Conservation Laws in Particle Physics

Conservation laws are the most powerful tools for predicting whether a particle interaction can occur. If any conserved quantity is violated, the interaction is forbidden — it simply cannot happen. This lesson covers the conservation of charge, baryon number, lepton number, and strangeness, including the crucial distinction between when strangeness is and is not conserved. This is assessed in AQA section 3.2.1.

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The Conservation Laws

1. Conservation of Charge (Q)

Charge is conserved in all interactions — no exceptions. The total charge before the interaction must equal the total charge after.

2. Conservation of Baryon Number (B)

Baryon number is conserved in all interactions — no exceptions.

Particle type	Baryon number
Baryons (p, n, Σ, Ξ, etc.)	+1
Antibaryons (p̄, n̄, etc.)	−1
Mesons (π, K, etc.)	0
Leptons (e, μ, τ, neutrinos)	0
Photons	0

3. Conservation of Lepton Number (L)

Lepton number is conserved in all interactions. Each generation of lepton has its own lepton number, and each is conserved separately.

Particle	Lₑ	L_μ	L_τ
e⁻	+1	0	0
e⁺	−1	0	0
νₑ	+1	0	0
ν̄ₑ	−1	0	0
μ⁻	0	+1	0
μ⁺	0	−1	0
ν_μ	0	+1	0
ν̄_μ	0	−1	0
τ⁻	0	0	+1
τ⁺	0	0	−1
All hadrons, photons	0	0	0

4. Conservation of Strangeness (S)

Strangeness is conserved in strong and electromagnetic interactions, but can change by ±1 in weak interactions.

Particle	Strangeness
K⁺ (us̄)	+1
K⁰ (ds̄)	+1
K⁻ (ūs)	−1
K̄⁰ (d̄s)	−1
Σ⁺, Σ⁰, Σ⁻	−1
Ξ⁰, Ξ⁻	−2
Ω⁻	−3
p, n, π, e, μ, γ, neutrinos	0

Key Point: Strange particles are always produced in pairs in strong interactions (associated production) — for example, a K⁺ (S = +1) is produced alongside a Σ⁻ (S = −1), so the total strangeness change is zero. However, when strange particles decay, they do so via the weak interaction (one at a time), which is why they have relatively long lifetimes.

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Applying the Conservation Laws — Method

To determine whether an interaction is allowed or forbidden:

1. Add up each conserved quantity on both sides of the equation.
2. Compare the totals.
3. If any quantity is not conserved, the interaction is forbidden.
4. If all quantities are conserved, the interaction is allowed (though it may still be very unlikely or require specific conditions).

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Worked Examples

Worked Example 1 — Is this interaction allowed?

p + p → p + p + π⁰

Quantity	Before	After
Charge	+1 + 1 = +2	+1 + 1 + 0 = +2 ✓
Baryon number	+1 + 1 = +2	+1 + 1 + 0 = +2 ✓
Lepton number	0	0 ✓
Strangeness	0	0 ✓

Allowed ✓ (strong interaction — strangeness conserved, no leptons involved)

Worked Example 2 — Is this interaction allowed?

p → n + e⁺ + νₑ