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Neutrino oscillation is a quantum mechanical phenomenon in which a neutrino created with a specific lepton family number ("lepton flavor": electron, muon, or tau) can later be measured to have a different lepton family number. The probability of measuring a particular flavor for a neutrino varies between three known states, as it propagates through space.^[1]

First predicted by Bruno Pontecorvo in 1957,^[2][3] neutrino oscillation has since been observed by a multitude of experiments in several different contexts. Most notably, the existence of neutrino oscillation resolved the long-standing solar neutrino problem.

Neutrino oscillation is of great theoretical and experimental interest, as the precise properties of the process can shed light on several properties of the neutrino. In particular, it implies that the neutrino has a non-zero mass outside the Einstein-Cartan torsion,^[4][5] which requires a modification to the Standard Model of particle physics.^[1] The experimental discovery of neutrino oscillation, and thus neutrino mass, by the Super-Kamiokande Observatory and the Sudbury Neutrino Observatories was recognized with the 2015 Nobel Prize for Physics.^[6]

A great deal of evidence for neutrino oscillation has been collected from many sources, over a wide range of neutrino energies and with many different detector technologies.^[7] The 2015 Nobel Prize in Physics was shared by Takaaki Kajita and Arthur B. McDonald for their early pioneering observations of these oscillations.

Neutrino oscillation is a function of the ratio  ⁠ L / E ⁠ , where L is the distance traveled and E is the neutrino's energy. (Details in § Propagation and interference below.) All available neutrino sources produce a range of energies, and oscillation is measured at a fixed distance for neutrinos of varying energy. The limiting factor in measurements is the accuracy with which the energy of each observed neutrino can be measured. Because current detectors have energy uncertainties of a few percent, it is satisfactory to know the distance to within 1%.

The first experiment that detected the effects of neutrino oscillation was Ray Davis' Homestake experiment in the late 1960s, in which he observed a deficit in the flux of solar neutrinos with respect to the prediction of the Standard Solar Model, using a chlorine-based detector.^[8] This gave rise to the solar neutrino problem. Many subsequent radiochemical and water Cherenkov detectors confirmed the deficit, but neutrino oscillation was not conclusively identified as the source of the deficit until the Sudbury Neutrino Observatory provided clear evidence of neutrino flavor change in 2001.^[9]

Solar neutrinos have energies below 20 MeV. At energies above 5 MeV, solar neutrino oscillation actually takes place in the Sun through a resonance known as the MSW effect, a different process from the vacuum oscillation described later in this article.^[1]

Following the theories that were proposed in the 1970s suggesting unification of electromagnetic, weak, and strong forces, a few experiments on proton decay followed in the 1980s. Large detectors such as IMB, MACRO, and Kamiokande II have observed a deficit in the ratio of the flux of muon to electron flavor atmospheric neutrinos (see muon decay). The Super-Kamiokande experiment provided a very precise measurement of neutrino oscillation in an energy range of hundreds of MeV to a few TeV, and with a baseline of the diameter of the Earth; the first experimental evidence for atmospheric neutrino oscillations was announced in 1998.^[10]

Many experiments have searched for oscillation of electron anti-neutrinos produced in nuclear reactors. No oscillations were found until a detector was installed at a distance 1–2 km. Such oscillations give the value of the parameter θ₁₃. Neutrinos produced in nuclear reactors have energies similar to solar neutrinos, of around a few MeV. The baselines of these experiments have ranged from tens of meters to over 100 km (parameter θ₁₂). Mikaelyan and Sinev proposed to use two identical detectors to cancel systematic uncertainties in reactor experiment to measure the parameter θ₁₃.^[11]

In December 2011, the Double Chooz experiment found that θ₁₃ ≠ 0 .^[12] Then, in 2012, the Daya Bay experiment found that  θ₁₃ ≠ 0  with a significance of 5.2 σ ;^[13] These results have since been confirmed by RENO.^[14]

Neutrino beams produced at a particle accelerator offer the greatest control over the neutrinos being studied. Many experiments have taken place that study the same oscillations as in atmospheric neutrino oscillation using neutrinos with a few GeV of energy and several-hundred-km baselines. The MINOS, K2K, and Super-K experiments have all independently observed muon neutrino disappearance over such long baselines.^[1]

Data from the LSND experiment appear to be in conflict with the oscillation parameters measured in other experiments. Results from the MiniBooNE appeared in Spring 2007 and contradicted the results from LSND, although they could support the existence of a fourth neutrino type, the sterile neutrino.^[1]

In 2010, the INFN and CERN announced the observation of a tauon particle in a muon neutrino beam in the OPERA detector located at Gran Sasso, 730 km away from the source in Geneva.^[15]

T2K, using a neutrino beam directed through 295 km of earth and the Super-Kamiokande detector, measured a non-zero value for the parameter θ₁₃ in a neutrino beam.^[16] NOνA, using the same beam as MINOS with a baseline of 810 km, is sensitive to the same.

Neutrino oscillation arises from mixing between the flavor and mass eigenstates of neutrinos. That is, the three neutrino states that interact with the charged leptons in weak interactions are each a different superposition of the three (propagating) neutrino states of definite mass. Neutrinos are emitted and absorbed in weak processes in flavor eigenstates^[a] but travel as mass eigenstates.^[17]

As a neutrino superposition propagates through space, the quantum mechanical phases of the three neutrino mass states advance at slightly different rates, due to the slight differences in their respective masses. This results in a changing superposition mixture of mass eigenstates as the neutrino travels; but a different mixture of mass eigenstates corresponds to a different mixture of flavor states. For example, a neutrino born as an electron neutrino will be some mixture of electron, mu, and tau neutrino after traveling some distance. Since the quantum mechanical phase advances in a periodic fashion, after some distance the state will nearly return to the original mixture, and the neutrino will be again mostly electron neutrino. The electron flavor content of the neutrino will then continue to oscillate – as long as the quantum mechanical state maintains coherence. Since mass differences between neutrino flavors are small in comparison with long coherence lengths for neutrino oscillations, this microscopic quantum effect becomes observable over macroscopic distances.

In contrast, due to their larger masses, the charged leptons (electrons, muons, and tau leptons) have never been observed to oscillate. In nuclear beta decay, muon decay, pion decay, and kaon decay, when a neutrino and a charged lepton are emitted, the charged lepton is emitted in incoherent mass eigenstates such as  |
e⁻
⟩ , because of its large mass. Weak-force couplings compel the simultaneously emitted neutrino to be in a "charged-lepton-centric" superposition such as  |
ν
_e ⟩ , which is an eigenstate for a "flavor" that is fixed by the electron's mass eigenstate, and not in one of the neutrino's own mass eigenstates. Because the neutrino is in a coherent superposition that is not a mass eigenstate, the mixture that makes up that superposition oscillates significantly as it travels. No analogous mechanism exists in the Standard Model that would make charged leptons detectably oscillate. In the four decays mentioned above, where the charged lepton is emitted in a unique mass eigenstate, the charged lepton will not oscillate, as single mass eigenstates propagate without oscillation.

The case of (real) W boson decay is more complicated: W boson decay is sufficiently energetic to generate a charged lepton that is not in a mass eigenstate; however, the charged lepton would lose coherence, if it had any, over interatomic distances (0.1 nm) and would thus quickly cease any meaningful oscillation. More importantly, no mechanism in the Standard Model is capable of pinning down a charged lepton into a coherent state that is not a mass eigenstate, in the first place; instead, while the charged lepton from the W boson decay is not initially in a mass eigenstate, neither is it in any "neutrino-centric" eigenstate, nor in any other coherent state. It cannot meaningfully be said that such a featureless charged lepton oscillates or that it does not oscillate, as any "oscillation" transformation would just leave it the same generic state that it was before the oscillation. Therefore, detection of a charged lepton oscillation from W boson decay is infeasible on multiple levels.^[18][19]

The idea of neutrino oscillation was first put forward in 1957 by Bruno Pontecorvo, who proposed that neutrino–antineutrino transitions may occur in analogy with neutral kaon mixing.^[2] Although such matter–antimatter oscillation had not been observed, this idea formed the conceptual foundation for the quantitative theory of neutrino flavor oscillation, which was first developed by Maki, Nakagawa, and Sakata in 1962^[20] and further elaborated by Pontecorvo in 1967.^[3] One year later the solar neutrino deficit was first observed,^[21] and that was followed by the famous article by Gribov and Pontecorvo published in 1969 titled "Neutrino astronomy and lepton charge".^[22]

The concept of neutrino mixing is a natural outcome of gauge theories with massive neutrinos, and its structure can be characterized in general.^[23] In its simplest form it is expressed as a unitary transformation relating the flavor and mass eigenbasis and can be written as

${\displaystyle \left|\nu _{i}\right\rangle =\sum _{\alpha }U_{\alpha i}^{*}\left|\nu _{\alpha }\right\rangle ,}$

${\displaystyle \left|\nu _{\alpha }\right\rangle =\sum _{i}U_{\alpha i}\left|\nu _{i}\right\rangle ,}$

where

• ${\displaystyle \ \left|\nu _{\alpha }\right\rangle \ }$ is a neutrino with definite flavor α = e (electron), μ (muon) or τ (tauon),
• ${\displaystyle \ \left|\nu _{i}\right\rangle \ }$ is a neutrino with definite mass ${\displaystyle \ m_{i}\ ,}$ ${\displaystyle i=1,2,3,}$
• the asterisk (${\displaystyle ^{*}}$) represents a complex conjugate; for antineutrinos, the complex conjugate should be removed from the first equation and inserted into the second.

${\displaystyle U_{\alpha i}}$ represents the Pontecorvo–Maki–Nakagawa–Sakata matrix (also called the PMNS matrix, lepton mixing matrix, or sometimes simply the MNS matrix). It is the analogue of the CKM matrix describing the analogous mixing of quarks. If this matrix were the identity matrix, then the flavor eigenstates would be the same as the mass eigenstates. However, experiment shows that it is not.

When the standard three-neutrino theory is considered, the matrix is 3×3. If only two neutrinos are considered, a 2×2 matrix is used. If one or more sterile neutrinos are added (see later), it is 4×4 or larger. In the 3×3 form, it is given by^[24]