Mikheyev–Smirnov–Wolfenstein effect

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. 1978 work by American physicist Lincoln Wolfenstein and 1986 work 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.

Explanation

The presence of electrons in matter changes the energy levels of the propagation 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 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 as the higher mass eigenstate in matter ν_2m, 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 ν_e = 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 P_ee = sin²θ. This was dramatically confirmed in the Sudbury Neutrino Observatory, where the solar neutrino problem was finally solved. There it was shown that only ~34% of the electron neutrinos (measured with one charged current reaction of the electron neutrinos) reach the detector, whereas the sum of rates for all three neutrinos (measured with one neutral current reaction) agrees well with the expectations. This allowed the determination sin²θ ≈ 1/3. 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 one should apply the vacuum oscillation formula P_ee = 1 − (sin²2θ)/2. For the same value of the solar mixing angle, θ, this would correspond to a suppression P_ee ≈ 60%. This is consistent with the experimental observations on such neutrinos by the Homestake experiment, the first experiment to reveal the solar neutrino problem, followed by those of GALLEX, GNO, and SAGE (collectively, gallium experiments) that measured the lowest energy neutrinos and provided a strong support to the Homestake experiment. These results are supported by the results of 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 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.

See also

• Neutrino oscillations

References

• G. Brooijmans (28 July 1998). "Neutrino Oscillations in Matter: the MSW Effect". A New Limit on ν_μ → ν_τ Oscillations. Université catholique de Louvain. p. 40. http://www.fynu.ucl.ac.be/librairie/theses/gustaaf.brooijmans/node31.html. Retrieved 2010-04-24. 
• P. Langacker (27 November 1995). "Mikheyev–Smirnov–Wolfenstein (MSW)". Solar Neutrinos. University of Pennsylvania. http://dept.physics.upenn.edu/neutrino/sun-nu/node8.html. Retrieved 2010-04-24. 
• B. Schwarzschild (2003). "Antineutrinos From Distant Reactors Simulate the Disappearance of Solar Neutrinos". Physics Today 56: 14. Bibcode 2003PhT....56c..14S. doi:10.1063/1.1570758. http://grattalab3.stanford.edu/neutrino/KamLAND/ArticlesAboutKamLAND/KL_PhysTodArt.html. 
• L. Wolfenstein (1978). "Neutrino oscillations in matter". Physical Review D 17 (9): 2369. Bibcode 1978PhRvD..17.2369W. doi:10.1103/PhysRevD.17.2369.