Conservation laws in particle physics are the bedrock of understanding subatomic interactions. They dictate how particles behave, interact, and transform, providing a framework for predicting outcomes and discovering new particles.

These laws, including energy, momentum, and charge conservation, play a crucial role in elementary particle physics. They help explain everything from particle decays to the stability of matter, connecting the microscopic world of particles to the broader universe we observe.

Conservation Laws in Particle Physics

Fundamental Conservation Principles

• Energy, momentum, and charge conservation apply to all particle interactions and decays
  • Total energy before and after a reaction or decay remains equal
  • Vector sum of all particle momenta stays constant
  • Net charge of an isolated system remains unchanged
• Angular momentum conservation dictates total angular momentum, including spin, must be preserved
• Color charge conservation in strong interactions maintains neutral total color charge in quark interactions and hadron formation
• Parity conservation applies to electromagnetic and strong interactions
  • Overall parity of a system remains unchanged during these processes
• Charge conjugation symmetry implies replacing particles with antiparticles does not affect interaction outcomes (when conserved)

Quantum Number Conservation

• Lepton number conservation requires constant total lepton number in all processes
  • Leptons assigned +1, antileptons -1, all other particles 0
  • Lepton flavor numbers (electron, muon, tau) separately conserved, except in neutrino oscillations
• Baryon number conservation maintains constant total baryon number
  • Baryons assigned +1, antibaryons -1, all other particles 0
• Combined lepton and baryon number conservation explains allowed and forbidden particle decays or reactions

Applying Conservation Laws to Particles

Energy and Momentum Conservation

• Center-of-mass energy conservation in particle collisions determines producible particle types
• Missing energy concept in particle detectors infers undetected particles (neutrinos)
• Two-body decay momentum conservation creates specific kinematic relationships between decay product momenta and energies
• Energy conservation includes rest mass energy and kinetic energy
  • Example: In positron-electron annihilation, rest mass energy converts to photon energy
• Momentum conservation applies to vector sum of momenta
  • Example: In pion decay ($\pi^+ \rightarrow \mu^+ + \nu_\mu$), muon and neutrino momenta balance

Charge Conservation Applications

• Electric charge conservation restricts possible decay modes of charged particles
  • Example: A positively charged pion cannot decay into two positively charged particles
• Charge conservation in particle production requires equal creation of particles and antiparticles
  • Example: In proton-proton collisions, quark-antiquark pairs are produced in equal numbers

Lepton and Baryon Number Conservation

Lepton Number Conservation

• Total lepton number remains constant in all particle interactions and decays
• Lepton flavor conservation applies separately to electron, muon, and tau numbers
  • Example: Muon decay ($\mu^- \rightarrow e^- + \bar{\nu}_e + \nu_\mu$) conserves total lepton number and individual flavor numbers
• Neutrino oscillations violate individual lepton flavor conservation but preserve total lepton number

Baryon Number Conservation

• Total baryon number remains constant in all particle interactions and decays
• Explains stability of lightest baryon (proton) against decay into lighter particles
  • Example: Proton decay into positron and neutral pion ($p \rightarrow e^+ + \pi^0$) forbidden by baryon number conservation
• Allows for production of baryon-antibaryon pairs in high-energy collisions
  • Example: Proton-antiproton pair production in electron-positron annihilation

Implications of Conservation Laws

Predictions and Constraints

• Conservation laws impose strict constraints on allowed particle reactions and decays
• Enable prediction of allowed processes and forbidden reactions
  • Example: Beta decay ($n \rightarrow p + e^- + \bar{\nu}_e$) allowed by all conservation laws
• Determine kinematic properties of decay products
  • Energies and angular distributions of particles produced in decays or collisions

Particle Discovery and Detection

• Combined application of conservation laws aids in identifying new particles
• Analysis of decay products and missing quantities in particle detectors reveals new particles
  • Example: Discovery of the neutrino through analysis of missing energy and momentum in beta decay
• Apparent conservation law violations indicate presence of unknown particles or interactions
  • Example: Observation of apparent energy non-conservation in beta decay led to neutrino hypothesis

Theoretical Implications

• Baryon number conservation prevents spontaneous proton decay in most theories
  • Leads to predictions of extremely long proton lifetimes (>10^34 years)
• Potential violations of baryon number conservation could explain matter-antimatter asymmetry in the universe
• Conservation law violations drive further research and theoretical developments
  • Example: Discovery of CP violation led to expanded theories of particle physics and cosmology