Leptons and neutrinos are key players in the Standard Model. They come in three families, each with a charged lepton and a neutrino. These particles have unique properties and follow conservation rules that shape our understanding of particle physics.

Neutrino oscillations shake things up by showing that neutrinos can change flavors as they travel. This discovery proves neutrinos have mass, challenging the original Standard Model and opening doors to new physics beyond what we currently know.

Lepton Families and Neutrinos

Lepton Family Structure

• Three lepton families in particle physics encompass electron, muon, and tau, each paired with a corresponding neutrino
• Electron family contains the electron (e⁻) and electron neutrino (νₑ)
• Muon family incorporates the muon (μ⁻) and muon neutrino (νμ)
• Tau family consists of the tau (τ⁻) and tau neutrino (ντ)
• Each lepton family possesses unique mass and flavor quantum numbers
• Antiparticles exist for every lepton, exhibiting opposite electric charge and lepton number
  • Positron (e⁺) serves as the antiparticle for the electron
  • Antimuon (μ⁺) acts as the antiparticle for the muon
• Lepton masses vary significantly across families
  • Electron mass ≈ 0.511 MeV/c²
  • Muon mass ≈ 105.7 MeV/c²
  • Tau mass ≈ 1776.9 MeV/c²

Neutrino Properties

• Neutrinos possess extremely small but non-zero masses
• Interact very weakly with matter through weak nuclear force and gravity
• Neutrinos come in three flavors corresponding to their associated leptons (electron, muon, tau)
• Originally thought to be massless in the Standard Model
• Neutrino mass hierarchy remains unknown (normal or inverted)
• Neutrinos can be left-handed or right-handed, but only left-handed neutrinos have been observed in nature
• Majorana vs. Dirac nature of neutrinos still undetermined
  • Majorana neutrinos would be their own antiparticles
  • Dirac neutrinos would have distinct antiparticles

Lepton Number Conservation

Lepton Number Quantum Rules

• Lepton number represents a quantum number assigned to each lepton family
• Particles carry a lepton number of +1
• Antiparticles possess a lepton number of -1
• Total lepton number remains conserved in all known particle interactions and decays
• Lepton family number conservation applies separately to electron, muon, and tau numbers in most interactions
  • Electron number conservation (e⁻ + νₑ remains constant)
  • Muon number conservation (μ⁻ + νμ remains constant)
  • Tau number conservation (τ⁻ + ντ remains constant)
• Neutrino oscillations violate individual lepton family number conservation but preserve total lepton number

Applications and Implications

• Lepton number conservation plays a fundamental role in understanding particle interactions and decay processes in the Standard Model
• Guides predictions and analysis of particle reactions (beta decay)
• Hypothetical processes like neutrinoless double beta decay would violate lepton number conservation if observed
  • Could indicate Majorana nature of neutrinos
  • Actively searched for in experiments (GERDA, EXO-200)
• Baryon-lepton number conservation suggests proton stability
• Lepton number violation could be linked to matter-antimatter asymmetry in the universe
• Some beyond Standard Model theories propose lepton number violation at high energies

Neutrino Oscillations

Mechanism and Description

• Neutrino oscillations describe quantum mechanical phenomenon where neutrinos change flavor as they propagate through space
• Oscillation occurs due to mixing of neutrino mass eigenstates, which differ from flavor eigenstates
• Neutrino mixing described by PMNS (Pontecorvo–Maki–Nakagawa–Sakata) matrix, relating flavor and mass eigenstates
• PMNS matrix characterized by three mixing angles (θ₁₂, θ₂₃, θ₁₃) and one CP-violating phase (δ)
• Probability of flavor change depends on neutrino energy, propagation distance, and mass-squared differences between neutrino states
• Oscillation probability given by $P(\nu_α → ν_β) = sin²(2θ) * sin²(1.27 * Δm² L/E)$
  • θ mixing angle
  • Δm² mass-squared difference in eV²
  • L propagation distance in km
  • E neutrino energy in GeV

Implications and Significance

• Neutrino oscillations imply non-zero neutrino masses, contradicting original Standard Model predictions
• Provides potential explanation for solar neutrino problem and atmospheric neutrino anomaly
• Oscillations carry significant implications for particle physics, cosmology, and understanding of early universe
• Suggests need for extension or modification of the Standard Model
• Offers insights into leptonic CP violation and matter-antimatter asymmetry
• Impacts neutrino astronomy and detection of astrophysical neutrinos
• Influences design of long-baseline neutrino experiments and neutrino factories

Evidence for Neutrino Oscillations

Atmospheric and Solar Neutrino Experiments

• Super-Kamiokande experiment provided strong evidence for atmospheric neutrino oscillations
  • Observed deficit in muon neutrinos coming from below (longer path through Earth)
  • Showed zenith angle dependence of muon neutrino flux
• Sudbury Neutrino Observatory (SNO) confirmed solar neutrino oscillations
  • Detected all neutrino flavors from the Sun using heavy water
  • Resolved solar neutrino problem by showing flavor transformation
• Homestake experiment first observed solar neutrino deficit (Ray Davis Jr.)
• GALLEX and SAGE experiments corroborated solar neutrino deficit using gallium detectors

Reactor and Accelerator Experiments

• Reactor neutrino experiments precisely measured oscillation parameters for reactor antineutrinos
  • KamLAND observed reactor antineutrino disappearance over long baselines
  • Daya Bay determined the value of θ₁₃ mixing angle with high precision
• Long-baseline accelerator experiments studied muon neutrino disappearance and electron neutrino appearance
  • K2K (KEK to Kamioka) first long-baseline neutrino oscillation experiment
  • MINOS measured atmospheric neutrino oscillation parameters
  • T2K observed electron neutrino appearance in a muon neutrino beam
• Short-baseline experiments like LSND and MiniBooNE produced anomalous results
  • Hinted at possible sterile neutrinos, requiring further investigation
• These experiments collectively establish three-flavor neutrino oscillation paradigm
• Provide measurements of mixing angles (θ₁₂, θ₂₃, θ₁₃) and mass-squared differences (Δm²₂₁, |Δm²₃₂|)
• Ongoing and future experiments aim to determine neutrino mass hierarchy and search for CP violation in lepton sector
  • DUNE (Deep Underground Neutrino Experiment)
  • Hyper-Kamiokande
• Discovery of neutrino oscillations led to 2015 Nobel Prize in Physics for Takaaki Kajita and Arthur B. McDonald