The Mikheyev–Smirnov–Wolfenstein effect (often referred to as the ''matter effect'') is a
particle physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
process which modifies
neutrino oscillations in
matter
In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic part ...
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.
In free space, the separate rates of neutrino eigenstates lead to standard neutrino flavor oscillation. Within matter – such as within the
Sun
The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
– the analysis is more complicated, as shown by Mikheyev, Smirnov and Wolfenstein. It leads to a wide admixture of emanating neutrino flavors, which provides a compelling solution to the
solar neutrino problem
The solar neutrino problem concerned a large discrepancy between the flux of solar neutrinos as predicted from the Sun's luminosity and as measured directly. The discrepancy was first observed in the mid-1960s and was resolved around 2002.
The fl ...
.
Works in 1978 and 1979 by
American
American(s) may refer to:
* American, something of, from, or related to the United States of America, commonly known as the "United States" or "America"
** Americans, citizens and nationals of the United States of America
** American ancestry, pe ...
physicist
Lincoln Wolfenstein led to understanding that the oscillation parameters of neutrinos are changed in matter. In 1985, the
Soviet
The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...
physicists
Stanislav Mikheyev
Stanislav Pavlovich Mikheyev (russian: Станисла́в Па́влович Михе́ев; 1940 – 23 April 2011) was a Russian physicist known for the discovery of the MSW effect.
Education and research
Stanislav Mikheyev graduated from F ...
and
Alexei Smirnov predicted that a slow decrease of the density of matter can resonantly enhance the neutrino mixing. Later in 1986,
Stephen Parke of
Fermilab
Fermi National Accelerator Laboratory (Fermilab), located just outside Batavia, Illinois, near Chicago, is a United States Department of Energy national laboratory specializing in high-energy particle physics. Since 2007, Fermilab has been oper ...
,
Hans Bethe
Hans Albrecht Bethe (; July 2, 1906 – March 6, 2005) was a German-American theoretical physicist who made major contributions to nuclear physics, astrophysics, quantum electrodynamics, and solid-state physics, and who won the 1967 Nobel ...
of
Cornell University
Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to tea ...
, and
S. Peter Rosen and James Gelb of
Los Alamos National Laboratory
Los Alamos National Laboratory (often shortened as Los Alamos and LANL) is one of the sixteen research and development laboratories of the United States Department of Energy (DOE), located a short distance northwest of Santa Fe, New Mexico, ...
provided analytic treatments of this effect.
Mikheyev, Smirnov and Wolfenstein were nominated in 2015 for the
Nobel Prize in Physics
)
, image = Nobel Prize.png
, alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then " ...
, but did not win, the prize instead going to Takaaki Kajita and Arthur B. McDonald for their discovery of neutrino oscillations.
Summary
The presence of
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have n ...
s in matter changes the instantaneous
Hamiltonian eigenstates (mass eigenstates) of neutrinos due to the
charged current
Charged current interactions are one of the ways in which subatomic particles can interact by means of the weak force. These interactions are mediated by the and bosons.
In simple terms
Charged current interactions are the most easily det ...
's elastic forward scattering of the electron neutrinos (i.e.,
weak interactions
In nuclear physics and particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction, ...
). This coherent forward scattering is analogous to the electromagnetic process leading to the
refractive index
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
The refractive index determines how much the path of light is bent, ...
of light in a medium and can be described either as the classical
refractive index
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
The refractive index determines how much the path of light is bent, ...
,
or the
electric potential
The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work energy needed to move a unit of electric charge from a reference point to the specific point in ...
,
. The difference of potentials for different neutrinos
and
:
induces the evolution of mixed neutrino flavors (either
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have n ...
,
muon
A muon ( ; from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with an electric charge of −1 '' e'' and a spin of , but with a much greater mass. It is classified as a lepton. As w ...
, or
tau).
In the presence of matter, the Hamiltonian of the system changes with respect to the potential:
, where
is the Hamiltonian in vacuum. Correspondingly, the mass eigenstates and eigenvalues of
change, which means that the neutrinos in matter now have a different effective mass than they did in vacuum:
. Since neutrino oscillations depend upon the squared mass difference of the neutrinos, neutrino oscillations experience different dynamics than they did in vacuum.
Similar to the vacuum case, the mixing angle
describes the change of flavors of the eigenstates. In matter, the mixing angle depends on the number density of electrons
and the energy of the neutrinos:
. As the neutrinos propagate through density-variant matter,
changes – and with it, the flavors of the eigenstates.
With antineutrinos, the conceptual point is the same but the effective charge that the weak interaction couples to (called ''
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 or , with the third component written as or . It c ...
'') has an opposite sign. If the electron density of matter changes along the path of neutrinos, the mixing of neutrinos grows to maximum at some value of the density, and then turns back; it leads to resonant conversion of one type of neutrinos to another one.
The effect is important at the very large electron densities of the
Sun
The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
where electron neutrinos are produced. The high-energy neutrinos seen, for example, in
Sudbury Neutrino Observatory
The Sudbury Neutrino Observatory (SNO) was a neutrino observatory located 2100 m underground in Vale's Creighton Mine in Sudbury, Ontario, Canada. The detector was designed to detect solar neutrinos through their interactions with a large ...
(SNO) and in
Super-Kamiokande
Super-Kamiokande (abbreviation of Super-Kamioka Neutrino Detection Experiment, also abbreviated to Super-K or SK; ja, スーパーカミオカンデ) is a Neutrino detector, neutrino observatory located Kamioka Observatory, under Mount Ikeno ...
, are produced mainly as the higher mass eigenstate in matter
, and remain as such as the density of solar material changes. Thus, the neutrinos of high energy leaving the Sun are in a vacuum propagation eigenstate,
, that has a reduced overlap with the electron neutrino
seen by charged current reactions in the detectors.
Resonance in the MSW effect
Neutrino flavor mixing experiences
resonance
Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscil ...
and becomes maximal under certain conditions of the relationship between the vacuum oscillation length
and the matter density-dependent refraction length
, where
is the
Fermi coupling constant
In particle physics, Fermi's interaction (also the Fermi theory of beta decay or the Fermi four-fermion interaction) is an explanation of the beta decay, proposed by Enrico Fermi in 1933. The theory posits four fermions directly interacting ...
. The refraction length
is understood as the distance over which the matter "
phase" from the coherent scattering is equal to
.
The resonance condition is given by
, which is when the neutrino system experiences resonance and the mixing becomes maximal. For very small
, this condition becomes
, that is, the eigenfrequency for a system of mixed neutrinos becomes approximately equal to the eigenfrequency of medium.
The resonance density
is informed by the resonance condition:
and is directly related the number density of electrons
. If vacuum density reaches the maximal value,
, the resonance density goes to zero. In a medium with fluctuating density,
itself fluctuates – the interval between its maximum and minimum values is called the resonance layer.
Solar neutrinos and the MSW effect
For high-energy solar neutrinos the MSW effect is important, and leads to the expectation that
, where
is the solar
mixing angle. This was dramatically confirmed in the
Sudbury Neutrino Observatory
The Sudbury Neutrino Observatory (SNO) was a neutrino observatory located 2100 m underground in Vale's Creighton Mine in Sudbury, Ontario, Canada. The detector was designed to detect solar neutrinos through their interactions with a large ...
(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
Charged current interactions are one of the ways in which subatomic particles can interact by means of the weak force. These interactions are mediated by the and bosons.
In simple terms
Charged current interactions are the most easily det ...
reaction, and the total flux via the
neutral current
Weak neutral current interactions are one of the ways in which subatomic particles can interact by means of the weak force. These interactions are mediated by the Z boson. The discovery of weak neutral currents was a significant step towar ...
reaction). The SNO results agree well with the expectations. Earlier,
Kamiokande
The is a neutrino and gravitational waves laboratory located underground in the Mozumi mine of the Kamioka Mining and Smelting Co. near the Kamioka section of the city of Hida in Gifu Prefecture, Japan. A set of groundbreaking neutrino experimen ...
and
Super-Kamiokande
Super-Kamiokande (abbreviation of Super-Kamioka Neutrino Detection Experiment, also abbreviated to Super-K or SK; ja, スーパーカミオカンデ) is a Neutrino detector, neutrino observatory located Kamioka Observatory, under Mount Ikeno ...
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
. For
= 34° this corresponds to a survival probability of ''P''
ee ≈ 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
Gallium is a chemical element with the Symbol (chemistry), symbol Ga and atomic number 31. Discovered by France, French chemist Paul-Émile Lecoq de Boisbaudran in 1875, Gallium is in boron group, group 13 of the periodic table and is similar to ...
radiochemical experiments), and, more recently, the
Borexino
Borexino is a particle physics experiment to study low energy (sub-MeV) solar neutrinos. The detector is the world's most radio-pure liquid scintillator calorimeter. It is placed within a stainless steel sphere which holds the photomultiplier tu ...
experiment, which observed the neutrinos from
pp (< 420 keV),
7Be (862 keV), pep (1.44 MeV), and
8B (< 15 MeV) separately. Th
measurements of Borexinoalone verify the MSW pattern; however all these experiments are consistent with each other and provide us strong evidence of the MSW effect.
These results are further supported by the reactor experiment
KamLAND, that is uniquely able to measure the parameters of oscillation that are also 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
In particle physics, CP violation is a violation of CP-symmetry (or charge conjugation parity symmetry): the combination of C-symmetry (charge symmetry) and P-symmetry ( parity symmetry). CP-symmetry states that the laws of physics should be t ...
may make use of this property.
Supernova neutrinos and the MSW effect
Supernovae
A supernova is a powerful and luminous explosion of a star. It has the plural form supernovae or supernovas, and is abbreviated SN or SNe. This transient astronomical event occurs during the last evolutionary stages of a massive star or when ...
are calculated to emit of the order of
neutrinos and antineutrinos of all flavors, and
supernova neutrinos
Supernova neutrinos are weakly interactive elementary particles produced during a core-collapse supernova explosion. A massive star collapses at the end of its life, emitting of the order of 1058 neutrinos and antineutrinos in all lepton flav ...
carry away about 99% of the gravitational energy of the supernova and are considered strongest source of cosmic neutrinos in the MeV range. 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
SN 1987A was a type II supernova in the Large Magellanic Cloud, a dwarf satellite galaxy of the Milky Way. It occurred approximately from Earth and was the closest observed supernova since Kepler's Supernova. 1987A's light reached Earth on ...
. In the case of normal neutrino mass hierarchy,
and
, transitions occurred inside the star, then
and
oscillated inside the Earth. Due to the differences in the distance traveled by neutrinos to
Kamiokande
The is a neutrino and gravitational waves laboratory located underground in the Mozumi mine of the Kamioka Mining and Smelting Co. near the Kamioka section of the city of Hida in Gifu Prefecture, Japan. A set of groundbreaking neutrino experimen ...
,
IMB and
Baksan within the Earth, the MSW effect can partially explain the difference of the Kamiokande and IMB energy spectrum of events.
See also
*
Neutrino oscillations
References
Bibliography
*
*
*
*
*
*
*
*
*
{{DEFAULTSORT:Mikheyev-Smirnov-Wolfenstein effect
Neutrinos
Astroparticle physics