Episode 536: Vector bosons and Feynman diagrams

You need to check your own specification here for details of what students will need to do in examinations, and to look at past papers: although Feynman diagrams give clarity to particle interactions, they are not required by all specifications.

Feynman diagram for electron repulsion

Summary

  • Demonstration: Exchange particles (5 minutes)
  • Discussion: Interactions of different types (15 minutes)
  • Demonstration: Model Feynman diagrams (15 minutes)
  • Discussion: Rules for Feynman diagrams (10 minutes)
  • Student activity: Constructing Feynman diagrams (20 minutes)

Demonstration: Exchange particles
Yukawa’s theory of an exchange particle to explain repulsive and attractive forces in nuclei is worth demonstrating with two students and a football or other large object.

If two students throw (gently) a heavy object such as a schoolbag or football to each other, each will report feeling an outwards force both on throwing and on catching (Why? Conservation of momentum). If the rules are changed so that, instead of throwing, each student pulls the object from the other’s hands in turn, then each will report feeling an inwards force both on gaining and on losing the particle.

Discussion: Interactions of different types
This crude model in the demonstration above will illustrate the idea of an exchange particle originated by Yukawa, who suggested that a nuclear exchange particle (it turned out to be the pion) could explain the strong interaction between protons and neutrons. In the last episode, it will be clear that a similar fundamental exchange works at a level that is more fundamental than mesons and baryons.

The electromagnetic interaction, which consists of just the well-known attractions and repulsions of static electricity (pre-16 level), is a different interaction, much weaker than the strong interaction. Here the exchange particle is the photon.

The weak interactions, which are harder to classify, and are similar in strength to the electromagnetic interactions, are associated with changes in the nature of particles.

Demonstration: Model Feynman diagrams
Feynman diagrams can be introduced via a physical model that can be twisted to show different interactions. The key aspects – direction of time, transfer of the force-carrying boson, difference between particles and anti-particles – can be quickly illustrated for an electromagnetic interaction.

As an example of these points (including the last), you may wish to use a simple physical model. It is quick and easy to use cheap coat hangers linked by their hooks, with triangles of card attached midway across the ‘shoulder’ of each. The supporting ‘shoulders’ of the coat hangers are the interacting particles, while the interlocked hooks constitute the vector boson. With one twist each time, it is possible to go from electron-electron interaction to electron positron interaction to positron-positron interaction to electron-positron annihilation.

For these electromagnetic interactions, the particle exchanged is a photon. For the weak interaction, there are three particles, depending on the changes in charge taking place. If you deal with quark interactions later, the exchange particle is the gluon.

Some teacher notes:

Episode 536-1: Feynman diagrams (Word, 53 KB)

Episode 536-2: Coat-hanger Feynman diagrams (Word, 37 KB)

Discussion: Rules for Feynman diagrams
If your specification requires Feynman diagrams, you will need to emphasise the rules for drawing them. These are not consistent from source to source! In this episode, the following conventions are followed.

Time goes vertically up the diagram (many sources have time horizontal).

Side-to-side displacement in the diagrams has no meaning other than to show separate particles. If two paths are heading outwards, it does not imply that particles are repelling each other.

Particles are shown by ‘normal’ arrow-heads, while anti-particles are shown by reversed arrow-heads (remember that the direction of time is upwards), so a collision between a proton and an anti-proton can be represented as:

Proton anti-proton scattering

From any vertex, such as the collision point of the proton and anti-proton, a boson can be drawn. This can be a photon (wavy line), a weak interaction boson (a dotted line).

A Feynman diagram – certainly the simple ones in this episode – can be pivoted about any of the vertices to produce another valid diagram.

Student activity: Constructing Feynman diagrams
Students are supplied with cards from which they can construct Feynman diagrams. They use the different ‘left-hand sides’ of the diagrams with the single vector boson and the appropriate ‘right-hand side’ to produce the different possible weak interactions, and then to label the boson with W+, W- or Z0 as appropriate.

Episode 536-3: Feynman diagram student activities (Word, 49 KB)

Episode 536-4: Feynman weak interaction cards (Word, 32 KB)

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Episode 536: Vector bosons and Feynman diagrams (Word, 140 KB)