Feynman Diagrams (AQA A Level Physics)

• Particle interactions and decays can be represented using Feynman diagrams
• They are a way of visualising particle equations and the exchange particles involved

Rules for Feynman diagrams

• The y-axis represents time and the x-axis represents space
• A vertex is where particles and exchange particles meet - these represent points of interaction (e.g. electromagnetic, weak or strong)
• Incoming particles come in at the bottom, and outgoing particles leave at the top
• Particles are represented by straight lines which have arrows
• Each straight line must have an arrow with its direction forward in time
• Exchange particles are represented by wavy lines which have no arrows
• The transfer of exchange particles is from left to right unless indicated by an arrow above the wavy line
• Hadrons/quarks are present on the left and leptons on the right, they must never meet at a vertex
• Charge, baryon number and lepton number must be conserved at each vertex
• Lines must not cross over

Features of Feynman diagrams

Feynman diagrams follow a set of rules which are needed to draw and interpret them accurately

Exchange particles

• Exchange particles act as a force carrier between particles in an interaction
  
  • In electromagnetic interactions, the exchange particle is a virtual photon
  • In weak interactions, the exchange particle is the W boson

• Exchange particles are represented as wavy lines
• Charged exchange particles, such as W⁺ and W^–, sometimes have an arrow above the wavy line to indicate their direction

Electromagnetic Interactions

• When two electrons approach each other, they experience repulsion due to the electromagnetic force
• This can be represented on a Feynman diagram to show the exchange of a virtual photon

Electrostatic repulsion between electrons

Two electrons approach each other and exchange a virtual photon before moving apart due to electrostatic repulsion

Beta-minus decay

• Beta-minus decay is an example of the weak interaction
  • The exchange particle is a W⁻ boson 
  • This is because the β⁻ particle (electron) has a negative charge

• During beta-minus decay:
  • A neutron decays into a proton and a W⁻ boson
  • Then, the W⁻ boson decays into an electron and anti-electron neutrino

Feynman diagram for beta-minus decay

Beta-minus decay can be represented on a Feynman diagram with the W⁻ boson as the exchange particle

Beta-plus decay

• Beta-plus decay is another example of the weak interaction
  • The exchange particle is a W⁺ boson 
  • This is because the β⁺ particle (positron) has a positive charge

• During beta-plus decay:
  • A proton decays into a neutron and a W⁺ boson
  • Then, the W⁺ boson decays into a positron and electron neutrino

Feynman diagram for beta-plus decay

Beta-plus decay can be represented on a Feynman diagram with the W⁺ boson as the exchange particle

Electron Capture

• Electron capture is another example of the weak interaction
  • The exchange particle is a W⁺ boson 
  • This is because the proton acts on the electron

• During electron capture:
  • A proton absorbs an electron and decays into a neutron and W⁺ boson
  • Then, the interaction between the electron and W⁺ boson forms an electron neutrino

Feynman diagram for electron capture

The proton acts on the electron during electron capture. This is shown by an arrow indicating the W⁺ particle is exchanged from left to right

Electron-proton collision

• When an electron and proton collide, they transfer a W⁻ boson 
  
  • This is because the electron acts on the proton
  • The equation for an electron-proton collision is the same as for electron capture

• During an electron-proton collision:
  • An electron collides with a proton and decays into a neutron and W⁻ boson
  • Then, the interaction between the electron and W⁻ boson forms an electron neutrino

Feynman diagram for an electron-proton collision

 An electron collides with a proton. This is shown by an arrow indicating the W⁻ particle is exchanged from right to left

• β decay occurs because of the weak interaction between quarks

Quark Composition: β^– decay

• β^– decay is when a neutron turns into a proton emitting an electron and anti-electron neutrino
• More specifically, a neutron turns into a proton because a down quark turns into an up quark

Beta minus decay is when a down quark turns into an up quark

• The W^– boson ‘carries away’ the negative charge of the down quark which provides the negative charge for the electron and anti-neutrino

In beta minus decay, the weak interaction turns a down quark into an up quark

Quark Composition: β⁺ decay

• β⁺ decay is when a proton turns into a neutron emitting an positron and an electron neutrino
• More specifically, a proton turns into a neutron because an up quark turns into a down quark

Beta plus decay is when an up quark turns into a down quark

• The W⁺ boson ‘carries away’ the positive charge of the up quark which provides the positive charge for the positron and neutrino

In beta plus decay, the weak interaction turns an up quark into a down quark