Quarks, leptons, hadrons and the exchange particles of the four fundamental forces
AQA A-Level Physics 2
🧱Classify particles as quarks, leptons or hadrons
⚛️State the quark composition of protons, neutrons and pions
🔄Apply conservation laws (charge, baryon, lepton number) to interactions
📡Describe exchange particles for the four fundamental forces
🌀Represent interactions using Feynman diagrams
⚖️Identify whether a given interaction is allowed or forbidden
Quarks and the Hadron Family
Quarks are fundamental particles that combine to form composite particles called hadrons. There are six quarks, but AQA A-Level only requires knowledge of up (u), down (d) and strange (s) quarks.
Quark
Symbol
Charge
Baryon number B
Strangeness S
Up
u
+²⁄₃ e
+¹⁄₃
0
Down
d
−¹⁄₃ e
+¹⁄₃
0
Strange
s
−¹⁄₃ e
+¹⁄₃
−1
Baryons: Made of 3 quarks (qqq). Baryon number B = +1. Examples: proton (uud), neutron (udd).
Mesons: Made of 1 quark + 1 antiquark (qq̄). Baryon number B = 0. Examples: pion π⁺ (ud̄), π⁻ (ūd), π⁰ (uū or dd̄).
Particle
Quark content
Charge
Proton (p)
uud
+1
Neutron (n)
udd
0
π⁺
ud̄
+1
π⁻
ūd
−1
π⁰
uū
0
Leptons
Leptons are fundamental particles that do not experience the strong nuclear force. They are not made of quarks.
Particle
Symbol
Charge
Lepton number L_e
Electron
e⁻
−1
+1
Electron-neutrino
ν_e
0
+1
Positron
e⁺
+1
−1
Antineutrino
ν̄_e
0
−1
Leptons have lepton number L_e = +1; antileptons have L_e = −1. Lepton number is conserved in all interactions.
The Four Fundamental Forces and Their Exchange Particles
Forces in particle physics are mediated by the exchange of virtual particles called gauge bosons. Each force has its own exchange particle(s).
Force
Acts on
Exchange particle
Range
Gravitational
All particles with mass
Graviton (not yet detected)
Infinite
Electromagnetic
Charged particles
Photon (γ)
Infinite
Weak nuclear
All quarks and leptons
W⁺, W⁻, Z⁰ bosons
~10⁻¹⁸ m
Strong nuclear
Quarks (and hadrons)
Gluons (pions for residual)
~3 × 10⁻¹⁵ m
W bosons: The W⁺ and W⁻ bosons mediate beta decay. They carry both charge and lepton/baryon number. In β⁻ decay: n → p + W⁻ → p + e⁻ + ν̄_e. In β⁺ decay: p → n + W⁺ → n + e⁺ + ν_e.
Electron capture: p + e⁻ → n + ν_e. A proton captures an orbital electron via the W⁺ boson. This is an alternative to β⁺ decay for proton-rich nuclei.
Conservation Laws in Particle Interactions
For any interaction to be allowed, ALL of the following must be conserved:
Conserved Quantity
Conserved in...
Charge (Q)
All interactions
Baryon number (B)
All interactions
Lepton number (L_e)
All interactions
Strangeness (S)
Strong and EM interactions only (not weak)
Mass-energy
All interactions
Momentum
All interactions
Strangeness is NOT conserved in weak interactions. Strange particles are produced in strong interactions (conserving strangeness) but decay via the weak interaction (strangeness can change by ±1).
Verify that the quark composition of the proton (uud) gives the correct charge and baryon number.
1Charge: u = +²⁄₃e, u = +²⁄₃e, d = −¹⁄₃e → total = +²⁄₃ + ²⁄₃ − ¹⁄₃ = +³⁄₃ = +1e ✓
2Baryon number: each quark has B = +¹⁄₃ → total = 3 × ¹⁄₃ = +1 ✓
Proton: charge = +1e, baryon number = +1 — consistent with known values
Determine whether the interaction p + p → p + n + π⁺ is allowed. Check charge, baryon number and lepton number.
1Charge: left = 1 + 1 = 2; right = 1 + 0 + 1 = 2 ✓
2Baryon number: left = 1 + 1 = 2; right = 1 + 1 + 0 = 2 ✓ (π⁺ is a meson, B = 0)
3Lepton number: all are non-leptons → L_e = 0 on both sides ✓
All conservation laws satisfied — interaction is allowed
In beta-minus decay, describe the quark-level change and the exchange particle involved.
1A neutron (udd) changes to a proton (uud): one down quark → up quark
2The quark change d → u is mediated by a W⁻ boson
3The W⁻ then decays: W⁻ → e⁻ + ν̄_e
d → u + W⁻; W⁻ → e⁻ + ν̄_e. Net: n → p + e⁻ + ν̄_e
Show that the interaction n → p + e⁻ (without a neutrino) violates lepton number conservation.
1Left side: neutron has L_e = 0 → total L_e = 0
2Right side: proton L_e = 0, electron L_e = +1 → total L_e = +1
30 ≠ 1 → lepton number not conserved → interaction is forbidden
Lepton number violation: this interaction is forbidden. An antineutrino (L_e = −1) must also be emitted to balance L_e.
Beta decay is mediated by the weak nuclear force via W bosons: W⁻ in β⁻ decay (n→p), W⁺ in β⁺ decay (p→n).
3. A kaon K⁺ has strangeness S = +1. It decays to π⁺ + π⁰. Is strangeness conserved? What force mediates this decay?
Pions have S = 0, so right side total S = 0. Left side S = +1. Strangeness NOT conserved (ΔS = −1) → this is a weak interaction decay. Strangeness is only conserved in strong and EM interactions.
4. What is the baryon number of a π⁻ meson?
Mesons are quark-antiquark pairs. π⁻ = ūd. B = B(ū) + B(d) = −¹⁄₃ + ¹⁄₃ = 0.
5. State the exchange particle and the force involved when two electrons repel each other.
1. Check all conservation laws (charge, baryon number, lepton number) for the interaction: p + ν̄_e → n + e⁺. Is this interaction allowed?
Charge: left = +1 + 0 = +1; right = 0 + 1 = +1 ✓. Baryon number: left = 1 + 0 = 1; right = 1 + 0 = 1 ✓. Lepton number L_e: left = 0 + (−1) = −1; right = 0 + (−1) = −1 ✓ (positron has L_e = −1). All laws conserved → this interaction IS allowed. This is inverse beta decay (antineutrino capture), and was used by Cowan and Reines (1956) to detect antineutrinos from a nuclear reactor.
2. A strange particle Λ⁰ (baryon, S = −1, quark content uds) decays to p + π⁻. Show whether this decay conserves strangeness, and state the force responsible.
Strangeness: Λ⁰ has S = −1; p has S = 0; π⁻ has S = 0. Right side S = 0. ΔS = 0 − (−1) = +1 → strangeness NOT conserved. This is a weak interaction (only the weak force allows strangeness to change). Charge: left = 0; right = +1 + (−1) = 0 ✓. Baryon number: left = 1; right = 1 + 0 = 1 ✓. Lepton number: all zero ✓. The decay is allowed by all laws except strangeness — confirming it proceeds via the weak interaction.
3. Explain what is meant by an exchange particle and why the short range of the weak force is related to the large mass of the W boson.
Exchange particles (gauge bosons) are virtual particles that carry the force between interacting particles. They are "borrowed" from the vacuum, with the energy allowed by the Heisenberg uncertainty principle: ΔE × Δt ≥ h/4π. A more massive exchange particle requires more energy, so it can only exist for a shorter time (smaller Δt), and therefore travel a shorter distance at speeds approaching c. The W boson has mass ~80 GeV/c² — enormously massive — so it can only travel ~10⁻¹⁸ m before being reabsorbed. This limits the weak force to an extremely short range. By contrast, the photon is massless, so it can travel infinite distances, giving the electromagnetic force infinite range.