Leptons, Exchange Particles and Fundamental Forces

This lesson covers the lepton family of particles, the four fundamental forces of nature, and the exchange particles (gauge bosons) that mediate each force. Understanding how forces are transmitted at the quantum level is central to the Standard Model. This is assessed in AQA section 3.2.1.

---

Leptons

Leptons are fundamental particles that do not feel the strong nuclear force. They interact via the weak force, the electromagnetic force (if charged), and gravity.

The Three Generations of Leptons

Generation	Charged Lepton	Neutrino
1st	Electron (e⁻)	Electron neutrino (νₑ)
2nd	Muon (μ⁻)	Muon neutrino (ν_μ)
3rd	Tau (τ⁻)	Tau neutrino (ν_τ)

Each charged lepton has a corresponding antiparticle (e⁺, μ⁺, τ⁺), and each neutrino has a corresponding antineutrino (ν̄ₑ, ν̄_μ, ν̄_τ).

Properties of Leptons

Particle	Charge (e)	Lepton number (Lₑ)	Lepton number (L_μ)	Lepton number (L_τ)	Mass
e⁻	−1	+1	0	0	0.511 MeV/c²
νₑ	0	+1	0	0	≈ 0 (very small)
μ⁻	−1	0	+1	0	105.7 MeV/c²
ν_μ	0	0	+1	0	≈ 0
τ⁻	−1	0	0	+1	1777 MeV/c²
ν_τ	0	0	0	+1	≈ 0

Antileptons have all quantum numbers negated: e⁺ has Lₑ = −1, ν̄ₑ has Lₑ = −1, etc.

Lepton Number Conservation

Lepton number is conserved in all interactions. Each generation has its own lepton number (Lₑ, L_μ, L_τ), and each is conserved separately.

Worked Example 1 — Check lepton number conservation in muon decay

The muon decays as follows:

μ⁻ → e⁻ + ν̄ₑ + ν_μ

Check Lₑ: 0 → +1 + (−1) + 0 = 0 ✓

Check L_μ: +1 → 0 + 0 + 1 = +1 ✓

Both lepton numbers are conserved. ✓

Worked Example 2 — Check lepton number in beta-minus decay

n → p + e⁻ + ν̄ₑ

Check Lₑ: 0 → 0 + 1 + (−1) = 0 ✓

(Neutrons and protons are not leptons, so they have lepton number 0.)

Key Point: In beta-minus decay, an electron and an electron antineutrino are emitted together. In beta-plus decay, a positron and an electron neutrino are emitted together. These pairings ensure conservation of electron lepton number.

---

The Four Fundamental Forces

All interactions in nature are governed by four fundamental forces:

Force	Relative strength	Range	Exchange particle	Acts on
Strong nuclear	1	~10⁻¹⁵ m (1 fm)	Gluon (g)	Quarks and gluons (colour charge)
Electromagnetic	~10⁻²	Infinite (∝ 1/r²)	Photon (γ)	Electrically charged particles
Weak nuclear	~10⁻⁶	~10⁻¹⁸ m	W⁺, W⁻, Z⁰ bosons	All fermions (quarks and leptons)
Gravitational	~10⁻³⁹	Infinite (∝ 1/r²)	Graviton (hypothetical)	All particles with mass/energy

---

Exchange Particles (Gauge Bosons)

In quantum field theory, forces are transmitted by the exchange of virtual particles called gauge bosons. The analogy is two people on ice throwing a ball between them — the ball carries momentum and causes the throwers to move apart (repulsive force). While this analogy is imperfect, it captures the essential idea that forces arise from particle exchange.

The Photon (γ) — Electromagnetic Force