Neutrino Oscillations

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Neutrino oscillations are a phenomenon of quantum mechanical nature, intrinsically connected to the question of neutrino mass. The neutrino was originally theorized by Wolfgang Pauli in 1931 to reconcile data on radioactive decay of neutrons with energy conservation. While the postulated neutrino had no mass, no electric charge, and essentially did not react with matter, its inclusion as an emitted particle balanced energy conservation—the observed energy range for the electron corresponded to the many ways in which the emitted proton, electron, and neutrino can share energy.

Scientists now know that there are three "flavors" of neutrinos (labeled after their leptonic companions): the electron neutrino, νe, the muon neutrino,νμ, and tau neutrino, ντ. Similarly, up quarks and down quarks, which make up neutrons and protons, each have two siblings. No one yet knows why two apparently useless copies of the "useful" particles exist.

Pauli calculated that for the neutrino to function as theorized, the upper limit on its mass must be less than 1 percent of the proton mass. Subsequent experiments derived an upper limit of 108 times the proton mass—thus, the neutrino would be virtually massless. This is somewhat puzzling because no basic principle such as gauge invariance prevents neutrino mass, as it does for photons. However, modern theories have ways to accommodate small but nonvanishing neutrino masses. Flavor oscillations of neutrinos traveling from a source to a detector provide a powerful experimental signature of such small masses.

The concept of oscillating neutrinos originated in the late 1960s with Bruno Pontecorvo and requires the introduction of quantum states, in particular those describing quarks and leptons participating in weak interactions. It is an empirical fact that the states describing down (d ) and its heavier sibling strange (s ) quarks of definite mass are not the states of definite quark flavor that participate in weak interactions. Mixtures of the d and s flavor states, quantified by the Cabibbo angle, are the relevant quark quantum states with definite mass. So, it is also expected that the neutrino quantum states of definite flavor that participate in the weak interactions by which neutrinos are created and detected are also admixtures of neutrino quantum states of definite mass. Conversely, a neutrino of definite mass does not have a definite flavor—it carries an admixture of flavors. For the simplified case of two neutrinos, the νμ and ντ flavor states are related to states ν1 and ν2 of mass m1 and m2 by where θ is the Cabibbo-like "mixing angle," a constant of nature whose value will hopefully be under-stood some day in the context of a theory beyond the Standard Model in which neutrinos have nonvanishing masses. A neutrino created, for instance in the weak decay of a charged pion
pion → muon + neutrino, is born in the pure flavor state νμ. This is the meaning of the statement that "the flavor states participate in the weak interaction." This state is a superposition of the ν1 and ν2 mass states and their admixture is described by the above equation. The propagation of these mixed states is described by the Schrödinger equation; their interference causes the probability of detecting a particular flavor to change with the distance traveled by the neutrino. In other words, because the ν1 and ν2 states slightly differ in mass, the flavor admixture of the states fluctuates back and forth as the neutrino propagates through space. For instance, for a neutrino born as a νμ, the probability P that it will be observed as a ντ after traveling a distance L has a sinusoidal (i.e., oscillating) dependence on Δm2L/E , where is the mass-squared difference and E is the neutrino energy: The probability that a is observed at L is This is illustrated in Figure 1. The appearance of tauneutrinos in a beam of muon-neutrinos, or the disappearance of muon-neutrinos, are thus signatures that neutrinos have different masses. Conversely, massless neutrinos do not oscillate because all Δm2values vanish.

Examples of experimental evidence for neutrino oscillations include

  • A deficit of electron neutrinos born in nuclear processes that make the sun shine has been observed in several deep-underground detectors. Recently, by combining data from experiments in Japan and Canada, the first evidence has been produced that the missing electron neutrinos have indeed transformed into muon neutrinos and tau neutrinos.
  • Cosmic rays interacting with the nitrogen and oxygen in the Earth's atmosphere at an average height of 20 kilometers produce pions that decay

    FIGURE 1

    into muon neutrinos. The observed neutrino flux agrees with relatively straightforward computations. However, for neutrinos produced by exactly the same mechanism on the other side of the Earth, a deficit of neutrinos of muon flavor relative to expectations is observed after they travel roughly 10,000 meters through the Earth. (Because they only participate in the weak interaction, atmospheric neutrinos penetrate the Earth with no attenuation.) There is mounting evidence that they have oscillated into tau neutrinos. The accumulated evidence for neutrino oscillations is summarized in Figure 2.

The quest for precise information on neutrino masses and mixings has only just begun. There are plans on three continents to shoot accelerator beams of neutrinos to underground detectors over baselines of hundreds or even thousands of kilometers. One such experiment has already produced supporting evidence for oscillations of atmospheric neutrinos by observing a beam produced at a laboratory in Tsukuba, Japan at the SuperKamiokande detector, 250 kilometers away.

See also:Case Study: Super-Kamiokande and the Discovery of Neutrino Oscillations; Neutrino; Neutrino, Solar


Bahcall, J. Neutrino Astrophysics (Cambridge University Press, Cambridge, UK, 1989).


Caldwell, D. O., ed. Current Aspects of Neutrino Physics (Springer-Verlag, Heidelberg, Germany, 2001).

Kim, C. W., and Pevsner, A. Neutrinos in Physics and Astrophysics (Harwood Academic Press, Langhorne, PA, 1993).

Sutton, C. Spaceship Neutrino (Cambridge University Press, Cambridge, UK, 1992).

M.C. Gonzalez-Garcia

Francis Halzen