The Standard Model
The Standard Model
The Standard Model of particle physics classifies all known fundamental particles and describes three of the four fundamental forces (electromagnetic, strong nuclear, and weak nuclear — but not gravity).
Fundamental Particles
There are two families of fundamental (elementary) particles:
Quarks
Quarks are the building blocks of hadrons. There are six flavours of quark, grouped in three generations:
| Generation | Quark | Symbol | Charge (e) | Approx. mass |
|---|---|---|---|---|
| 1st | Up | u | +2/3 | ~2 MeV/c² |
| 1st | Down | d | −1/3 | ~5 MeV/c² |
| 2nd | Charm | c | +2/3 | ~1.3 GeV/c² |
| 2nd | Strange | s | −1/3 | ~100 MeV/c² |
| 3rd | Top | t | +2/3 | ~173 GeV/c² |
| 3rd | Bottom | b | −1/3 | ~4.2 GeV/c² |
Each quark has a corresponding antiquark with opposite charge (e.g., anti-up ū has charge −2/3).
Quarks are never found in isolation — they are always confined within hadrons (a phenomenon called colour confinement).
Leptons
Leptons are fundamental particles that do not experience the strong force:
| Generation | Lepton | Symbol | Charge (e) | Notes |
|---|---|---|---|---|
| 1st | Electron | e⁻ | −1 | Stable |
| 1st | Electron neutrino | νₑ | 0 | Very low mass |
| 2nd | Muon | μ⁻ | −1 | Unstable, ~207 × electron mass |
| 2nd | Muon neutrino | ν_μ | 0 | Very low mass |
| 3rd | Tau | τ⁻ | −1 | Unstable, ~3477 × electron mass |
| 3rd | Tau neutrino | ν_τ | 0 | Very low mass |
Each lepton has a corresponding antilepton (e.g., positron e⁺, anti-electron neutrino ν̄ₑ).
Hadrons
Hadrons are composite particles made of quarks, held together by the strong force:
Baryons (3 quarks): e.g., proton (uud), neutron (udd)
Antibaryons (3 antiquarks): e.g., antiproton (ū ū d̄)
Mesons (quark-antiquark pair): e.g., pion π⁺ (ud̄), kaon K⁺ (us̄)
Conservation Laws
In particle interactions, the following quantities are always conserved:
- Energy (including mass-energy)
- Momentum
- Charge
- Baryon number (B): quarks have B = +1/3, antiquarks B = −1/3
- Lepton number (L): leptons have L = +1, antileptons L = −1 (separate conservation for each generation at A-Level)
Strangeness (S): conserved in strong and electromagnetic interactions, but can change by ±1 in weak interactions. Strange quark s has S = −1; anti-strange s̄ has S = +1.
Force Carriers (Gauge Bosons)
Each fundamental force is mediated by the exchange of gauge bosons:
| Force | Carrier | Symbol | Mass | Range |
|---|---|---|---|---|
| Electromagnetic | Photon | γ | 0 | Infinite |
| Strong nuclear | Gluon | g | 0 | ~10⁻¹⁵ m |
| Weak nuclear | W⁺, W⁻, Z⁰ | W±, Z⁰ | ~80–91 GeV/c² | ~10⁻¹⁸ m |
| Gravity | Graviton | (hypothetical) | 0 | Infinite |
The massive W and Z bosons explain the short range of the weak force (heavier exchange particles → shorter range, by the Heisenberg uncertainty principle).
Beta Decay and the Weak Interaction
Beta-minus decay (β⁻): A neutron decays into a proton, electron, and anti-electron neutrino:
n → p + e⁻ + ν̄ₑ
At the quark level: d → u + e⁻ + ν̄ₑ (a W⁻ boson is exchanged)
Beta-plus decay (β⁺): A proton decays into a neutron, positron, and electron neutrino:
p → n + e⁺ + νₑ
At the quark level: u → d + e⁺ + νₑ (a W⁺ boson is exchanged)
The Higgs Boson
The Higgs boson (discovered at CERN in 2012, mass ~125 GeV/c²) is associated with the Higgs field, which gives other particles their mass through the Higgs mechanism. Particles that interact strongly with the Higgs field are massive (like the top quark); those that do not interact (like the photon) are massless.
Feynman Diagrams
Feynman diagrams represent particle interactions. Conventions:
- Time runs left to right (or upward)
- Straight lines = fermions (quarks, leptons)
- Wavy lines = photons; curly lines = gluons; dashed lines = W/Z/Higgs
- Antiparticles have arrows pointing backward in time
- Each vertex must conserve charge, baryon number, and lepton number
Electron Capture
An inner orbital electron is captured by a proton in the nucleus:
p + e⁻ → n + νₑ
This is a weak interaction mediated by a W⁺ boson. It competes with β⁺ decay and is common in proton-rich nuclei.
Pair Production and Annihilation
Pair production: A photon creates a particle-antiparticle pair (e.g., e⁻ + e⁺). The photon must have energy ≥ 2m₀c² and be near a nucleus (to conserve momentum).
Annihilation: A particle meets its antiparticle and they convert to photons (usually two, to conserve momentum). For electron-positron: E = 2 × 0.511 MeV = 1.022 MeV minimum (producing two 511 keV gamma photons).