosonic fields have integer spin. Interactions arise from terms in a Lagrangian density that respect the required symmetries.

A schematic Standard Model Lagrangian can be organized as

$ℒ_{S M} = ℒ_{g a u g e} + ℒ_{f e r m i o n} + ℒ_{H i g g s} + ℒ_{Y u k a w a} .$

This expression is intentionally compact. The gauge term contains field strengths and self-interactions, the fermion term contains kinetic terms and gauge couplings, the Higgs term produces electroweak symmetry breaking, and Yukawa terms generate charged-fermion masses after the Higgs field acquires a vacuum expectation value.

Symmetry as a Design Principle

A global symmetry applies the same transformation everywhere. A local gauge symmetry allows the transformation to vary from point to point. Requiring local gauge invariance introduces gauge fields and strongly constrains allowed interactions. In the Standard Model:

Quantum chromodynamics is based on $S U (3)_{C}$ and governs the strong interaction.
The electroweak theory is based on $S U (2)_{L} \times U (1)_{Y}$ .
After electroweak symmetry breaking, the observed photon, W bosons, and Z boson emerge from the electroweak gauge fields.

Symmetry also leads to conservation laws. Electric charge, energy, momentum, and angular momentum are essential checks in reaction analysis. Other quantities, such as flavor quantum numbers, may be conserved only by particular interactions.

The Standard Model Particle Content

Quarks and Hadrons

There are six quark flavors: up, down, charm, strange, top, and bottom. Quarks carry electric charge, spin one-half, and a three-valued color charge. They participate in the strong, weak, and electromagnetic interactions. Because of color confinement, isolated quarks are not observed under ordinary conditions. Instead, quarks and gluons form color-neutral hadrons such as baryons and mesons.

A proton has valence content $u u d$ , but a realistic proton is a dynamical QCD system that also contains gluons and transient quark-antiquark pairs. At high momentum transfer, scattering experiments probe this partonic structure through parton distribution functions.

Leptons

The charged leptons are the electron, muon, and tau. Each has an associated neutrino flavor. Charged leptons participate in electromagnetic and weak interactions; neutrinos participate in weak interactions and gravity, but they carry no electric charge. Neutrino oscillations demonstrate that neutrino flavor states are not identical to neutrino mass states, requiring physics beyond the minimal massless-neutrino formulation of the Standard Model.

As you watch the Fermilab explanation of neutrino oscillations, distinguish carefully between a flavor eigenstate, which is tied to weak interaction production and detection, and a mass eigenstate, which propagates with a definite mass.

Gauge Bosons and the Higgs Boson

The photon mediates electromagnetism. The W and Z bosons mediate the weak interaction. Eight gluons mediate the strong interaction and themselves carry color charge, which makes QCD non-Abelian and gives gluons self-interactions. The Higgs boson is the observable quantum excitation associated with the Higgs field.

The Higgs field has a nonzero vacuum expectation value of about 246 GeV. Electroweak symmetry breaking gives masses to the W and Z bosons while leaving the photon massless. Yukawa interactions with the Higgs field generate masses for charged leptons and quarks. The Standard Model does not predict the numerical values of those Yukawa couplings; they are measured parameters.

The Fermilab video gives historical and conceptual context for identifying the Higgs-like particle found in 2012. Modern precision studies go beyond discovery and test whether its spin, parity, production rates, and couplings match Standard Model expectations.

Fundamental Interactions

Electromagnetism and Quantum Electrodynamics

Quantum electrodynamics describes interactions of electrically charged particles and photons. At leading order, a Feynman diagram can represent processes such as electron-positron annihilation followed by production of another charged particle pair.

For the reaction $e^{+} e^{-} \to μ^{+} μ^{-}$ , energy-momentum conservation constrains the final state, while the quantum amplitude encodes the interaction dynamics. A Feynman diagram is not a literal space-time photograph; it is a bookkeeping representation of terms contributing to a perturbative amplitude.

Weak Interaction

The weak interaction changes particle flavor and violates parity maximally in charged-current processes. W bosons carry electric charge and mediate charged-current reactions; the Z boson mediates neutral-current weak interactions.

Beta decay can be described at the quark level as a down quark transforming into an up quark through emission of a virtual W boson, followed by the W producing an electron and an electron antineutrino.

The weak interaction is central to nuclear beta decay, neutrino scattering, stellar fusion chains, and flavor-changing particle decays. Flavor mixing among quarks is described by the CKM matrix, while lepton mixing is described by the PMNS matrix.

Strong Interaction and QCD

Quantum chromodynamics describes quarks and gluons. Its non-Abelian gauge symmetry has two especially important consequences:

Asymptotic freedom: the effective strong coupling becomes weaker at very high momentum transfer, allowing perturbative calculations for sufficiently hard processes.
Confinement: at long distances, colored objects are not observed as isolated particles; quarks and gluons hadronize into color-neutral states.

Jets in collider detectors are experimental signatures of energetic quarks or gluons after parton showering and hadronization. A jet is not a single fundamental particle; it is a collimated collection of particles reconstructed by an algorithm.

Feynman Diagrams, Amplitudes, and Observables

A Feynman diagram represents one term in a perturbative expansion of a transition amplitude. External lines correspond to incoming or outgoing states, internal lines correspond to propagators, and vertices correspond to interaction terms. The physically measurable quantity is not the diagram itself but an observable derived from the total amplitude.

If several diagrams contribute to the same initial and final states, their amplitudes must be added before squaring:

$ℳ_{t o t a l} = \sum_{i} ℳ_{i},$

and probabilities depend on $| ℳ_{t o t a l} |^{2}$ . This produces interference, a defining quantum effect.

Cross Sections

A scattering cross section measures the effective probability for a process. Experimentally, the expected number of events is approximately

$N = σ ℒ_{i n t} ϵ,$

where $σ$ is the production cross section, $ℒ_{i n t}$ is integrated luminosity, and $ϵ$ represents detector acceptance and selection efficiency. Real analyses also include branching fractions, backgrounds, systematic uncertainties, and correlations.

Decay Widths and Lifetimes

An unstable particle has a decay width $Γ$ related to its mean lifetime $τ$ by

$τ = \frac{ℏ}{Γ} .$

A larger width generally corresponds to a shorter lifetime. Branching fractions specify the probability for decay through particular channels, and their sum over all possible modes is one.

Accelerators: Creating High-Energy Collisions

Particle accelerators use electric fields to increase particle energy and magnetic fields to steer and focus charged beams. Colliders bring beams into interaction regions so that a large fraction of the center-of-mass energy can be available to create new states.

The Large Hadron Collider uses a chain of pre-accelerators before injecting beams into its roughly 27 km ring. In proton-proton collisions, the hard interaction occurs between partons inside the protons, so the partonic center-of-mass energy varies event by event.

While watching this accelerator overview, identify the separate roles of radio-frequency acceleration, bending magnets, focusing magnets, vacuum systems, and collision points.

Luminosity and Event Yield

Instantaneous luminosity describes collision intensity per unit area and time. Integrated luminosity accumulates this exposure over a data-taking period. Increasing luminosity can raise the number of rare events, but it also increases overlapping proton-proton interactions known as pileup, creating additional reconstruction challenges.

Collider design therefore involves trade-offs among energy, intensity, beam stability, detector occupancy, radiation tolerance, and computing capacity.

Detectors: Turning Collisions into Data

Modern collider detectors are layered instruments designed to reconstruct different particle properties.

Typical subsystems include:

Tracking detectors that measure trajectories of charged particles in a magnetic field and help reconstruct momenta and decay vertices.
Electromagnetic calorimeters that measure energy deposited mainly by electrons and photons.
Hadronic calorimeters that measure energy associated with hadrons and jets.
Muon systems that identify penetrating muons outside much of the calorimetry.
Trigger and data-acquisition systems that select potentially interesting events from very high collision rates.

Neutral weakly interacting particles such as neutrinos usually escape collider detectors without direct detection. Their presence can be inferred from an imbalance in transverse momentum when the event is otherwise well reconstructed.

Large General-Purpose Detectors

ATLAS and CMS are large general-purpose detectors at the LHC. Their engineering differs, but both combine precision tracking, calorimetry, muon detection, powerful magnets, fast triggers, and distributed computing to reconstruct collision events.

Event displays are visual representations of reconstructed detector information. They are useful for intuition but are not substitutes for statistical analyses of large data sets.

From Raw Signals to Physics Objects

Detector electronics convert energy deposits and induced charge into digitized signals. Reconstruction software transforms these signals into tracks, clusters, vertices, jets, electrons, photons, muons, and missing transverse momentum. Calibration aligns detector response with known physical standards. Simulation models particle interactions and detector response, but it must be validated against data.

A high-quality analysis distinguishes among detector effects, reconstruction choices, theoretical modeling, statistical fluctuations, and genuine physical differences between hypotheses.

Particle Identification in Tracks and Event Topology

Before electronic detectors, cloud chambers and bubble chambers made ionizing tracks directly visible. They remain excellent teaching tools because track curvature, length, ionization density, and decay topology make abstract particle behavior tangible.

In a magnetic field, the curvature of a charged track depends on charge sign and momentum. In collider experiments, modern silicon trackers perform this measurement with far greater precision and at far higher event rates than historical visual detectors.

The Higgs Mechanism and Electroweak Symmetry Breaking

The electroweak theory begins with a gauge symmetry in which the underlying gauge fields do not simply correspond to the observed photon, W, and Z particles. The Higgs field develops a nonzero vacuum expectation value. After symmetry breaking, combinations of electroweak gauge fields become the photon and the massive W and Z bosons.

In a simplified form, the Higgs potential can be written

$V (Φ) = - μ^{2} Φ^{†} Φ + λ (Φ^{†} Φ)^{2} .$

Its minimum occurs away from zero field magnitude when the parameters take the symmetry-breaking form. Expanding around the vacuum produces a physical scalar excitation: the Higgs boson.

What the Higgs Does and Does Not Explain

The Higgs mechanism explains how the Standard Model can contain massive W and Z bosons while preserving the underlying gauge consistency of the theory. Yukawa couplings relate the Higgs field to charged-fermion masses. However, the Standard Model does not explain why the Yukawa couplings have their observed hierarchical values, and the minimal formulation does not account for neutrino masses.

The 2012 observation of a new boson near 125 GeV by ATLAS and CMS was established through multiple decay channels. Precision measurements continue to test whether its properties agree with Standard Model predictions.

Neutrino Physics

Neutrinos are produced and detected in flavor states associated with electrons, muons, or tau leptons. During propagation, different mass eigenstate components accumulate different quantum phases. Because flavor states are mixtures of mass eigenstates, the probability of detecting a particular flavor changes with distance and energy.

For a simplified two-flavor system,

$P (ν_{α} \to ν_{β}) = \sin^{2} (2 θ) \sin^{2} (\frac{Δ m^{2} L}{4 E}) .$

This formula highlights the dependence on mixing angle $θ$ , mass-squared difference $Δ m^{2}$ , baseline $L$ , and neutrino energy $E$ . Full three-flavor oscillations use the PMNS matrix and include additional phases and matter effects when relevant.

Neutrino oscillation experiments therefore provide evidence that at least two neutrino mass eigenstates have nonzero mass differences. Oscillation data measure mass-squared differences rather than the absolute mass scale.

Antimatter and Discrete Symmetries

For each charged matter particle, quantum field theory includes a corresponding antiparticle with opposite additive quantum numbers such as electric charge. Particle-antiparticle pairs can be created when sufficient energy is available and can annihilate into allowed final states.

Three important discrete transformations are charge conjugation C, parity P, and time reversal T. The weak interaction violates C and P strongly. CP symmetry is also violated in certain weak decays. By the CPT theorem, local Lorentz-invariant quantum field theories with standard assumptions are invariant under the combined CPT transformation.

CP violation in the Standard Model is real but appears insufficient by itself to explain the observed cosmological dominance of matter over antimatter, making baryogenesis an important topic in physics beyond the Standard Model.

Statistical Reasoning in Particle Physics

Particle-physics discoveries are statistical statements made in the presence of backgrounds, finite samples, detector effects, and systematic uncertainties. You should distinguish:

a test statistic, which summarizes how data compare with hypotheses;
a p-value, which quantifies the probability of data at least as incompatible with a hypothesis under specified assumptions;
a confidence interval, which is constructed to have a stated long-run coverage under a chosen procedure;
a systematic uncertainty, which represents uncertainty in modeling, calibration, efficiencies, theoretical inputs, or other non-statistical effects.

A local excess in a distribution may occur by chance when many regions or channels are searched. The look-elsewhere effect accounts for this multiple-testing context. Reproducibility, independent channels, control regions, blind analysis strategies, and open data all strengthen the reliability of conclusions.

Significance Is Not the Same as Importance

A highly statistically significant effect may be physically small, while an important hypothesis may remain weakly constrained because the relevant process is rare or difficult to observe. Good scientific interpretation combines significance, effect size, uncertainty, robustness, and theoretical context.

Beyond the Standard Model

The Standard Model is extraordinarily successful, but it is not a complete theory of nature. Important open questions include:

How should gravity be reconciled with quantum field theory?
What particle or field constitutes cosmological dark matter, if dark matter is particulate?
What mechanism produced the observed matter-antimatter asymmetry?
What generates neutrino masses and their mixing pattern?
Why do fermion masses and mixing angles span such different scales?
Is the Higgs sector elementary and minimal, or part of a richer structure?

Proposed frameworks include supersymmetry, extra dimensions, axions, dark-sector particles, sterile neutrinos, leptoquarks, compositeness, grand unification, and various approaches to quantum gravity. These ideas differ greatly in motivation and evidence. A responsible analysis separates a mathematically possible model from an experimentally supported conclusion.

How New Physics Is Searched For

There are several complementary strategies:

Energy frontier: collide particles at the highest achievable energies to produce heavy new states directly.
Intensity frontier: study extremely rare processes or tiny symmetry violations with very large data sets.
Precision frontier: measure known processes so accurately that small deviations from Standard Model predictions become visible.
Cosmic frontier: use astrophysical and cosmological observations to probe particles and interactions not easily accessible in laboratories.

Null results also carry information: they exclude regions of parameter space and force models to become more precise.

A Worked Reasoning Example: Reconstructing a Resonance

Suppose a detector records events containing two oppositely charged muons. You want to test whether some events come from the decay of a short-lived neutral particle.

Reconstruct each muon's momentum from its track curvature and detector measurements.
Combine the four-momenta to calculate the dimuon invariant mass.
Plot the invariant-mass distribution for many selected events.
Model known backgrounds using simulation, control regions, or data-driven methods.
Search for a localized excess consistent with detector mass resolution.
Estimate the signal yield, background uncertainty, and statistical significance.
Compare the observed rate and kinematic distributions with theoretical predictions.
Test the result in independent categories or data samples.

The key conceptual move is that the unstable parent particle may never leave a direct detector track. Its existence is inferred from correlated properties of its decay products.

Interactive Tasks

Quiz: Test Your Knowledge

Which fundamental interaction is not included in the Standard Model? (Gravity) (!Electromagnetism) (!Strong interaction) (!Weak interaction)

Which particle mediates the strong interaction? (Gluon) (!Photon) (!Electron) (!Neutrino)

Why are isolated quarks not normally observed? (Color confinement) (!Electric neutrality) (!Neutrino mixing) (!Higgs decay)

Which quantity is Lorentz invariant and useful for reconstructing a resonance? (Invariant mass) (!Laboratory speed) (!Beam direction) (!Track color)

Which symmetry structure underlies the Standard Model gauge interactions? (SU3 times SU2 times U1) (!SO3 times U1) (!SU5 only) (!U1 only)

Which pair of quantities primarily determines an expected collider event count before efficiencies? (Cross section and luminosity) (!Spin and parity) (!Mass and charge) (!Lifetime and rapidity)

What is a central role of the Higgs field in the electroweak theory? (Electroweak symmetry breaking) (!Color confinement) (!Photon decay) (!Gravity quantization)

What do neutrino oscillations demonstrate? (Flavor states mix different mass states) (!Neutrinos carry color charge) (!Photons have mass) (!Quarks are elementary leptons)

How is a larger decay width generally related to lifetime? (It corresponds to a shorter lifetime) (!It corresponds to a longer lifetime) (!It makes the particle stable) (!It removes all decay channels)

What is a primary function of a calorimeter in a collider detector? (Measuring deposited particle energy) (!Producing accelerator beams) (!Generating neutrino flavors) (!Defining gauge symmetry)

Memory Game

Cross section	Effective measure of the probability for a scattering process
Luminosity	Measure of collision exposure used to predict event yields
Hadronization	Formation of color neutral hadrons from energetic quarks and gluons
Rapidity	Kinematic variable useful for relativistic motion along a beam direction
Vertex	Reconstructed point where particles are produced or decay
Gauge boson	Force carrying field quantum associated with a gauge interaction
Yukawa coupling	Interaction strength connecting a fermion to the Higgs field
Missing transverse momentum	Momentum imbalance used to infer invisible particles

Drag and Drop

Match the correct terms.	Topic
Photon	Electromagnetic interaction
Gluon	Strong interaction
W boson	Charged weak interaction
Silicon tracker	Charged particle trajectories
Calorimeter	Deposited particle energy

...

Crossword Puzzle

Fermion	What type of particle has half integer spin and obeys Fermi Dirac statistics?
Gluon	Which boson carries the strong interaction?
Neutrino	Which electrically neutral lepton undergoes flavor oscillations?
Collider	What machine brings energetic particle beams into collision?
Hadron	What color neutral composite state is built from quarks and gluons?
Symmetry	What organizing principle strongly constrains allowed interactions in field theory?

LearningApps

Cloze Text

The Standard Model is a relativistic

of known elementary particles and three fundamental interactions. Quarks carry a type of charge called

that is associated with the strong interaction. The mediator of electromagnetism is the

. The weak charged current is mediated by the

. A resonance can often be reconstructed as a peak in an

distribution. Collider event yields depend on production cross section and integrated

. Neutrino oscillations show that flavor states are mixtures of

. The Higgs field is central to electroweak

.

Open-Ended Tasks

Easy

Particle classification map: Create a one-page concept map that connects quarks, leptons, gauge bosons, the Higgs boson, interactions, charges, and spin; annotate at least three connections with short explanations.
Feynman diagram commentary: Choose one simple reaction from this course, redraw its Feynman diagram, and record a two-minute explanation of what the external lines, internal line, and vertices represent.
Detector media analysis: Use one detector image from this course to produce an annotated image identifying tracking, calorimetry, and muon-detection regions and explain what each subsystem measures.
Particle physics interview: Interview a physics student, teacher, researcher, engineer, or data scientist about how evidence is established in particle physics and summarize the interview in 400 to 600 words.

Standard

Invariant mass investigation: Build or obtain a small synthetic two-particle data set, calculate invariant masses, plot the distribution, and explain how a resonance signal would differ from a smooth background.
Cloud chamber observation: Visit a science museum, teaching laboratory, or supervised university demonstration with a cloud chamber, or use a live or recorded open demonstration, then classify visible track types and discuss what can and cannot be inferred from them.
Higgs evidence video: Produce a four-minute educational video explaining why discovery of the Higgs boson required multiple decay channels, background estimates, detector calibration, and statistical analysis rather than one striking event display.
CERN Open Data exploration: Use a beginner-friendly data sample from the CERN Open Data Portal to formulate a measurable question, document your selection criteria, and present one physics plot with a short interpretation.

Advanced

Monte Carlo event study: Design a toy Monte Carlo simulation for a resonance plus background, vary signal strength and detector resolution, and analyze how these changes affect the ability to identify a peak.
Neutrino oscillation model: Implement the two-flavor oscillation probability as a function of baseline and energy, investigate at least three parameter choices, and explain the physical meaning of the resulting oscillation patterns.
Systematic uncertainty audit: Choose a published particle-physics measurement and create an uncertainty budget that distinguishes statistical, detector, modeling, calibration, and theoretical uncertainties; evaluate which uncertainty most limits the result.
Beyond Standard Model research proposal: Write a 1,500-word mini-proposal for testing one motivated extension of the Standard Model, specifying the signal, likely backgrounds, experimental observable, statistical strategy, and what a null result would constrain.

Learning Assessment

Reaction consistency assessment: Given several proposed particle reactions, use charge, lepton number, baryon number, energy-momentum, and interaction type to decide which are allowed or forbidden at leading order and justify each decision.
Collider analysis assessment: Starting from a hypothetical excess in a mass spectrum, design a sequence of checks that separates detector artifacts, background mismodeling, statistical fluctuation, and a possible new resonance.
Detector reasoning assessment: For electron, photon, muon, charged pion, and neutrino signatures, predict which detector layers respond and explain how combined subsystem information supports identification.
Symmetry and interaction assessment: Explain how local gauge symmetry constrains interactions in the Standard Model and compare the physical consequences of Abelian electromagnetic gauge structure with non Abelian QCD.
Neutrino transfer assessment: Use the oscillation formula to reason qualitatively how changing energy or baseline shifts an appearance probability and connect the result to experimental design.
Higgs interpretation assessment: Evaluate the claim that the Higgs boson explains all mass in the universe, identifying what the Higgs mechanism actually provides in the Standard Model and what major forms of mass require additional explanation.

Evidence of Learning

Strong evidence of learning includes four connected dimensions. Knowledge is shown when you can accurately describe Standard Model fields, quantum numbers, symmetries, kinematics, decay, scattering, and detector principles. Skills are shown when you can calculate invariant quantities, read Feynman diagrams, estimate event yields, analyze uncertainty, interpret plots, and distinguish observation from model-dependent inference. Products may include reproducible code, annotated detector diagrams, analysis notebooks, concept maps, research videos, data visualizations, and concise scientific reports. Transfer is demonstrated when you can apply these tools to an unfamiliar reaction, detector signature, or beyond-Standard-Model hypothesis and defend your reasoning with conservation laws, statistical evidence, and clearly stated assumptions.

OERs on the Topic

The following resources can support deeper study and independent projects:

CERN Physics: Introductions to particle physics, accelerators, experiments, and open scientific context from CERN.
CERN Open Data Portal: Public research data, software, documentation, and educational data samples from CERN experiments.
Particle Data Group: Authoritative reviews, tables, and particle-property summaries used throughout high-energy physics.
The Particle Adventure: An accessible introduction to fundamental particles and interactions.

Linked Learning Areas

Particle Physics

Particle physics links naturally with mathematics through group theory, linear algebra, differential equations, probability, and statistics; with computer science through simulation, distributed computing, machine learning, and reproducible analysis; with engineering through superconducting magnets, cryogenics, electronics, vacuum technology, and detector design; and with astronomy and cosmology through dark matter, neutrinos, cosmic rays, and the early universe.