Feynman Diagrams (AQA A Level Physics): Revision Note

Feynman diagrams

• 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

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

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

${}_0{}^1\mathrm{n}\to {}_1{}^1\mathrm{p}+{}_{-1}{}^0\mathrm{\beta }+{\overline{v}}_{\mathrm{e}}$

• During beta-minus decay:

  • A neutron decays into a proton and a W⁻ boson

  • Then, the W⁻ boson decays into an electron and electron anti-neutrino

Feynman diagram for beta-minus decay

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

${}_1{}^1\mathrm{p}\to {}_0{}^1\mathrm{n}+{}_{+1}{}^0\mathrm{\beta }+v_{\mathrm{e}}$

• 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

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

${}_1{}^1\mathrm{p}+{}_{-1}{}^0\mathrm{e}\to {}_0{}^1\mathrm{n}+v_{\mathrm{e}}$

• 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

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

${}_1{}^1\mathrm{p}+{}_{-1}{}^0\mathrm{e}\to {}_0{}^1\mathrm{n}+v_{\mathrm{e}}$

• 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

Quark transformation in β decay

• 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

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

Quark composition: β⁺ decay

• β⁺ decay is when a proton turns into a neutron emitting a positron and an electron neutrino

• More specifically, a proton turns into a neutron because 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