You are viewing a free preview of this lesson.
Subscribe to unlock all 10 lessons in this course and every other course on LearningBro.
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.
Specification mapping. This lesson develops AQA A-Level Physics (7408) sub-strand 3.2.1.4 (particle interactions — drawing and interpreting Feynman diagrams). It builds directly on the leptons / exchange-particles lesson (order 4), which establishes the cast of fermions and bosons that Feynman diagrams arrange. The diagrammatic conventions taught here are then used in the conservation-laws lesson (order 6) for checking allowed-versus-forbidden interactions. Refer to the official AQA 7408 specification document for the authoritative wording — at A-Level, examinable diagrams cover β⁻ decay, β⁺ decay, electron capture, neutrino interactions and the basic electromagnetic vertex.
Synoptic links. Three connections make this lesson synoptic. First, conservation laws (3.2.1.7, our order 6) — every Feynman vertex enforces charge, baryon-number and lepton-number conservation, and the choice of W⁺ versus W⁻ at a vertex is what implements that conservation in the diagram. Second, the photoelectric effect and pair production (3.2.2.1, our order 7; 3.2.1.2, our order 2) — pair production γ → e⁻ + e⁺ is itself a Feynman vertex, where a virtual electron line bends in time to become a positron. Third, nuclear physics (course 6, 3.8) — the underlying picture of α, β⁺ and β⁻ decay at the nucleon level is sharpened by the Feynman-diagram picture at the quark level, justifying why some isotopes prefer β⁻ over β⁺.
At A-Level, the following conventions are used:
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.
Straight lines represent fermions (quarks and leptons). An arrow on the line shows the direction of the particle:
Wavy lines represent exchange particles (photons, W±, Z⁰).
Vertices: Every vertex (junction point) must conserve charge, baryon number, and lepton number.
Labelling: Every line must be labelled with the particle name or symbol.
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.
Two electrons approach, exchange a virtual photon (γ), and scatter apart.
Description of the diagram:
At each vertex: an electron enters, a photon is emitted/absorbed, and an electron leaves. Charge is conserved: −1 = −1 at each vertex ✓.
An electron and a positron meet and annihilate, producing two gamma-ray photons.
Description of the diagram:
Conservation checks:
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:
At the quark level: d → u + e⁻ + ν̄ₑ
Description of the diagram:
Conservation at the first vertex (quark vertex):
Conservation at the second vertex (lepton vertex):
At the quark level: u → d + e⁺ + νₑ
Description of the diagram:
Conservation at the first vertex:
Conservation at the second vertex:
A proton in a nucleus captures an orbiting electron and converts into a neutron, emitting an electron neutrino:
p + e⁻ → n + νₑ
At the quark level: u + e⁻ → d + νₑ
Description of the diagram:
Alternatively, this can be drawn with a W⁻ going in the opposite direction — both representations are equivalent.
νₑ + n → e⁻ + p
At the quark level: νₑ + d → e⁻ + u
A W⁺ boson is exchanged between the neutrino and the down quark.
Description of the diagram:
Exam Tip: When drawing Feynman diagrams, always check that charge, baryon number, and lepton number are conserved at every vertex. If they are not, your diagram is wrong. The W boson must carry the correct charge to balance the vertex. Remember that the W⁺ has charge +1 and the W⁻ has charge −1.
It is worth understanding why beta decay always appears in Feynman diagrams as a two-vertex process — never a single vertex. At each vertex of a Feynman diagram, charge, baryon number and lepton number must all be conserved exactly. A single vertex with the structure "neutron emits e⁻ + ν̄ₑ and becomes a proton" would have to conserve all three quantities at that vertex and would require a single direct neutron-to-proton conversion involving emission of two leptons. The Standard Model's electroweak Lagrangian does not allow any such direct vertex; the only vertex involving the W boson is the single-fermion-flavour-change vertex (e.g. d → u + W⁻ at the quark level, or e⁻ → νₑ + W⁻ at the lepton level).
The W boson, as a virtual exchange particle, links the two vertices: at vertex 1, a quark changes flavour and the W boson is emitted (or absorbed); at vertex 2, the W boson decays into a lepton-antilepton pair (or interacts with another fermion). The W boson cannot exist as a real (on-shell) free particle in this process because the energy budget of a typical beta decay (a few MeV) is far less than the W mass (80 GeV), but it can exist as a virtual particle for a vanishingly short time, mediated by the energy-time uncertainty principle.
Draw a Feynman diagram for electron capture (p + e⁻ → n + νₑ) at the quark level.
Step 1: Identify the quark-level transition. Electron capture converts a proton (uud) into a neutron (udd), so one up quark must become a down quark: u → d. This requires emission of a W⁺ boson at the quark vertex (since the charge change is +⅔ → −⅓, so the W must carry +1 charge).
Step 2: Identify the lepton-level transition. The electron (e⁻, charge −1, Lₑ = +1) must be absorbed at a vertex with the W⁺ to become a neutrino (νₑ, charge 0, Lₑ = +1). At this vertex, the W⁺ carries off the +1 charge from the e⁻ entering and the νₑ leaving.
Step 3: Describe the diagram:
Step 4: Verify conservation at each vertex:
This diagram represents the quark-level mechanism by which electron capture in nuclei converts a proton-rich nucleus into a more stable neutron-rich nucleus. Note that the neutrino emitted in electron capture carries off almost the entire decay energy (about 0.78 MeV for ⁷Be → ⁷Li), since the daughter nucleus recoils with very little kinetic energy due to its much larger mass.
An equivalent way to draw electron capture is with a W⁻ going from the lepton vertex to the quark vertex (instead of W⁺ going the other way). This is just a matter of convention — physically, a W⁺ moving rightward and a W⁻ moving leftward in time describe the same virtual exchange, since the W⁻ is the antiparticle of the W⁺. At A-Level, examiners accept either drawing provided the conservation arithmetic is consistent.
Subscribe to continue reading
Get full access to this lesson and all 10 lessons in this course.