03Elementary Particle Physics
Survey the Standard Model: quarks, leptons, gauge bosons, the four fundamental forces, conservation laws, and the role of particle accelerators.
Particle physics probes the deepest structure of matter. The Standard Model is one of the most successful theories in all of science.
What are the fundamental building blocks of all matter, and what forces hold them together?
The Standard Model of particle physics is our best description of the elementary particles that make up all matter and the forces through which they interact. It classifies particles into two broad families — fermions (matter particles, half-integer spin) and bosons(force carriers, integer spin) — and identifies four fundamental forces: gravitational, electromagnetic, weak nuclear, and strong nuclear. In this lesson you will learn the names, charges, and roles of quarks, leptons, and gauge bosons; how protons and neutrons are built from quarks; how conservation laws constrain every particle reaction; and how particle accelerators and cosmic rays allow physicists to probe this sub-atomic world.
Standard Model — Particle Families
Quarks (6 flavors)
Up (u) — charge +2/3 e
Down (d) — charge −1/3 e
Charm (c) — charge +2/3 e
Strange (s) — charge −1/3 e
Top (t) — charge +2/3 e
Bottom (b) — charge −1/3 e
Baryon number B = 1/3 each
Leptons (6 particles)
Electron (e⁻) — −1 e
Muon (μ⁻) — −1 e
Tau (τ⁻) — −1 e
ν_e — 0
ν_μ — 0
ν_τ — 0
Lepton number L = +1 each
Gauge Bosons (force carriers)
Photon (γ) — EM force
W⁺, W⁻, Z⁰ — Weak force
Gluons (g) — Strong force (8 types)
Graviton* — Gravity (theoretical)
Spin-1 (graviton spin-2)
Higgs Boson
Symbol: H⁰
Charge: 0
Spin: 0
Mass: ≈ 125 GeV/c²
Discovered: 2012 (LHC)
Gives particles mass via the Higgs field
The Four Fundamental Forces
| Force | Carrier Boson | Range | Relative Strength | Acts On |
|---|---|---|---|---|
| Strong Nuclear | Gluon (g) | ~10⁻¹⁵ m (nuclear) | 1 (reference) | Quarks, hadrons |
| Electromagnetic | Photon (γ) | Infinite (1/r²) | ~10⁻² | Charged particles |
| Weak Nuclear | W⁺, W⁻, Z⁰ | ~10⁻¹⁸ m (sub-nuclear) | ~10⁻⁶ | All fermions |
| Gravitational | Graviton* (theoretical) | Infinite (1/r²) | ~10⁻³⁸ | All particles with mass/energy |
* Graviton has not yet been detected experimentally.
Key Equations & Quantities
E = mc²
Mass–energy equivalence (Einstein)
E_annihilation = 2m_e c² = 1.022 MeV
Energy from e⁺e⁻ annihilation (each γ = 0.511 MeV)
ΔB = 0 (baryon number conserved)
B = +1/3 per quark, −1/3 per antiquark
ΔL = 0 (lepton number conserved)
L = +1 per lepton, −1 per antilepton
Q_u = +2/3 e | Q_d = −1/3 e
Up-type and down-type quark charges
Proton: uud | Neutron: udd
Quark composition of nucleons
Worked Examples
Verify the electric charge of the proton using its quark composition (uud).
The proton is composed of two up quarks and one down quark: uud.
Charge of each up quark: Q_u = +2/3 e
Charge of each down quark: Q_d = −1/3 e
Total charge = Q_u + Q_u + Q_d = (+2/3) + (+2/3) + (−1/3) = +3/3 = +1 e ✓
Baryon number check: B = 1/3 + 1/3 + 1/3 = 1 ✓ (proton is a baryon)
Verify the electric charge of the neutron using its quark composition (udd).
The neutron is composed of one up quark and two down quarks: udd.
Charge of up quark: Q_u = +2/3 e
Charge of each down quark: Q_d = −1/3 e
Total charge = (+2/3) + (−1/3) + (−1/3) = +2/3 − 2/3 = 0 ✓
Baryon number check: B = 1/3 + 1/3 + 1/3 = 1 ✓ (neutron is a baryon)
Calculate the total energy released when an electron and a positron annihilate: e⁻ + e⁺ → 2γ.
Rest mass of electron: m_e = 9.109 × 10⁻³¹ kg → rest-mass energy = 0.511 MeV
Rest mass of positron equals that of the electron (antimatter partner): 0.511 MeV
By conservation of energy, total energy of the two photons = 2 × 0.511 MeV = 1.022 MeV
The two photons travel in opposite directions (conservation of momentum).
Each photon carries exactly 0.511 MeV of energy.
Is the decay p → e⁺ + π⁰ allowed? Check conservation laws.
Assign baryon numbers: proton B = 1; positron B = 0; neutral pion π⁰ B = 0.
Left side: B = 1. Right side: B = 0 + 0 = 0.
ΔB = 1 − 0 = 1 ≠ 0 → Baryon number is NOT conserved. ✗
This decay is FORBIDDEN by baryon number conservation.
This is why the proton is stable — no lighter baryon exists for it to decay into while conserving B.
Note: lepton number check — left L = 0; right L = −1 (positron is antilepton) → also violated.
Describe beta-minus decay (n → p + e⁻ + ν̄_e) at the quark level, identifying the force carrier.
Neutron quark content: udd. Proton quark content: uud.
One down quark (d) converts to an up quark (u): d → u + W⁻
The W⁻ boson is the carrier of the weak nuclear force responsible for this change.
The W⁻ then decays: W⁻ → e⁻ + ν̄_e
Full quark-level reaction: udd → uud + W⁻ → uud + e⁻ + ν̄_e
Conservation checks: Charge: 0 → +1 + (−1) + 0 = 0 ✓; Baryon number: 1 → 1 ✓; Lepton number: 0 → 0 + 1 + (−1) = 0 ✓
Guided Practice
A particle has quark composition uus. Calculate its total electric charge and determine whether it is a baryon or meson.
Hint: Use Q_u = +2/3 e and Q_s = −1/3 e (strange quark has the same charge as down). Count the number of quarks to determine the hadron type.
A pion π⁺ is a meson with quark composition ud̄ (up quark + anti-down quark). Verify its charge of +1 e.
Hint: The anti-down quark d̄ has charge opposite to d: Q_d̄ = +1/3 e. Add the charges of u and d̄.
Check whether the reaction μ⁻ → e⁻ + ν̄_e + ν_μ conserves lepton number.
Hint: Assign lepton numbers: μ⁻ has L_μ = +1; e⁻ has L_e = +1; ν̄_e has L_e = −1; ν_μ has L_μ = +1. Check each lepton flavor separately.
Identify which fundamental force is responsible for each process: (a) an electron orbiting a nucleus, (b) a neutron decaying into a proton, (c) two protons being held together in a nucleus.
Hint: Match each process to its force: EM acts on charged particles; weak force changes quark flavor; strong force binds quarks and holds nucleons together.
A particle accelerator collides two protons, each with kinetic energy 6.5 TeV (LHC conditions). Why must the total collision energy exceed 2m_p c² to create new particles?
Hint: Use E = mc² — new particles require energy equivalent to their rest mass. The threshold energy for creating a particle–antiparticle pair is 2 × (rest-mass energy of the particle).
Key Vocabulary
Quark
A fundamental fermion that carries fractional electric charge (+2/3 e or −1/3 e) and combines via the strong force to form hadrons. Quarks are never found in isolation (confinement).
Example: The proton is made of two up quarks and one down quark (uud).
Lepton
A fundamental fermion that does not participate in the strong force. Includes the electron, muon, tau, and their associated neutrinos (6 total).
Example: The electron (e⁻) is the lightest charged lepton; it orbits the nucleus and carries charge −1 e.
Hadron
A composite particle made of quarks bound together by the strong force. Hadrons are subdivided into baryons (3 quarks) and mesons (quark–antiquark pair).
Example: Protons and neutrons are baryons; pions are mesons.
Baryon
A hadron composed of three quarks (or three antiquarks for an antibaryon). Baryons have baryon number B = 1 and half-integer spin.
Example: Proton (uud, B = 1) and neutron (udd, B = 1) are the most stable baryons.
Meson
A hadron composed of one quark and one antiquark. Mesons have baryon number B = 0 and integer spin. They are unstable and decay via the weak or electromagnetic force.
Example: The pion π⁺ (ud̄) has charge +1 e and decays to μ⁺ + ν_μ.
Gauge Boson
A force-carrier particle with integer spin that mediates one of the fundamental forces. The Standard Model includes photons (EM), W/Z bosons (weak), and gluons (strong).
Example: The photon (γ) is the massless gauge boson of the electromagnetic force.
Standard Model
The theoretical framework that classifies all known elementary particles and describes three of the four fundamental forces (electromagnetic, weak, strong) using quantum field theory.
Example: The Standard Model predicted the existence of the Higgs boson before it was discovered at the LHC in 2012.
Antimatter
Matter composed of antiparticles, which have the same mass as their matter counterparts but opposite charge and quantum numbers. When matter meets antimatter, they annihilate, converting all mass to energy.
Example: The positron (e⁺) is the antiparticle of the electron. e⁻ + e⁺ → 2γ releases 1.022 MeV.
Workbook Check
Interactive Practice — 5 Questions
What is the electric charge of the proton, and which quark combination produces it?
Which gauge boson mediates the electromagnetic force?
An electron and a positron annihilate. What is the minimum total energy of the photons produced?
Which of the following is a meson?
Why is the decay p → e⁺ + π⁰ forbidden?
Independent Practice
A proton is made of two up quarks and one down quark. Verify that the total charge equals +1e. (q_up = +2/3 e, q_down = −1/3 e)
Identify the type of interaction (strong, weak, electromagnetic, or gravitational) responsible for each process: (a) beta decay of a neutron, (b) binding of quarks inside a proton, (c) electron-positron annihilation, (d) a falling apple.
A pion (π⁺) decays into a muon and a muon neutrino: π⁺ → μ⁺ + ν_μ. Verify that lepton number and charge are conserved in this decay.
In the reaction p + p → p + p + π⁰, verify conservation of baryon number, charge, and lepton number.
★ An electron and a positron annihilate at rest, producing two gamma-ray photons: e⁻ + e⁺ → 2γ. (a) Explain why two photons (not one) must be produced. (b) Calculate the energy of each photon in MeV. (c) Calculate the wavelength of each photon. (d) Verify conservation of momentum. (e) If instead the particles had kinetic energy of 0.50 MeV each, what would be the energy of each photon? (m_e = 9.11 × 10⁻³¹ kg, c = 3.0 × 10⁸ m/s)
ChallengeCommon Mistakes
Thinking protons and neutrons are fundamental particles
Protons (uud) and neutrons (udd) are composite particles made of quarks bound by the strong force (gluons). Quarks and leptons are the truly fundamental fermions
Confusing baryon number conservation with mass number conservation
Baryon number B = +1 for baryons, −1 for antibaryons, 0 for mesons and leptons. It is conserved in ALL interactions. Mass number A is only approximately conserved (binding energy effects)
Thinking antimatter annihilates only with the same type of particle (e.g., electron only with positron)
A particle annihilates with its own antiparticle: e⁻ with e⁺, p with p̄, n with n̄. The products are typically photons (γ rays) or other particle-antiparticle pairs
Assuming all four fundamental forces have the same range and strength
Strong force: strongest, range ~10⁻¹⁵ m (nuclear scale). EM: infinite range, 1/r². Weak: very short range ~10⁻¹⁸ m. Gravity: infinite range but weakest by far
Forgetting that neutrinos have lepton number +1 and antineutrinos have lepton number −1
Lepton number is conserved separately for each generation. In β⁻ decay: n → p + e⁻ + ν̄_e. The antineutrino (L = −1) balances the electron (L = +1) so total ΔL = 0
Math Tips
Quark charge rule: up-type quarks (u, c, t) have charge +2/3e; down-type quarks (d, s, b) have charge −1/3e. Proton (uud): +2/3+2/3−1/3 = +1. Neutron (udd): +2/3−1/3−1/3 = 0
Annihilation energy: e⁺ + e⁻ → 2γ. Each photon carries E = m_ec² = 0.511 MeV. Total energy released = 2 × 0.511 = 1.022 MeV. Use E = mc² for any particle-antiparticle pair
Conservation law checklist for any reaction: (1) charge Q, (2) baryon number B, (3) lepton number L (separately for e, μ, τ), (4) energy-momentum. If any is violated → reaction is forbidden
Force carrier summary: photon (γ) carries EM force; W±/Z⁰ carry weak force; gluons (g) carry strong force; graviton (hypothetical) carries gravity. The Higgs boson gives particles mass via the Higgs field
Threshold energy for pair production: γ → e⁺ + e⁻ requires E_photon ≥ 2m_ec² = 1.022 MeV. For proton-antiproton: E ≥ 2m_pc² ≈ 1876 MeV. Higher mass particles need higher energy photons