Questions: Conservation Laws in Particle Reactions: Baryon Number, Lepton Number, and Strangeness

Question 1

Which of these processes is allowed by all the conservation laws?

• A. n → p + e⁻ + νₑ
• B. n → p + e⁻ + ν̄ₑ
• C. p → π⁰ + e⁺
• D. π⁻ → μ⁻ + ν_μ

Answer: (B)

Neutron decay produces an electron (Lₑ = +1) and an electron antineutrino (Lₑ = −1), keeping Lₑ = 0. The first option has Lₑ = 2, the third changes baryon number from 1 to 0, and the fourth has L_μ = 2.

Question 2

The decay Λ⁰ → p + π⁻ conserves strangeness.

• T. True
• F. False

Answer: False

The Λ⁰ (uds) has strangeness −1, while the proton and pion have strangeness 0. Strangeness changes by one unit, so the decay must proceed by the weak interaction, giving the Λ⁰ a lifetime of about 2.6 × 10⁻¹⁰ s.

Question 3

Why is the proton stable, even though lighter particles such as positrons and pions exist?

• A. It has no electric charge
• B. It is the lightest baryon, so any decay would have to change baryon number
• C. It is a lepton
• D. It has zero strangeness

Answer: (B)

Every decay product lighter than the proton is a meson or lepton with baryon number 0. Experiments set the proton lifetime above about 10³⁴ years.

Question 4

Check the decay μ⁻ → e⁻ + ν̄ₑ + ν_μ for electron and muon lepton number.

Model answer: L_μ: 1 → 0 + 0 + 1 = 1. Lₑ: 0 → 1 + (−1) + 0 = 0. Both are conserved.

The muon's L_μ passes to the muon neutrino, while the electron and electron antineutrino carry opposite Lₑ values that sum to zero.