Mikheyev-Smirnov-Wolfenstein effect
Encyclopedia
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.
s in matter changes the energy level
s 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 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. 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. The size of the source (i.e. the Solar core) is significantly larger than the oscillation length, therefore, averaging over the oscillatory factor, one obtains Pee = 1 − (sin22θ)/2. For the same value of the solar mixing angle, θ, this would correspond to a suppression Pee ≈ 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 GALLEX
, GNO, and SAGE (collectively, gallium
radiochemical experiments), and, more recently, the Borexino
experiment. All these experiments measured the flux of the lowest energy solar neutrinos, and provided a strong 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 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.
Particle physics
Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...
process which can act to modify neutrino oscillations in matter
Matter
Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...
. 1978 work by American
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
physicist Lincoln Wolfenstein
Lincoln Wolfenstein
Lincoln Wolfenstein is an American particle physicist who studies the weak interaction. Wolfenstein was born in 1923 and obtained his PhD in 1949 from the University of Chicago. He retired from Carnegie Mellon University in 2000 after being a faculty member for 52 years, but still lectures there...
and 1986 work by Soviet
Soviet Union
The Soviet Union , officially the Union of Soviet Socialist Republics , was a constitutionally socialist state that existed in Eurasia between 1922 and 1991....
physicists Stanislav Mikheyev
Stanislav Mikheyev
Stanislav Pavlovich Mikheyev was a Russian physicist known for a co-discovering of the MSW effect.-Education and research:Stanislav Mikheyev graduated from Faculty of Physics of Moscow State University in 1965. Then he became a researcher at Lebedev Physical Institute...
and Alexei Smirnov led to an understanding of this effect. Later in 1986, Stephen Parke
Stephen Parke
Stephen Parke is a New Zealand physicist. He is currently a Senior Scientist and Head of the Theoretical Physics Department at the Fermi National Accelerator Laboratory .-Biography:...
of Fermilab
Fermilab
Fermi National Accelerator Laboratory , located just outside Batavia, Illinois, near Chicago, is a US Department of Energy national laboratory specializing in high-energy particle physics...
provided the first full analytic treatment of this effect.
Explanation
The presence of electronElectron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s in matter changes the energy level
Energy level
A quantum mechanical system or particle that is bound -- that is, confined spatially—can only take on certain discrete values of energy. This contrasts with classical particles, which can have any energy. These discrete values are called energy levels...
s of the propagation eigenstates of neutrinos due to charged current
Charged current
The Charged current interaction is one of the ways in which subatomic particles can interact by means of the weak force. It is mediated by the and bosons....
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
Refractive index
In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....
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
Weak isospin
In particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol T or I with the third component written as Tz, T3, Iz or I3...
) has opposite sign.
The effect is important at the very large electron densities of the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
where electron neutrinos are produced. The high-energy neutrinos seen, for example, in SNO (Sudbury Neutrino Observatory) and in Super-Kamiokande
Super-Kamiokande
Super-Kamiokande is a neutrino observatory which is under Mount Kamioka near the city of Hida, Gifu Prefecture, Japan...
, are produced 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. This was dramatically confirmed in the Sudbury Neutrino Observatory
Sudbury Neutrino Observatory
The Sudbury Neutrino Observatory is a neutrino observatory located 6,800 feet underground in Vale Inco's Creighton Mine in Sudbury, Ontario, Canada. The detector was designed to detect solar neutrinos through their interactions with a large tank of heavy water. The detector turned on in May 1999,...
, where the solar neutrino problem
Solar neutrino problem
The solar neutrino problem was a major discrepancy between measurements of the numbers of neutrinos flowing through the Earth and theoretical models of the solar interior, lasting from the mid-1960s to about 2002...
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
Super-Kamiokande
Super-Kamiokande is a neutrino observatory which is under Mount Kamioka near the city of Hida, Gifu Prefecture, Japan...
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. The size of the source (i.e. the Solar core) is significantly larger than the oscillation length, therefore, averaging over the oscillatory factor, one obtains Pee = 1 − (sin22θ)/2. For the same value of the solar mixing angle, θ, this would correspond to a suppression Pee ≈ 60%. This is consistent with the experimental observations on such neutrinos by the Homestake experiment
Homestake Experiment
The Homestake experiment was an experiment headed by astrophysicists Raymond Davis, Jr. and John N. Bahcall in the late 1960s. Its purpose was to collect and count neutrinos emitted by nuclear fusion taking place in the Sun. Bahcall did the theoretical calculations and Davis designed the experiment...
(the first experiment to reveal the solar neutrino problem), followed by GALLEX
GALLEX
GALLEX or Gallium Experiment was a radiochemical neutrino detection experiment that ran between 1991 and 1997 at the Laboratori Nazionali del Gran Sasso...
, GNO, and SAGE (collectively, gallium
Gallium
Gallium is a chemical element that has the symbol Ga and atomic number 31. Elemental gallium does not occur in nature, but as the gallium salt in trace amounts in bauxite and zinc ores. A soft silvery metallic poor metal, elemental gallium is a brittle solid at low temperatures. As it liquefies...
radiochemical experiments), and, more recently, the Borexino
Borexino
Borexino is a particle physics experiment to study low energy solar neutrinos. The primary aim of the experiment is to make a precise measurement of the beryllium-7 neutrino flux from the sun and comparing it to the Standard solar model prediction...
experiment. All these experiments measured the flux of the lowest energy solar neutrinos, and provided a strong 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 MSW effect can also modify neutrino oscillations in the Earth, and future search for new oscillations and/or leptonic CP violation
CP violation
In particle physics, CP violation is a violation of the postulated CP-symmetry: the combination of C-symmetry and P-symmetry . CP-symmetry states that the laws of physics should be the same if a particle were interchanged with its antiparticle , and left and right were swapped...
may make use of this property.