Feynman Diagrams

Feynman diagrams are visual representations of particle interactions. They show which particles interact, what exchange particles are involved, and the overall structure of the process. Named after Richard Feynman, these diagrams are essential tools in particle physics. At A-Level, you need to be able to draw and interpret Feynman diagrams for electromagnetic and weak interactions. This is assessed in AQA section 3.2.1.

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Rules for Drawing Feynman Diagrams

At A-Level, the following conventions are used:

1. Time axis: Time runs upward (from bottom to top) or from left to right. AQA typically uses time going upward, but both are acceptable — always label the time axis.

2. Straight lines represent fermions (quarks and leptons). An arrow on the line shows the direction of the particle:

   • Particles have arrows pointing forward in time (upward).
   • Antiparticles have arrows pointing backward in time (downward).

3. Wavy lines represent exchange particles (photons, W±, Z⁰).

4. Vertices: Every vertex (junction point) must conserve charge, baryon number, and lepton number.

5. Labelling: Every line must be labelled with the particle name or symbol.

6. At A-Level, you draw the external (observable) particles as straight lines entering from below and leaving above. The exchange particle connects two vertices.

Exam Tip: In AQA exams, Feynman diagrams are typically drawn with time going upward. Always label the time axis, all particles, and the exchange particle. Arrows on fermion lines must be correct — particles go forward in time, antiparticles go backward.

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Electromagnetic Interactions

Electron-Electron Repulsion (Electromagnetic)

Two electrons approach, exchange a virtual photon (γ), and scatter apart.

Description of the diagram:

• Time axis points upward.
• Two electrons enter from below (straight lines with upward arrows, labelled e⁻).
• A wavy line (labelled γ) connects the two electron lines horizontally (exchange of a virtual photon).
• Two electrons exit upward (straight lines with upward arrows, labelled e⁻).
• The photon carries momentum from one electron to the other, causing repulsion.

At each vertex: an electron enters, a photon is emitted/absorbed, and an electron leaves. Charge is conserved: −1 = −1 at each vertex ✓.

Electron-Positron Annihilation (Electromagnetic)

An electron and a positron meet and annihilate, producing two gamma-ray photons.

Description of the diagram:

• Time axis points upward.
• An electron (e⁻) enters from the bottom left with an upward arrow.
• A positron (e⁺) enters from the bottom right with a downward arrow (antiparticle convention).
• The electron and positron lines meet at a single vertex.
• Two wavy lines (labelled γ) emerge from the vertex, going upward to the left and right.

Conservation checks:

• Charge: (−1) + (+1) = 0 on the left; 0 + 0 = 0 on the right ✓
• Lepton number: (+1) + (−1) = 0 on the left; 0 + 0 = 0 on the right ✓
• Energy: the total energy of the two photons equals the rest mass energy plus kinetic energy of the electron-positron pair. Minimum energy = 2 × 0.511 MeV = 1.022 MeV.

Pair Production (Electromagnetic)

A high-energy photon converts into a particle-antiparticle pair (e.g., e⁻ and e⁺). This is the reverse of annihilation. The photon must have energy at least equal to the combined rest mass energy of the pair:

E_photon ≥ 2m₀c² = 2 × 0.511 = 1.022 MeV for an electron-positron pair

Pair production must occur near a nucleus (to conserve momentum — the nucleus absorbs recoil momentum).

Description of the diagram:

• A wavy line (γ) enters from below.
• At the vertex, it splits into two straight lines: an electron (e⁻, arrow pointing upward) and a positron (e⁺, arrow pointing downward, following antiparticle convention).
• A nearby nucleus is shown to absorb the recoil momentum.

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Weak Interactions — Beta Decay

Beta-Minus Decay (β⁻)

At the quark level: d → u + e⁻ + ν̄ₑ