Neutrino Oscillation

Neutrino oscillation is a fundamental quantum phenomenon in which a neutrino created with a specific flavour (electron, muon, or tau) changes into another flavour as it propagates through space. This process provides direct evidence that neutrinos have mass contrary to the original assumption in the Standard Model of particle physics that they are massless. The discovery of neutrino oscillation represents one of the most important breakthroughs in modern particle physics, reshaping our understanding of the subatomic world and leading to a revision of the Standard Model.

Background and Discovery

Neutrinos were first proposed in 1930 by Wolfgang Pauli to explain the apparent loss of energy and momentum in beta decay. Later, Enrico Fermi developed the theory of weak interactions, formally introducing neutrinos as neutral, nearly massless particles that interact only via the weak nuclear force.
Initially, only one type of neutrino was known, but the discovery of the muon neutrino (νμ) in 1962 and the tau neutrino (ντ) in 2000 established three distinct neutrino flavours corresponding to the three charged leptons electron, muon, and tau.
The idea that neutrinos might change flavour was first proposed by Bruno Pontecorvo in the 1950s, inspired by the phenomenon of neutral kaon mixing. However, experimental confirmation came much later, primarily through studies of solar neutrinos and atmospheric neutrinos, which revealed discrepancies between predicted and observed fluxes.
Key experimental milestones include:

• Solar Neutrino Problem (1960s–1990s): Experiments such as Ray Davis’s Homestake experiment detected only one-third of the expected number of electron neutrinos from the Sun, suggesting a transformation into other flavours.
• Atmospheric Neutrinos (1998): The Super-Kamiokande experiment in Japan observed a deficit of muon neutrinos produced by cosmic rays, depending on their travel distance through Earth, confirming flavour oscillation.
• Reactor and Accelerator Experiments: Subsequent experiments such as KamLAND, SNO, Daya Bay, T2K, and NOνA provided precise measurements of oscillation parameters and confirmed the phenomenon beyond doubt.

The confirmation of neutrino oscillations led to the 2002 Nobel Prize in Physics being awarded to Raymond Davis Jr. and Masatoshi Koshiba, and the 2015 Nobel Prize to Takaaki Kajita and Arthur B. McDonald for their decisive contributions to the discovery.

Theoretical Framework

Neutrino oscillation arises because the flavour eigenstates (νe, νμ, ντ) in which neutrinos are produced and detected are not identical to the mass eigenstates (ν1, ν2, ν3) that propagate through space. The two sets of states are related by a quantum mechanical transformation represented by the Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix, analogous to the CKM matrix in quark mixing.
Mathematically,
∣να⟩=∑iUαi∣νi⟩|\nu_\alpha\rangle = \sum_i U_{\alpha i} |\nu_i\rangle∣να​⟩=i∑​Uαi​∣νi​⟩
where ∣να⟩|\nu_\alpha\rangle∣να​⟩ represents the flavour state (α = e, μ, τ), ∣νi⟩|\nu_i\rangle∣νi​⟩ represents the mass state (i = 1, 2, 3), and UαiU_{\alpha i}Uαi​ are the elements of the unitary PMNS matrix.
As neutrinos travel, the difference in their masses causes the mass eigenstates to accumulate different phase factors, leading to interference and oscillation between flavour states. The probability that a neutrino of flavour α transforms into flavour β after travelling a distance L is given by:
P(να→νβ)=sin⁡2(2θ)sin⁡2(1.27Δm2LE)P(\nu_\alpha \rightarrow \nu_\beta) = \sin^2(2\theta) \sin^2\left(\frac{1.27 \Delta m^2 L}{E}\right)P(να​→νβ​)=sin2(2θ)sin2(E1.27Δm2L​)
where:

• θ\thetaθ = mixing angle between the flavours,
• Δm2\Delta m^2Δm2 = difference in the squares of neutrino masses (m₂² – m₁²) in eV²,
• L = distance travelled (in km),
• E = neutrino energy (in GeV).

This equation implies that oscillations depend on the ratio of distance to energy (L/E), which determines the oscillation wavelength.

Mixing Angles and Mass Differences

Experimental results show that three mixing angles and two independent mass-squared differences govern neutrino oscillations:

• Solar neutrino parameters:
  • Δm212≈7.5×10−5 eV2\Delta m_{21}^2 ≈ 7.5 × 10^{-5} \, \text{eV}^2Δm212​≈7.5×10−5eV2
  • Mixing angle θ12≈33°θ_{12} ≈ 33°θ12​≈33°
• Atmospheric neutrino parameters:
  • ∣Δm322∣≈2.5×10−3 eV2|\Delta m_{32}^2| ≈ 2.5 × 10^{-3} \, \text{eV}^2∣Δm322​∣≈2.5×10−3eV2
  • Mixing angle θ23≈45°θ_{23} ≈ 45°θ23​≈45°
• Reactor neutrino mixing:
  • θ13≈8.5°θ_{13} ≈ 8.5°θ13​≈8.5° (small but non-zero)

These parameters describe a nearly maximal mixing between νμ and ντ and substantial mixing between νe and νμ.
However, the absolute mass scale of neutrinos remains unknown; only the mass differences are measurable from oscillations. Cosmological and beta decay experiments suggest that the total neutrino mass is less than 0.1–0.2 eV.

Types of Neutrino Oscillations

Neutrino oscillations occur in various contexts, depending on the neutrino source and medium:

• Solar Neutrino Oscillation:
  • Electron neutrinos produced in the Sun oscillate into muon or tau neutrinos during their journey to Earth.
  • Enhanced by the Mikheyev–Smirnov–Wolfenstein (MSW) effect, where oscillations are modified due to interactions with solar matter.
• Atmospheric Neutrino Oscillation:
  • Caused by cosmic ray interactions with Earth’s atmosphere.
  • Observed as a deficit in muon neutrinos passing through the Earth compared with those coming from above.
• Reactor Neutrino Oscillation:
  • Electron antineutrinos emitted from nuclear reactors oscillate over distances of 1–100 km, measured by experiments such as Daya Bay and Double Chooz.
• Accelerator Neutrino Oscillation:
  • Artificial neutrino beams generated in particle accelerators are directed over hundreds of kilometres to distant detectors (e.g., T2K in Japan and NOνA in the USA).

These experiments collectively provide consistent measurements of oscillation parameters and confirm the three-flavour neutrino model.

The MSW Effect

The Mikheyev–Smirnov–Wolfenstein (MSW) effect describes the modification of neutrino oscillation behaviour as neutrinos pass through matter, such as the Sun or Earth. In matter, neutrinos interact differently with electrons, altering their effective masses and mixing angles. This leads to a resonant enhancement of oscillations, particularly for solar neutrinos, explaining the observed suppression of electron neutrino flux at specific energies.

Experimental Facilities and Observations

Numerous international collaborations have advanced neutrino oscillation research:

• Super-Kamiokande (Japan): Provided decisive evidence for atmospheric neutrino oscillation.
• Sudbury Neutrino Observatory (Canada): Demonstrated total neutrino flux conservation, confirming flavour conversion.
• KamLAND (Japan): Verified solar neutrino oscillation parameters using reactor neutrinos.
• Daya Bay (China): Measured the small but crucial θ₁₃ angle.
• T2K (Japan) and NOνA (USA): Investigate neutrino–antineutrino asymmetry and CP violation in the neutrino sector.
• India-based Neutrino Observatory (INO): Planned to study atmospheric neutrinos using a magnetised iron calorimeter to determine the neutrino mass hierarchy.

Implications for Physics

The discovery of neutrino oscillations has profound implications:

• Evidence of Neutrino Mass: Confirms that neutrinos have non-zero masses, requiring an extension to the Standard Model.
• Lepton Mixing and CP Violation: Suggests possible CP violation in the lepton sector, potentially explaining the matter–antimatter asymmetry in the Universe.
• Cosmological Impact: Neutrinos influence large-scale structure formation and the evolution of the early Universe.
• Beyond the Standard Model: Oscillations hint at new physics, including sterile neutrinos, mass generation mechanisms (such as the see-saw mechanism), and Grand Unified Theories (GUTs).

Current Challenges and Future Prospects

Despite major progress, several questions remain unresolved:

• The absolute neutrino mass scale is still unknown.
• The mass hierarchy (whether m₃ is heavier or lighter than m₁ and m₂) is under investigation.
• The degree of CP violation in neutrinos remains to be precisely measured.
• The possible existence of sterile neutrinos beyond the three known flavours is still debated.

Upcoming experiments such as DUNE (Deep Underground Neutrino Experiment) in the United States, Hyper-Kamiokande in Japan, and JUNO in China aim to answer these open questions with greater precision.