Unit 5 · Lesson 3c

3cAntimatter and Particle Interactions

Discover antiparticles, pair production, annihilation, conservation laws, and why the universe is made of matter rather than antimatter.

Antimatter is not science fiction — it is produced in PET scanners, cosmic rays, and particle accelerators every day. Understanding conservation laws and CP violation is essential for particle physics and cosmology.

Lesson Overview

Every particle has a corresponding antiparticle with the same mass but opposite charge and quantum numbers. When a particle meets its antiparticle, they annihilate and convert entirely to energy (photons). Pair production is the reverse: a high-energy photon creates a particle–antiparticle pair. Conservation laws — charge, lepton number, baryon number — govern all particle interactions. The mystery of why the universe contains more matter than antimatter (CP violation) is one of the deepest unsolved problems in physics.

Key Concepts

Antiparticle

Same mass as its particle partner, but opposite charge and quantum numbers

Positron (e⁺)

The antiparticle of the electron; charge +1, mass same as electron

Pair Production

A photon converts into a particle–antiparticle pair (e.g., γ → e⁻ + e⁺)

Annihilation

A particle and antiparticle collide and convert entirely to photons (e⁻ + e⁺ → 2γ)

Conservation of Charge

Total electric charge is conserved in every interaction

Conservation of Lepton Number

Total lepton number (L) is conserved; leptons count +1, antileptons −1

Conservation of Baryon Number

Total baryon number (B) is conserved; baryons count +1, antibaryons −1

CP Violation

Slight asymmetry between matter and antimatter behavior; explains matter dominance in universe

Pair Production and Annihilation

Pair production: γ → e⁻ + e⁺ (requires photon energy ≥ 2mₑc² ≈ 1.022 MeV)

Annihilation: e⁻ + e⁺ → 2γ (each photon carries energy mₑc² ≈ 0.511 MeV)

Two photons are produced (not one) to conserve both energy and momentum.

Feynman Diagrams

Feynman diagrams are visual representations of particle interactions. Time flows left to right. Straight lines represent fermions (arrows forward = particles, backward = antiparticles). Wavy or curly lines represent bosons (force carriers). Each vertex where lines meet represents an interaction. They are a bookkeeping tool — each diagram corresponds to a mathematical term in the interaction probability.
Example 1

An electron and a positron annihilate. What are the products and why are two photons produced instead of one?

Answer:Products: 2 gamma-ray photons (e⁻ + e⁺ → 2γ). One photon cannot simultaneously conserve both energy and momentum in the center-of-mass frame. Two back-to-back photons each carrying 0.511 MeV satisfy both conservation laws.
Example 2

A photon with energy 1.5 MeV enters a lead plate. Can it undergo pair production? (Threshold = 1.022 MeV)

Answer:Yes — 1.5 MeV > 1.022 MeV (the minimum energy needed to create an electron–positron pair). The excess energy (0.478 MeV) becomes kinetic energy of the produced particles.
Example 3

Check whether the reaction p → e⁺ + π⁰ conserves baryon number.

Answer:Left side: baryon number B = +1 (proton). Right side: e⁺ has B = 0; π⁰ (meson) has B = 0. Total B on right = 0 ≠ 1. Baryon number is NOT conserved — this reaction is forbidden.
Example 4

In beta-minus decay: n → p + e⁻ + ν̄ₑ. Verify lepton number conservation.

Answer:Left side: L = 0 (neutron is a baryon, not a lepton). Right side: e⁻ has L = +1; ν̄ₑ (antineutrino) has L = −1. Total L on right = +1 + (−1) = 0. Lepton number IS conserved. ✓
Example 5

Why does the universe contain more matter than antimatter if the Big Bang produced equal amounts of each?

Answer:CP violation — a slight asymmetry in the laws of physics between matter and antimatter — caused matter to survive slightly more than antimatter during the early universe. For every ~10⁹ + 1 matter particles, there were ~10⁹ antimatter particles; after annihilation, the ~1 excess matter particle per billion survived to form all the matter we see today.
Guided Problem 1

What is the antiparticle of the proton? What are its charge and mass?

Hint: Antiparticles have the same mass but opposite charge.

Guided Problem 2

A photon produces a muon–antimuon pair (μ⁻ + μ⁺). What is the minimum photon energy required? (mμ = 105.7 MeV/c²)

Hint: Minimum energy = 2 × rest mass energy of one muon.

Guided Problem 3

Check charge conservation in: γ → e⁻ + e⁺.

Hint: Photon has charge 0; add the charges of the products.

Guided Problem 4

In a Feynman diagram for electron–electron scattering, what boson is exchanged?

Hint: Electrons interact via the electromagnetic force.

Guided Problem 5

Is the reaction n → p + e⁻ + ν̄ₑ allowed? Check charge, baryon number, and lepton number.

Hint: Check each conservation law separately.

Key Vocabulary

Antimatter

Matter composed of antiparticles, each with the same mass as its particle counterpart but opposite charge and quantum numbers.

Example: A positron (e⁺) is the antimatter counterpart of the electron (e⁻).

Pair Production

The creation of a particle–antiparticle pair from a high-energy photon (requires photon energy ≥ 2mc²).

Example: A gamma ray with energy > 1.022 MeV can produce an electron–positron pair near a nucleus.

Annihilation

The process in which a particle and its antiparticle collide and convert their combined mass entirely into photons.

Example: PET scans detect the two 0.511 MeV gamma rays produced when a positron annihilates with an electron in tissue.

CP Violation

A slight asymmetry in the behavior of matter and antimatter under combined charge conjugation (C) and parity (P) transformations.

Example: CP violation in kaon and B-meson decays explains why the universe has more matter than antimatter.

Interactive Practice — 5 Questions

1

What are the products of electron–positron annihilation?

2

Pair production requires a photon with energy of at least:

3

Which conservation law forbids the reaction p → e⁺ + γ?

4

In beta-minus decay (n → p + e⁻ + ν̄ₑ), why is an antineutrino produced?

5

CP violation is significant because it explains:

Independent Practice

1

Describe pair production and annihilation, including the minimum photon energy for pair production and the energy of photons produced in annihilation.

2

Check all three conservation laws (charge, lepton number, baryon number) for the reaction: π⁺ → μ⁺ + νμ.

3

Explain how PET (Positron Emission Tomography) scans use antimatter to create medical images.

4

What is CP violation and why is it necessary to explain the matter-dominated universe we observe?

5

★ Draw and label a Feynman diagram for electron–positron annihilation (e⁻ + e⁺ → 2γ). Identify all particles, antiparticles, and force carriers in your diagram.

Challenge
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Common Mistakes

Thinking annihilation destroys matter and violates conservation of energy.

Mass is converted to photon energy via E = mc². Total energy is conserved — it just changes form.

Assuming any photon can undergo pair production.

The photon must have energy ≥ 2mc² of the particle being created. For e⁻e⁺ pairs, this is 1.022 MeV minimum.

Forgetting that lepton number must be checked by family (electron, muon, tau separately).

In most Standard Model processes, each lepton family number is separately conserved. An electron neutrino cannot substitute for a muon neutrino.

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Math Tips

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For pair production threshold: E_photon ≥ 2mc². For annihilation: each photon carries energy mc² = 0.511 MeV (for e⁻e⁺). Always check charge, baryon number, AND lepton number for any reaction.