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Particle Physics: The Standard Model and Fundamental Interactions
The Standard Model Framework
The Standard Model describes all known fundamental particles and three of nature’s four forces:
| Particle Type | Examples | Properties |
|---|---|---|
| Quarks (6 flavors) | Up (u), Down (d), Charm (c) | Fractional charge (±1/3e, ±2/3e) |
| Leptons (6 types) | Electron (e⁻), Muon (μ⁻), Tau (τ⁻) | Integer charge (0 or -1e) |
| Gauge Bosons | Photon (γ), Gluon (g), W/Z | Force carriers (spin=1) |
| Higgs Boson | H⁰ | Mass mechanism (spin=0) |
Fundamental Interactions
Quantum Chromodynamics (QCD)
Describes quark interactions via gluons:
![\[ \mathcal{L}_{QCD} = -\frac{1}{4}G^a_{\mu\nu}G_a^{\mu\nu} + \sum_q \bar{q}(i\gamma^\mu D_\mu - m_q)q \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-4f558ad8a20b28d54523f3eb029adc07_l3.png "Rendered by QuickLaTeX.com")
Electroweak Theory
Unifies electromagnetic and weak forces:
![\[ \mathcal{L}_{EW} = \bar{\psi}\gamma^\mu(i\partial_\mu - gW_\mu - g'B_\mu)\psi \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-42403938c979e67741098cf9ceba2035_l3.png "Rendered by QuickLaTeX.com")
Experimental Frontiers
Large Hadron Collider
- Proton collisions at 13 TeV center-of-mass energy
- Detects particles via ATLAS/CMS detectors
- Precision measurements to 0.1% level
Neutrino Observatories
- Measure flavor oscillations (θ₁₂ ≈ 33°)
- Investigate CP violation in leptonic sector
Practical Applications
Medical Technology
- PET scans: e⁺e⁻ → 2γ (511 keV each)
- Proton therapy: Bragg peak at ~30cm depth
Materials Science
- Synchrotron radiation for crystallography
- Ion implantation in chip manufacturing
Conceptual Problems
- Hadron Composition:
- Proton: uud (Q = +2/3 +2/3 -1/3 = +1e)
- Neutron: udd (Q = +2/3 -1/3 -1/3 = 0)
- Decay Processes:
- β⁻ decay: n → p + e⁻ + ν̄ₑ
- μ decay: μ⁻ → e⁻ + ν̄ₑ + ν_μ
Practice Questions
- Calculate the quark composition for a π⁺ meson (ud̄)
- Explain how the Higgs field gives mass to W/Z bosons
- Compare QCD confinement with electromagnetic force range
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