2.2.4 Leptons

• Leptons are a group of fundamental (elementary) particles
  • This means they are not made up of any other particles (no quarks)

• Leptons interact with other particles via the weak, gravitational or electromagnetic interactions
  • They do not interact via the strong nuclear force

• The most common leptons are:
  • The electron, e^–
  • The electron neutrino, v_e
  • The muon, μ^–
  • The muon neutrino, v_μ

The most common leptons are the electron, muon and their respective neutrinos

• The muon is similar to the electron but is slightly heavier
• Electrons and muons both have a charge of -1e and a mass of 0.0005u
• Neutrinos are the most abundant leptons in the universe and have no charge and negligible mass (almost 0)
• Although quarks are fundamental particles too, they are not classed as leptons
  • Leptons do not interact with the strong force, whilst quarks do

• Similar to baryon number, the lepton number, L is the number of leptons in an interaction
• L depends on whether the particle is a lepton, anti-lepton or neither
  • Leptons have a lepton number L = +1
  • Anti-leptons have a lepton number L = –1
  • Particles that are not leptons have a lepton number L = 0

• Lepton number is a quantum number and is conserved in all interactions
• This is helpful for knowing whether an interaction is able to happen

The lepton number depends if the particle is a lepton, anti-lepton or neither

Step 1: Determine the lepton number of all the particles on both sides of the equation

0 + (–1) = 0 + X

Step 2: Identify the lepton number of X

             If the lepton number must be conserved, X must also have a lepton number of –1

Step 3: State the particle X

             Particle X is an anti-neutrino

• Muons are leptons that are slightly heavier than the electron
• Muons (μ^–) typically decay into an electron
• Anti-muons (μ⁺) typically decay into positrons

The Feynman diagram for muon decay

• Muon decay occurs through the weak interaction
• This can be recognised by the exchange of the W^– boson on a Feynman diagram

Step 1: Write out the equation for muon decay

μ^– → e^– + ṽ_e + ν_μ

Step 2: List the quantities which must be conserved in this interaction 

• • Charge, q
    • q = –1 for electrons and muons, q = 0 for neutrinos

  • Electron lepton number, L_e
    • L_e = +1 for electrons, L_e = –1 for anti-electron neutrinos, L_e = 0 for muons and muon neutrinos

  • Muon lepton number, L_μ
    • L_μ = +1 for muons and muon neutrinos, L_μ = 0 for electrons and electron neutrinos

Step 3: Determine if each quantity balances on each side of the equation

• • Charge, q:
    • μ^– → e^– + ṽ_e + ν_μ
    • –1 = –1 + 0 + 0 ✓ conserved

  • Electron lepton number, L_e:
    • μ^– → e^– + ṽ_e + ν_μ
    • 0 = +1 – 1 + 0 ✓ conserved

  • Muon lepton number, L_μ:
    • μ^– → e^– + ṽ_e + ν_μ
    • +1 = 0 + 0 + 1 ✓ conserved

Step 4: Write a conclusion

• • The numbers on each side of the equation are equal for charge, electron lepton number and muon lepton number, therefore, muon decay satisfies these conservation laws