Neutrino Physics: Fundamentals, Frontiers, and Probes

A 35-minute review (2026)

Dmitry V. Naumov

Neutrinos in the Standard Model

  • Three flavors: \(\nu_e\), \(\nu_\mu\), \(\nu_\tau\)
  • Neutral spin-\(1/2\) fermions
  • Produced and detected through the weak interaction
  • In the minimal renormalizable Standard Model, neutrinos are massless

Oscillations show that at least two neutrinos have nonzero mass.

The invisible width of the \(Z\) is consistent with three light active neutrinos.

Why neutrinos are unusual messengers

The mean free path is

\[ \lambda_\nu = \frac{1}{n\sigma}. \]

A 1 MeV solar neutrino

\[ \sigma(\nu_e e)\sim10^{-44}\ \mathrm{cm^2}, \qquad \lambda_\nu\sim10^{20}\ \mathrm{cm} \sim10^9 R_\odot. \]

The Sun is essentially transparent.

A 1 PeV neutrino crossing Earth

\[ \sigma(\nu N)\sim10^{-33}\ \mathrm{cm^2}, \qquad \lambda_\nu\sim3\times10^3\ \mathrm{km}. \]

At extreme energies, even Earth becomes opaque.

Weak interaction makes neutrinos both difficult to detect and uniquely informative.

How much lead stops a neutrino?

Flavor states and mass states

\[ \boxed{\displaystyle |\nu_\alpha\rangle=\sum_i U_{\alpha i}^{*}|\nu_i\rangle } \]

Flavor states \(\nu_e,\nu_\mu,\nu_\tau\)

Produced and detected in weak interactions.

Mass states \(\nu_1,\nu_2,\nu_3\)

Propagate with definite masses and accumulate different phases.

The two bases do not coincide. This mismatch and distinct neutrino masses are the origin of oscillations.

Neutrino oscillations

\[ P(\nu_e\!\to\!\nu_\mu)= \sin^2 2\theta\, \sin^2\!\left(\frac{\Delta m^2L}{4E}\right). \]

Different propagation phases convert one detectable flavor mixture into another.

How do we know?

Neutrino source Observed pattern What it establishes
Solar Energy-dependent \(\nu_e\) survival Flavor conversion in matter and vacuum
Atmospheric Zenith- and energy-dependent \(\nu_\mu\) disappearance Oscillations over Earth-scale baselines
Reactors Spectral disappearance of \(\bar\nu_e\) Precise mixing and mass splitting
Accelerators Disappearance and appearance Controlled tests across flavors

One three-neutrino framework describes independent sources, energies, and baselines.

The three-neutrino picture

Mixing

\[ \theta_{12}\approx34^\circ, \qquad \theta_{13}\approx9^\circ, \qquad \theta_{23}\approx45^\circ. \]

Mass splittings

\[ \Delta m^2_{21}\approx7.4\times10^{-5}\ \mathrm{eV^2}, \]

\[ |\Delta m^2_{31}|\approx2.5\times10^{-3}\ \mathrm{eV^2}. \]

The minimal oscillation picture contains

  • three mixing angles;
  • two independent mass-squared differences;
  • one Dirac CP phase, \(\delta_{\rm CP}\).

If neutrinos are Majorana particles, two additional phases do not affect oscillations.

Mass ordering

Normal ordering

\[m_1<m_2<m_3\]

Inverted ordering

\[m_3<m_1<m_2\]

Solar data fix \(m_2>m_1\). The sign of the atmospheric splitting distinguishes the two spectra.

JUNO reads the interference pattern

  • Reactor antineutrinos travel about 52.5 km to the detector.
  • Fine spectral ripples carry information on the ordering in a vacuum-dominated measurement.
  • A 20 kt liquid-scintillator target and precise energy response make the ripples measurable.
  • TAO and Daya Bay constrain the unoscillated reactor spectrum.

JUNO: larger data set, sharper parameters

JUNO analysis
Live time 207.2 days
IBD candidates 8294
\(\sin^2\theta_{12}\) \(0.3036\pm0.0064\)
\(\Delta m^2_{21}\) \((7.388\pm0.078)\times10^{-5}\ \mathrm{eV^2}\)
\(\Delta m^2_{31}\), NO \(+2.509^{+0.027}_{-0.025}\times10^{-3}\ \mathrm{eV^2}\)
  • Combining JUNO and Daya Bay with long-baseline constraints gives \(\chi^2_{\rm IO}-\chi^2_{\rm NO}=4.86\), corresponding to a one-sided \(2.1\sigma\) indication for normal ordering.

JUNO: one detector, a broad physics program

Cutaway view of Earth's crust, mantle, outer core, and inner core

The Sun seen as a bright orange disk

0.0 billion years One sweep compresses the age of the Universe
No proton decay has been observed
\(K^+\)\(\mu^+\)\(e^+\)

Run the cosmic clock: the proton remains. The candidate button then illustrates a possible signal.

Illustration only: the clock is compressed and the candidate is triggered deliberately, not predicted at the Universe's age. JUNO searches for \(p\to\bar\nu K^+\); the kaon, its decay daughter, and a later Michel positron can produce three time-correlated light pulses.

What is the neutrino mass?

Observable Sensitive to
Oscillations Differences \(\Delta m^2_{ij}\)
Beta-decay kinematics \(m_\beta^2=\sum_i|U_{ei}|^2m_i^2\)
Cosmology The mass sum \(\sum_i m_i\)

Oscillations set the spacing of the spectrum, not its absolute position.

KATRIN: electron motion through the MAC-E filter

KATRIN: the endpoint becomes a count rate

Dirac or Majorana?

Dirac neutrino Majorana neutrino
Particle and antiparticle are distinct Particle and antiparticle are identical
Lepton number can remain conserved Lepton-number violation becomes possible

The experimental path is neutrinoless double beta decay:

\[ \boxed{(A,Z)\rightarrow(A,Z+2)+2e^-} \]

No neutrinos appear in the final state. Observation would establish lepton-number violation and the Majorana nature of neutrinos.

CP violation

\[ \boxed{ P(\nu_\alpha\to\nu_\beta) \neq P(\bar\nu_\alpha\to\bar\nu_\beta) } \]

  • The phase \(\delta_{\rm CP}\) controls CP-odd effects in three-flavor oscillations.

  • Long-baseline experiments compare neutrino and antineutrino appearance while controlling matter effects.

The central question is whether lepton mixing violates CP, and by how much.

DUNE: a 1300 km matter baseline

  • A beam from Fermilab reaches the far detector in South Dakota.
  • The long baseline strengthens the matter effect, helping separate ordering from CP effects.
  • Near and far measurements constrain the beam and interaction model.
  • Appearance channels compare \(\nu_\mu\to\nu_e\) with \(\bar{\nu}_\mu\to\bar{\nu}_e\).

Neutrinos as probes

Source Typical energy Hidden information carried by neutrinos
Nucleon target GeV Quark-flavor content and parton distributions
Sun MeV Nuclear burning in the solar core
Earth MeV Radioactive heat from the crust and mantle
Core-collapse supernova MeV Collapse, bounce, accretion, and cooling
Cosmic accelerators TeV–PeV Hadronic processes in extreme environments

Neutrinos escape dense regions that are opaque to light and point back to their origin.

Looking inside the Sun

Solar neutrinos provide a direct, real-time view of nuclear reactions in the core.

Different components probe different reactions, temperatures, and production radii.

Looking inside the Earth

Crust enlarged; paths illustrative. Layers: USGS · U/Th sources: Borexino.

Electron antineutrinos from the \(^{238}\)U and \(^{232}\)Th decay chains reveal:

  • the radiogenic contribution to Earth’s heat;
  • the distribution of heat-producing elements;
  • the difficult separation of crust and mantle signals.

Geoneutrinos connect particle detection to the planet’s thermal history.

Supernova neutrinos

SN 1987A: NASA, ESA, CSA, STScI, and collaborators

The roughly two dozen neutrinos detected from SN 1987A opened neutrino astronomy beyond the Sun.

A future Galactic event could resolve:

  • collapse and core bounce;
  • accretion dynamics;
  • proto-neutron-star cooling;
  • flavor transformation in extreme matter.

High-energy neutrino astronomy

  • Neutral messengers point back to their sources.
  • Hadronic interactions produce neutrinos together with photons and cosmic rays.
  • IceCube, Baikal-GVD, and KM3NeT open complementary views of the sky.

The signal is faint, but it is unusually clean evidence of particle acceleration.

Baikal-GVD

Deployment on Lake Baikal. Photo: B. Shaybonov.

A cubic-kilometer-scale telescope uses deep, clear lake water as both target and Cherenkov medium.

The program addresses:

  • the diffuse astrophysical flux;
  • searches for point-like sources;
  • the Galactic plane;
  • multimessenger coincidences.

Summary

  • Fundamentals

    • Neutrino mass and mixing

  • Frontiers

    • Ordering, absolute mass, Majorana nature, and CP violation

  • Probes

    • The Sun, Earth, supernovae, and the high-energy Universe

Want to go deeper?

We teach this field from the ground up: a two-year online program, Neutrino Physics and Particle Astrophysics («Физика нейтрино и астрофизика частиц»).

  • More than 30 courses in four modules
  • A theory track or an experiment track, with research projects
  • Stipends for students who continue into the second module, from March 2027
  • Courses are taught in Russian

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