Mikheyev–Smirnov–Wolfenstein effect
The Mikheyev–Smirnov–Wolfenstein effect (often referred to as the matter effect) is a particle physics process which modifies neutrino oscillations in matter of varying density.
The MSW effect is broadly analogous to the differential retardation of sound waves in density-variable media, however it also involves the propagation dynamics of three separate quantum fields which experience distortion.
Within matter – such as within the Sun – the analysis is more complicated, as shown by Mikheyev, Smirnov and Wolfenstein.
Works in 1978 and 1979 by American physicist Lincoln Wolfenstein led to understanding that the oscillation parameters of neutrinos are changed in matter.
In 1985, the Soviet physicists Stanislav Mikheyev and Alexei Smirnov predicted that a slow decrease of the density of matter can resonantly enhance the neutrino mixing.
[1] Later in 1986, Stephen Parke of Fermilab, Hans Bethe of Cornell University, and S. Peter Rosen and James Gelb of Los Alamos National Laboratory provided analytic treatments of this effect.
The presence of electrons in matter changes the instantaneous Hamiltonian eigenstates (mass eigenstates) of neutrinos due to the charged current weak interaction's elastic forward scattering of the electron neutrinos.
This coherent forward scattering is analogous to the electromagnetic process leading to the refractive index of light in a medium and can be described either as the classical refractive index,
induces the evolution of mixed neutrino flavors (either electron, muon, or tau).
In the presence of matter, the Hamiltonian of the system changes with respect to the potential:
change, which means that the neutrinos in matter now have a different effective mass than they did in vacuum:
Similar to the vacuum case, the mixing angle
In matter, the mixing angle depends on the number density of electrons
With antineutrinos, the conceptual point is the same but the effective charge that the charged current weak interaction couples to (called weak isospin) has an opposite sign.
[2] Thus, the neutrinos of high energy leaving the Sun are in a vacuum propagation eigenstate,
Neutrino flavor mixing experiences resonance and becomes maximal under certain conditions of the relationship between the vacuum oscillation length
is understood as the distance over which the matter "phase" from the coherent scattering is equal to
which is when the neutrino system experiences resonance and the mixing becomes maximal.
and is directly related the number density of electrons
If vacuum density reaches the maximal value,
itself fluctuates – the interval between its maximum and minimum values is called the resonance layer.
For high-energy solar neutrinos the MSW effect is important, and leads to the expectation that
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.
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, which observed the neutrinos from pp (< 420 keV), 7Be (862 keV), pep (1.44 MeV), and 8B (< 15 MeV) separately.
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.
[4] As such, scientists have attempted to simulate and mathematically characterize the action of MSW dynamics on SN neutrinos.
Some effect of MSW flavor conversion has already been observed in SN 1987A.
Due to the differences in the distance traveled by neutrinos to Kamiokande, IMB and Baksan within the Earth, the MSW effect can partially explain the difference of the Kamiokande and IMB energy spectrum of events.
