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Neutrino Masses and Oscillations

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Postulates of Special RelativityStandard Model Overview→→Leptogenesis and BaryogenesisNeutrino Mixing (PMNS Matrix)
neutrino-oscillations neutrino-mass atmospheric-neutrinos solar-neutrinos

Core Idea

Neutrino oscillations -- the quantum mechanical transformation of one neutrino flavor into another during propagation -- provide direct evidence that neutrinos have nonzero masses, which is the first confirmed physics beyond the minimal Standard Model. The oscillation probability depends on the mass-squared differences Delta m2, the mixing angles, and the baseline-to-energy ratio L/E, and the phenomenon has been observed in solar, atmospheric, reactor, and accelerator neutrinos.

Explainer

Neutrino oscillations are the first and so far only confirmed phenomenon requiring physics beyond the minimal Standard Model. The Standard Model as originally formulated contains only left-handed neutrinos with zero mass (no right-handed neutrino fields, no Yukawa couplings, no mass terms). The discovery that neutrinos oscillate between flavors -- implying they have nonzero masses and mix -- was recognized with the 2015 Nobel Prize (Kajita and McDonald, for Super-Kamiokande and SNO).

The oscillation formalism is analogous to quark mixing but involves the PMNS matrix (Pontecorvo-Maki-Nakagawa-Sakata) relating the three flavor eigenstates (nu_e, nu_mu, nu_tau) to the three mass eigenstates (nu_1, nu_2, nu_3). The oscillation probability in vacuum for two flavors is P(nu_alpha -> nu_beta) = sin^2(2*theta) * sin^2(Delta m2 * L / 4E). The full three-flavor case involves three mixing angles (theta_12, theta_13, theta_23), one CP-violating phase (delta_CP), and two mass-squared differences. All three angles have been measured: theta_12 ~ 34 degrees (solar, large), theta_23 ~ 49 degrees (atmospheric, near-maximal), theta_13 ~ 8.5 degrees (reactor, small but nonzero -- measured by Daya Bay, RENO, Double Chooz in 2012).

In matter, neutrino oscillations are modified by the MSW effect (Mikheyev-Smirnov-Wolfenstein): electron neutrinos experience an additional potential from coherent forward scattering on electrons (via W exchange), which modifies the effective mass-squared difference and mixing angle. In the Sun, this effect produces a resonant enhancement of oscillation that converts the majority of electron neutrinos to other flavors. The MSW effect is also what makes it possible to determine the neutrino mass ordering using long-baseline experiments or atmospheric neutrinos propagating through the Earth.

The major open questions in neutrino physics are: (1) the mass ordering -- is nu_3 the heaviest (normal) or lightest (inverted)? (2) the value of the CP phase delta_CP -- is there CP violation in the lepton sector, and if so, how much? (3) are neutrinos Dirac or Majorana particles -- do neutrinos have distinct antiparticles, or are they their own antiparticle? The first two will be addressed by DUNE, Hyper-Kamiokande, and JUNO in the coming decade. The third requires observing neutrinoless double beta decay, a process that violates lepton number and is possible only if neutrinos are Majorana fermions.

Practice Questions 3 questions

Prerequisite Chain

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → One-to-One Correspondence → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Making 10 as an Addition Strategy → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Dividing Integers → Unit Rates → Proportions → Percent Concept → Converting Between Fractions, Decimals, and Percents → Operations with Rational Numbers → Two-Step Equations → Solving Multi-Step Equations → Equations with Variables on Both Sides → Angle Pairs: Complementary, Supplementary, and Vertical → Parallel Lines and Transversals → Corresponding Angles → Alternate Interior Angles → Triangle Angle Sum Theorem → Exterior Angle Theorem → Triangle Inequality Theorem → Similar Triangles: AA Similarity → Similar Triangles: SSS and SAS Similarity → Proportions in Similar Triangles → Right Triangle Trigonometry Introduction → Sine, Cosine, and Tangent Ratios → Trigonometric Ratios Review → Radian Measure → Converting Between Degrees and Radians → The Unit Circle → Graphing Sine and Cosine → Graphing Tangent and Reciprocal Trigonometric Functions → Derivatives of Trigonometric Functions → Antiderivatives → Iterated Integrals and Fubini's Theorem → Double Integrals in Cartesian Coordinates → Double Integrals in Polar Coordinates → Double Integrals in Polar Coordinates → Double Integrals: Definition and Setup → Iterated Integrals and Fubini's Theorem → Double Integrals over Rectangular Regions → Double Integrals over General Regions → Applications of Double Integrals: Area, Mass, and Moments → Triple Integrals in Cartesian Coordinates → Triple Integrals in Cylindrical and Spherical Coordinates → Change of Variables and the Jacobian Determinant → Applications of Triple Integrals: Volume and Mass → Vector Fields and Their Representations → Line Integrals of Vector Fields → Work and Circulation → Line Integrals of Scalar and Vector Functions → Fundamental Theorem for Line Integrals → Conservative Vector Fields → Conservative Vector Fields and Potential Functions → Curl and Divergence of Vector Fields → Curl and Divergence → Divergence Theorem → Electric Flux and Divergence Theorem → Gauss's Law: Integral Form and Meaning → Solving Problems with Gauss's Law → Conductors in Electrostatic Equilibrium → Capacitance and Capacitors → Dielectrics → Dielectric Constant and Relative Permittivity → Electric Field Inside Dielectric Materials → Dielectric Materials and Polarization → Dielectric Susceptibility and Permittivity → Energy Density in Electric Fields → Electric Current and Current Density → Electrical Resistance and Resistivity → Ohm's Law and Circuit Elements → Electromotive Force (EMF) and Batteries → Kirchhoff's Circuit Laws: Voltage and Current → DC Circuit Network Analysis Methods → Transient Response in RC Circuits → RC Circuits → LC and RLC Circuits → AC Circuits: Fundamentals → Impedance and Reactance → AC Power and Resonance → Electromagnetic Waves → Postulates of Special Relativity → Time Dilation → Length Contraction → Lorentz Transformation → Relativistic Velocity Addition → Relativistic Momentum and Energy → Mass-Energy Equivalence and E=mc² → Photons as Particles with Energy and Momentum → Planck-Einstein Relation: Energy and Frequency → Photoelectric Effect → The Photon: Light as Quanta → Compton Scattering → Wave-Particle Duality → de Broglie Wavelength → The Schrödinger Equation → State Vectors and Wavefunctions → Quantum Superposition → The Measurement Problem → Interpretations of Quantum Mechanics → Postulates of Quantum Mechanics → Observables and Quantum Operators → Commutators and Commutation Relations → Quantum Angular Momentum → Quantum Mechanical Treatment of Hydrogen → Solving the Schrödinger Equation for Hydrogen Atom → Quantum Numbers → Electron Configuration → Periodic Trends → Covalent Bonding → Electronegativity and Bond Polarity → Ionic Bonding → Lewis Structures → VSEPR Theory and Molecular Geometry → Molecular Geometry and Electron Pair Geometry → Molecular Polarity and Dipole Moments → Intermolecular Forces → States of Matter and Phase Changes: Melting, Boiling, and Sublimation → Gas Laws and the Ideal Gas Equation → Gas Stoichiometry and Volume-Volume Calculations → Thermochemistry and Enthalpy → Heat Capacity and Calorimetry → Entropy and Molecular Disorder → Spontaneity and ΔG → Entropy and Gibbs Free Energy → Chemical Equilibrium → Statistical Mechanics: Ensembles and the Boltzmann Distribution → Partition Function: Definition and Properties → Helmholtz Free Energy → Gibbs Free Energy → Phase Transitions: First Order and Second Order → Critical Phenomena and Critical Exponents → Landau Theory of Phase Transitions → Symmetry Breaking and Phase Transitions → Goldstone's Theorem and Gapless Modes → Goldstone Theorem → Higgs Mechanism → Electroweak Unification → Standard Model Overview → Neutrino Masses and Oscillations

Longest path: 187 steps · 1265 total prerequisite topics

Prerequisites (2)

Leads To (2)