The Mikheyev–Smirnov–Wolfenstein effect (often referred to as matter effect) is a particle physics process which can act to modify neutrino oscillations in matter. Work in 1978, by American physicist Lincoln Wolfenstein, and 1986, by Soviet physicists Stanislav Mikheyev and Alexei Smirnov, led to an understanding of this effect. Later in 1986, Stephen Parke of Fermilab provided the first full analytic treatment of this effect.
The presence of electrons in matter changes the energy levels of the propagation eigenstates (mass eigenstates) of neutrinos due to charged current coherent forward scattering of the electron neutrinos (i.e., weak interactions). The coherent forward scattering is analogous to the electromagnetic process leading to the refractive index of light in a medium. This means that neutrinos in matter have a different effective mass than neutrinos in vacuum, and since neutrino oscillations depend upon the squared mass difference of the neutrinos, neutrino oscillations may be different in matter than they are in vacuum. With antineutrinos, the conceptual point is the same but the effective charge that the weak interaction couples to (called weak isospin) has an opposite sign.
The effect is important at the very large electron densities of the Sun where electron neutrinos are produced. The high-energy neutrinos seen, for example, in SNO (Sudbury Neutrino Observatory) and in Super-Kamiokande, are produced mainly as the higher mass eigenstate in matter ν2m, and remain as such as the density of solar material changes. (When neutrinos go through the MSW resonance the neutrinos have the maximal probability to change their nature, but it happens that this probability is negligibly small—this is sometimes called propagation in the adiabatic regime). Thus, the neutrinos of high energy leaving the sun are in a vacuum propagation eigenstate, ν2, that has a reduced overlap with the electron neutrino νe = ν1 cosθ + ν2 sinθ seen by charged current reactions in the detectors.
For high-energy solar neutrinos the MSW effect is important, and leads to the expectation that Pee = sin²θ, where θ is the solar mixing angle. This was dramatically confirmed in the Sudbury Neutrino Observatory (SNO), which has resolved the solar neutrino problem. SNO measured the flux of Solar electron neutrinos to be ~34% of the total neutrino flux (the electron neutrino flux measured via the charged current reaction, and the total flux via the neutral current reaction). The SNO results agree well with the expectations. Earlier, Kamiokande and Super-Kamiokande measured a mixture of charged current and neutral current reactions, that also support the occurrence of the MSW effect with a similar suppression, but with less confidence.
For the low-energy solar neutrinos, on the other hand, the matter effect is negligible, and the formalism of oscillations in vacuum is valid. The size of the source (i.e. the Solar core) is significantly larger than the oscillation length, therefore, averaging over the oscillation factor, one obtains Pee = 1 − sin²2θ / 2. For θ = 34° this corresponds to a survival probability of Pee ≈ 60%. This is consistent with the experimental observations of low energy Solar neutrinos by the Homestake experiment (the first experiment to reveal the solar neutrino problem), followed by GALLEX, GNO, and SAGE (collectively, gallium radiochemical experiments), and, more recently, the Borexino experiment. These experiments provided further evidence of the MSW effect.
These results are further supported by the reactor experiment KamLAND, that alone is able to provide also a measurement of the parameters of oscillation that is consistent with all other measurements.
The transition between the low energy regime (the MSW effect is negligible) and the high energy regime (the oscillation probability is determined by matter effects) lies in the region of about 2 MeV for the Solar neutrinos.
The MSW effect can also modify neutrino oscillations in the Earth, and future search for new oscillations and/or leptonic CP violation may make use of this property.
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