Sterile neutrino

Sterile neutrinos (or inert neutrinos) are hypothetical particles[1] (neutral leptonsneutrinos) that interact only via gravity and do not interact via any of the fundamental interactions of the Standard Model. The term sterile neutrino is used to distinguish them from the known active neutrinos in the Standard Model, which are charged under the weak interaction.

This term usually refers to neutrinos with right-handed chirality (see right-handed neutrino), which may be added to the Standard Model. Occasionally it is used in a general sense for any neutral fermion, instead of the more cautiously vague name neutral heavy leptons (NHLs) or heavy neutral leptons (HNLs).

The existence of right-handed neutrinos is theoretically well-motivated, as all other known fermions have been observed with both left and right chirality, and they can explain the observed active neutrino masses in a natural way. The mass of the right-handed neutrinos themselves is unknown and could have any value between 1015 GeV and less than 1 eV.[2]

The number of sterile neutrino types (should they exist) is not yet theoretically established. This is in contrast to the number of active neutrino types, which has to equal that of charged leptons and quark generations to ensure the anomaly freedom of the electroweak interaction.

The search for sterile neutrinos is an active area of particle physics. If they exist and their mass is smaller than the energies of particles in the experiment, they can be produced in the laboratory, either by mixing between active and sterile neutrinos or in high energy particle collisions. If they are heavier, the only directly observable consequence of their existence would be the observed active neutrino masses. They may, however, be responsible for a number of unexplained phenomena in physical cosmology and astrophysics, including dark matter, baryogenesis or dark radiation.[2] In May 2018, physicists of the MiniBooNE experiment reported a stronger neutrino oscillation signal than expected, a possible hint of sterile neutrinos.[3][4]

Sterile neutrino, right-handed neutrino
CompositionElementary particle
Interactionsgravity; other potential unknown interactions
Electric charge0
Color chargenone
Spin states2
Weak isospin projection0
Weak hypercharge0
Chiralityright handed
BLdepends on L charge assignment


Experimental results show that all produced and observed neutrinos have left-handed helicities (spin antiparallel to momentum), and all antineutrinos have right-handed helicities, within the margin of error. In the massless limit, it means that only one of two possible chiralities is observed for either particle. These are the only helicities (and chiralities) included in the Standard Model of particle interactions.

Recent experiments such as neutrino oscillation, however, have shown that neutrinos have a non-zero mass, which is not predicted by the Standard Model and suggests new, unknown physics. This unexpected mass explains neutrinos with right-handed helicity and antineutrinos with left-handed helicity: Since they do not move at the speed of light, their helicity is not relativistic invariant (it is possible to move faster than them and observe the opposite helicity). Yet all neutrinos have been observed with left-handed chirality, and all antineutrinos right-handed. Chirality is a fundamental property of particles and is relativistic invariant: It is the same regardless of the particle's speed and mass in every inertial reference frame. Although note that a particle with mass that starts out left-handed can develop a right-handed component as it travels – chirality is not conserved in the propagation of a free particle.

The question, thus, remains: Do neutrinos and antineutrinos differ only in their chirality? Or do exotic right-handed neutrinos and left-handed antineutrinos exist as separate particles from the common left-handed neutrinos and right-handed antineutrinos?


Such particles would belong to a singlet representation with respect to the strong interaction and the weak interaction, having zero electric charge, zero weak hypercharge, zero weak isospin, and, as with the other leptons, no color, although they do have a B-L of −1. If the standard model is embedded in a hypothetical SO(10) grand unified theory, they can be assigned an X charge of −5. The left-handed anti-neutrino has a B-L of +1 and an X charge of +5.

Due to the lack of electric charge, hypercharge, and color, sterile neutrinos would not interact electromagnetically, weakly, or strongly, making them extremely difficult to detect. They have Yukawa interactions with ordinary leptons and Higgs bosons, which via the Higgs mechanism lead to mixing with ordinary neutrinos. In experiments involving energies larger than their mass they would participate in all processes in which ordinary neutrinos take part, but with a quantum mechanical probability that is suppressed by the small mixing angle. That makes it possible to produce them in experiments if they are light enough. They would also interact gravitationally due to their mass, and if they are heavy enough, could explain cold dark matter or warm dark matter. In some grand unification theories, such as SO(10), they also interact via gauge interactions which are extremely suppressed at ordinary energies because their gauge boson is extremely massive. They do not appear at all in some other GUTs, such as the Georgi–Glashow model (i.e. all its SU(5) charges or quantum numbers are zero).


All particles are initially massless under the Standard Model, since there are no Dirac mass terms in the Standard Model's Lagrangian. The only mass terms are generated by the Higgs mechanism, which produces non-zero Yukawa couplings between the left-handed components of fermions, the Higgs field, and their right-handed components. This occurs when the SU(2) doublet Higgs field acquires its non-zero vacuum expectation value, , spontaneously breaking its SU(2)L × U(1) symmetry, and thus yielding non-zero Yukawa couplings:

Such is the case for charged leptons, like the electron; but within the standard model, the right-handed neutrino does not exist, so even with a Yukawa coupling neutrinos remain massless. In other words, there are no mass terms for neutrinos under the Standard Model: the model only contains a left-handed neutrino and its antiparticle, a right-handed antineutrino, for each generation, produced in weak eigenstates during weak interactions. (See neutrino masses in the Standard Model for a detailed explanation.)

In the seesaw mechanism, one eigenvector of the neutrino mass matrix, which includes sterile neutrinos, is predicted to be significantly heavier than the other.

A sterile neutrino would have the same weak hypercharge, weak isospin, and mass as its antiparticle. For any charged particle, for example the electron, this is not the case: its antiparticle, the positron, has opposite electric charge, among other opposite charges. Similarly, an up quark has a charge of +​ 23 and (for example) a color charge of red, while its antiparticle has an electric charge of −​ 23 and a color charge of anti-red.

Dirac and Majorana terms

Sterile neutrinos allow the introduction of a Dirac mass term as usual. This can yield the observed neutrino mass, but it requires that the strength of the Yukawa coupling be much weaker for the electron neutrino than the electron, without explanation. Similar problems (although less severe) are observed in the quark sector, where the top and bottom masses differ by a factor of 40.

Unlike for the left-handed neutrino, a Majorana mass term can be added for a sterile neutrino without violating local symmetries (weak isospin and weak hypercharge) since it has no weak charge. However, this would still violate total lepton number.

It is possible to include both Dirac and Majorana terms: this is done in the seesaw mechanism (below). In addition to satisfying the Majorana equation, if the neutrino were also its own antiparticle, then it would be the first Majorana fermion. In that case, it could annihilate with another neutrino, allowing neutrinoless double beta decay. The other case is that it is a Dirac fermion, which is not its own antiparticle.

To put this in mathematical terms, we have to make use of the transformation properties of particles. For free fields, a Majorana field is defined as an eigenstate of charge conjugation. However, neutrinos interact only via the weak interactions, which are not invariant under charge conjugation (C), so an interacting Majorana neutrino cannot be an eigenstate of C. The generalized definition is: "a Majorana neutrino field is an eigenstate of the CP transformation". Consequently, Majorana and Dirac neutrinos would behave differently under CP transformations (actually Lorentz and CPT transformations). Also, a massive Dirac neutrino would have nonzero magnetic and electric dipole moments, whereas a Majorana neutrino would not. However, the Majorana and Dirac neutrinos are different only if their rest mass is not zero. For Dirac neutrinos, the dipole moments are proportional to mass and would vanish for a massless particle. Both Majorana and Dirac mass terms however can appear in the mass Lagrangian.

Seesaw mechanism

In addition to the left-handed neutrino, which couples to its family charged lepton in weak charged currents, if there is also a right-handed sterile neutrino partner (a weak isosinglet with zero charge) then it is possible to add a Majorana mass term without violating electroweak symmetry. Both neutrinos have mass and handedness is no longer preserved (thus "left or right-handed neutrino" means that the state is mostly left or right-handed). To get the neutrino mass eigenstates, we have to diagonalize the general mass matrix :

where is big and is of intermediate size terms.

Apart from empirical evidence, there is also a theoretical justification for the seesaw mechanism in various extensions to the Standard Model. Both Grand Unification Theories (GUTs) and left-right symmetrical models predict the following relation:

According to GUTs and left-right models, the right-handed neutrino is extremely heavy: 105 to 1012 GeV, while the smaller eigenvalue is approximately equal to

This is the seesaw mechanism: as the sterile right-handed neutrino gets heavier, the normal left-handed neutrino gets lighter. The left-handed neutrino is a mixture of two Majorana neutrinos, and this mixing process is how sterile neutrino mass is generated.

Detection attempts

The production and decay of sterile neutrinos could happen through the mixing with virtual ("off mass shell") neutrinos. There were several experiments set up to discover or observe NHLs, for example the NuTeV (E815) experiment at Fermilab or LEP-l3 at CERN. They all led to establishing limits to observation, rather than actual observation of those particles. If they are indeed a constituent of dark matter, sensitive X-ray detectors would be needed to observe the radiation emitted by their decays.[5]

Sterile neutrinos may mix with ordinary neutrinos via a Dirac mass after electroweak symmetry breaking, in analogy to quarks and charged leptons. Sterile neutrinos and (in more-complicated models) ordinary neutrinos may also have Majorana masses. In the type 1 seesaw mechanism both Dirac and Majorana masses are used to drive ordinary neutrino masses down and make the sterile neutrinos much heavier than the Standard Model's interacting neutrinos. In some models the heavy neutrinos can be as heavy as the GUT scale (≈1015 GeV). In other models they could be lighter than the weak gauge bosons W and Z as in the so-called νMSM model where their masses are between GeV and keV. A light (with the mass ≈1 eV) sterile neutrino was suggested as a possible explanation of the results of the Liquid Scintillator Neutrino Detector experiment. On 11 April 2007, researchers at the MiniBooNE experiment at Fermilab announced that they had not found any evidence supporting the existence of such a sterile neutrino.[6] More-recent results and analysis have provided some support for the existence of the sterile neutrino.[7][8]

Two separate detectors near a nuclear reactor in France found 3% of anti-neutrinos missing. They suggested the existence of a fourth neutrino with a mass of 1.2 eV.[9] Sterile neutrinos are also candidates for dark radiation. Daya Bay has also searched for a light sterile neutrino and excluded some mass regions.[10] Daya Bay Collaboration measured the anti-neutrino energy spectrum, and found that anti-neutrinos at an energy of around 5 MeV are in excess relative to theoretical expectations. It also recorded 6% missing anti-neutrinos.[11] This could suggest that sterile neutrinos exist or that our understanding of neutrinos is not complete.

The number of neutrinos and the masses of the particles can have large-scale effects that shape the appearance of the cosmic microwave background. The total number of neutrino species, for instance, affects the rate at which the cosmos expanded in its earliest epochs: more neutrinos means a faster expansion. The Planck Satellite 2013 data release is compatible with the existence of a sterile neutrino. The implied mass range is from 0–3 eV.[12] In 2016, scientists at the IceCube Neutrino Observatory did not find any evidence for the sterile neutrino.[13] However, in May 2018, physicists of the MiniBooNE experiment reported a stronger neutrino oscillation signal than expected, a possible hint of sterile neutrinos.[3][4]

See also


  • Drewes, M. (2013). "The phenomenology of right handed neutrinos". International Journal of Modern Physics E. 22 (8): 1330019. arXiv:1303.6912. Bibcode:2013IJMPE..2230019D. doi:10.1142/S0218301313300191.
  1. ^ "A major physics experiment just detected a particle that shouldn't exist". Live Science. NBC News. 2018.
  2. ^ a b Drewes, Marco (2013). "The phenomenology of right handed neutrinos". International Journal of Modern Physics E. 22 (8): 1330019–593. arXiv:1303.6912. Bibcode:2013IJMPE..2230019D. doi:10.1142/S0218301313300191.
  3. ^ a b Letzter, Rafi (1 June 2018). "A major physics experiment just detected a particle that shouldn't exist". LiveScience. Retrieved 3 June 2018.
  4. ^ a b Collaboration, MiniBooNE; Aguilar-Arevalo, A.A.; Brown, B.C.; Bugel, L.; Cheng, G.; Conrad, J.M.; et al. (2018). "Observation of a significant excess of electron-like events in the MiniBooNE short-baseline neutrino experiment". Physical Review Letters. 121 (22): 221801. arXiv:1805.12028. doi:10.1103/PhysRevLett.121.221801. PMID 30547637.
  5. ^ Battison, Leila (16 September 2011). "Dwarf galaxies suggest dark matter theory may be wrong". BBC News. Retrieved 18 September 2011.
  6. ^ "First results" (PDF). Booster Neutrino Experiment (BooNE). Fermi National Accelerator Laboratory (Fermilab).
  7. ^ "Dimensional shortcuts". Scientific American. August 2007.
  8. ^ Bulbul, E.; Markevitch, M.; Foster, A.; Smith, R.K.; Loewenstein, M.; Randall, S.W. (2014). "Detection of an unidentified emission line in the stacked X-ray spectrum of galaxy clusters". The Astrophysical Journal. 789 (1): 13. arXiv:1402.2301v2. Bibcode:2014ApJ...789...13B. doi:10.1088/0004-637X/789/1/13.
  9. ^ "The reactor antineutrino anomaly".
  10. ^ An, F. P.; Balantekin, A. B.; Band, H. R.; Beriguete, W.; Bishai, M.; Blyth, S.; et al. (1 October 2014). "Search for a light sterile neutrino at Daya Bay". Physical Review Letters. 113 (14): 141802. arXiv:1407.7259. Bibcode:2014PhRvL.113n1802A. doi:10.1103/PhysRevLett.113.141802. PMID 25325631.
  11. ^ "Daya Bay discovers a mismatch". Symmetry.
  12. ^ Ade, P.A.R.; et al. (Planck Collaboration) (2013). "Planck 2013 results. XVI. Cosmological parameters". Astronomy & Astrophysics. 571: A16. arXiv:1303.5076. Bibcode:2014A&A...571A..16P. doi:10.1051/0004-6361/201321591.
  13. ^ "Icy telescope throws cold water on sterile neutrino theory". Nature. 8 August 2016. Retrieved 12 August 2016.

External links


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 signal detectors (photomultiplier tubes or PMTs) and is shielded by a water tank to protect it against external radiation and tag incoming cosmic muons that manage to penetrate the overburden of the mountain above.

The primary aim of the experiment is to make a precise measurement of the individual neutrino fluxes from the Sun and compare them to the Standard solar model predictions. This will allow scientists to test and to further understand the functioning of the Sun (e.g., nuclear fusion processes taking place at the core of the Sun, solar composition, opacities, matter distribution, etc.) and will also help determine properties of neutrino oscillations, including the MSW effect. Specific goals of the experiment are to detect beryllium-7, boron-8, pp, pep and CNO solar neutrinos as well as anti-neutrinos from the Earth and nuclear power plants. The project may also be able to detect neutrinos from supernovae within our galaxy with a special potential to detect the elastic scattering of neutrinos onto protons, due to neutral current interactions. Borexino is a member of the Supernova Early Warning System. Searches for rare processes and potential unknown particles are also underway.

The name Borexino is the Italian diminutive of BOREX (BORon solar neutrino EXperiment), after the original 1 kT-fiducial experimental proposal with a different scintillator (TMB), was discontinued because of a shift in focus in physics goals as well as financial constraints. The experiment is located at the Laboratori Nazionali del Gran Sasso near the town of L'Aquila, Italy, and is supported by an international collaboration with researchers from Italy, the United States, Germany, France, Poland and Russia. The experiment is funded by multiple national agencies including the INFN (National Institute for Nuclear Physics) and the NSF (National Science Foundation). In May 2017, Borexino reached 10 years of continuous operation since the start of its data-taking period in 2007.

The SOX project was projected study the possible existence of sterile neutrinos or other anomalous effects in neutrino oscillations at short ranges through the use of a neutrino generator based on radioactive cerium-144. This project was cancelled in early 2018 due to unsurmountable technical problems in the fabrication of the antineutrino source.

Brane cosmology

Brane cosmology refers to several theories in particle physics and cosmology related to string theory, superstring theory and M-theory.

Dark radiation

Dark radiation (also dark electromagnetism) is a postulated type of radiation that mediates interactions of dark matter.

By analogy to the way photons mediate electromagnetic interactions between particles in the Standard Model (called baryonic matter in cosmology), dark radiation is proposed to mediate interactions between dark matter particles. Similar to dark matter particles, the hypothetical dark radiation does not interact with Standard Model particles.

There has been no notable evidence for the existence of such radiation, but since baryonic matter contains multiple interacting particle types, it is reasonable to suppose that dark matter does also. Moreover, it has been pointed out recently that the cosmic microwave background data seems to suggest that the number of effective neutrino degrees of freedom is more than 3.046, which is slightly more than the standard case for 3 types of neutrino. This extra degree of freedom could arise from having a non-trivial amount of dark radiation in the universe. One possible candidate for dark radiation is the sterile neutrino.

Daya Bay Reactor Neutrino Experiment

The Daya Bay Reactor Neutrino Experiment is a China-based multinational particle physics project studying neutrinos. The multinational collaboration includes researchers from China, Chile, the United States, Taiwan, Russia, and the Czech Republic. The US side of the project is funded by the US Department of Energy's Office of High Energy Physics.

It is situated at Daya Bay, approximately 52 kilometers northeast of Hong Kong and 45 kilometers east of Shenzhen. There is an affiliated project in the Aberdeen Tunnel Underground Laboratory in Hong Kong. The Aberdeen lab measures the neutrons produced by cosmic muons which may affect the Daya Bay Reactor Neutrino Experiment.

The experiment consists of eight antineutrino detectors, clustered in three locations within 1.9 km (1.2 mi) of six nuclear reactors. Each detector consists of 20 tons of liquid scintillator (linear alkylbenzene doped with gadolinium) surrounded by photomultiplier tubes and shielding.A much larger follow-up is in development in the form of the Jiangmen Underground Neutrino Observatory (JUNO) in Kaiping, which will use an acrylic sphere filled with 20,000 tons of liquid scintillator to detect reactor antineutrinos. Groundbreaking began 10 January 2015, with operation expected in 2020.

Electron neutrino

The electron neutrino (νe) is a subatomic lepton elementary particle which has zero net electric charge. Together with the electron it forms the first generation of leptons, hence the name electron neutrino. It was first hypothesized by Wolfgang Pauli in 1930, to account for missing momentum and missing energy in beta decay, and was discovered in 1956 by a team led by Clyde Cowan and Frederick Reines (see Cowan–Reines neutrino experiment).

Flipped SO(10)

Flipped SO(10) is a grand unified theory which is to standard SO(10) as flipped SU(5) is to SU(5).

Gauge boson

In particle physics, a gauge boson is a force carrier, a bosonic particle that carries any of the fundamental interactions of nature, commonly called forces. Elementary particles, whose interactions are described by a gauge theory, interact with each other by the exchange of gauge bosons—usually as virtual particles.

All known gauge bosons have a spin of 1. Therefore, all known gauge bosons are vector bosons.

Gauge bosons are different from the other kinds of bosons: first, fundamental scalar bosons (the Higgs boson); second, mesons, which are composite bosons, made of quarks; third, larger composite, non-force-carrying bosons, such as certain atoms.

Hidden sector

In particle physics, the hidden sector, also known as the "dark sector", is the hypothetical collections of yet-unobserved quantum fields and their corresponding hypothetical particles. The interactions between the hidden sector particles and the Standard Model particles are weak, indirect, and typically mediated through gravity or other new particles. Examples for the new mediating particles include dark photon, sterile neutrino, and axion.

In many cases, hidden sectors include a new gauge group that is independent from the Standard Model gauge group. The hidden sectors are commonly predicted by the models from string theory. They may be relevant as a source of dark matter and supersymmetry breaking, solving the Muon g-2 anomaly and Beryllium-8 decay anomaly.

IceCube Neutrino Observatory

The IceCube Neutrino Observatory (or simply IceCube) is a neutrino observatory constructed at the Amundsen–Scott South Pole Station in Antarctica.

Its thousands of sensors are located under the Antarctic ice, distributed over a cubic kilometre.

Similar to its predecessor, the Antarctic Muon And Neutrino Detector Array (AMANDA), IceCube consists of spherical optical sensors called Digital Optical Modules (DOMs), each with a photomultiplier tube (PMT) and a single-board data acquisition computer which sends digital data to the counting house on the surface above the array. IceCube was completed on 18 December 2010.DOMs are deployed on strings of 60 modules each at depths between 1,450 to 2,450 meters into holes melted in the ice using a hot water drill. IceCube is designed to look for point sources of neutrinos in the TeV range to explore the highest-energy astrophysical processes.

In November 2013 it was announced that IceCube had detected 28 neutrinos that likely originated outside the Solar System.

Illustris project

The Illustris project is an ongoing series of astrophysical simulations run by an international collaboration of scientists. The aim is to study the processes of galaxy formation and evolution in the universe with a comprehensive physical model. Early results are described in a number of publications following widespread press coverage. The project publicly released all data produced by the simulations in April, 2015. A followup to the project, IllustrisTNG, was presented in 2017.

Liquid Scintillator Neutrino Detector

The Liquid Scintillator Neutrino Detector (LSND) was a scintillation counter at Los Alamos National Laboratory that measured the number of neutrinos being produced by an accelerator neutrino source. The LSND project was created to look for evidence of neutrino oscillation, and its results conflict with the standard model expectation of only three neutrino flavors, when considered in the context of other solar and atmospheric neutrino oscillation experiments. Cosmological data bound the mass of the sterile neutrino to ms < 0.26eV (0.44eV) at 95% (99.9%) confidence limit, excluding at high significance the sterile neutrino hypothesis as an explanation of the LSND anomaly. The controversial LSND result was tested by the MiniBooNE experiment at Fermilab, which refuted a simple 2-neutrino oscillation interpretation of the LSND result.

The detector consisted of a tank filled with 167 tons (50,000 gallons) of mineral oil and 14 pounds (6.4 kg) of b-PDB (2-(4-tert-butylphenyl)-5-(4-biphenyl)-1,3,4-oxadiazole) organic scintillator material. Cherenkov light emitted by particle interactions was detected by an array of 1220 photomultiplier tubes. The experiment collected data from 1993 to 1998.

List of particles

This article includes a list of the different types of atomic and sub-atomic particles found or hypothesized to exist in the whole of the universe, categorized by type. Properties of the various particles listed are also given, as well as the laws that the particles follow. For individual lists of the different particles, see the list below.


MicroBooNE is a liquid argon time projection chamber (LArTPC) at Fermilab in Batavia, IL. It is located in the Booster Neutrino Beam (BNB) beamline where neutrinos are produced by colliding protons from Fermilab's booster-accelerator to a beryllium target; this produces a lot of short-lived particle that decay into neutrinos. The neutrinos then pass though solid ground (to filter out particles that are not neutrinos from the beam) through another experiment called ANNIE (under construction as of 2018), then solid ground, then through the Short Baseline Near Detector (SBND, in development, expected to begin operation 2020), then ground again and arrive at the MicroBooNE detector 470 meters downrange from the target. After MicroBooNE the neutrinos continue to MiniBooNE detector and to the ICARUS detector.

MicroBooNE's two main physics goals are to investigate the MiniBooNE low-energy excess and neutrino-argon cross sections. It will be part of a series of neutrino detectors along with the new Short-Baseline Near Detector (SBND) and moved ICARUS detector.

MicroBooNE was filled with argon in July 2015 and began data taking. The collaboration announced that they had found evidence of the experiment's first neutrino interactions in November 2015. As of 2018, the detector was operating.


MiniBooNE is an experiment at Fermilab designed to observe neutrino oscillations (BooNE is an acronym for the Booster Neutrino Experiment). A neutrino beam consisting primarily of muon neutrinos is directed at a detector filled with 800 tons of mineral oil (ultrarefined methylene compounds) and lined with 1,280 photomultiplier tubes. An excess of electron neutrino events in the detector would support the neutrino oscillation interpretation of the LSND (Liquid Scintillator Neutrino Detector) result.

MiniBooNE started collecting data in 2002 and was still running in 2017.

Muon neutrino

The muon neutrino is a lepton, an elementary subatomic particle which has the symbol νμ and no net electric charge. Together with the muon it forms the second generation of leptons, hence the name muon neutrino. It was first hypothesized in the early 1940s by several people, and was discovered in 1962 by Leon Lederman, Melvin Schwartz and Jack Steinberger. The discovery was rewarded with the 1988 Nobel Prize in Physics.


A neutrino ( or ) (denoted by the Greek letter ν) is a fermion (an elementary particle with half-integer spin) that interacts only via the weak subatomic force and gravity. The neutrino is so named because it is electrically neutral and because its rest mass is so small (-ino) that it was long thought to be zero. The mass of the neutrino is much smaller than that of the other known elementary particles. The weak force has a very short range, the gravitational interaction is extremely weak, and neutrinos, as leptons, do not participate in the strong interaction. Thus, neutrinos typically pass through normal matter unimpeded and undetected.Weak interactions create neutrinos in one of three leptonic flavors: electron neutrinos (νe), muon neutrinos (νμ), or tau neutrinos (ντ), in association with the corresponding charged lepton. Although neutrinos were long believed to be massless, it is now known that there are three discrete neutrino masses with different tiny values, but they do not correspond uniquely to the three flavors. A neutrino created with a specific flavor is in an associated specific quantum superposition of all three mass states. As a result, neutrinos oscillate between different flavors in flight. For example, an electron neutrino produced in a beta decay reaction may interact in a distant detector as a muon or tau neutrino. Although only differences of squares of the three mass values are known as of 2016, cosmological observations imply that the sum of the three masses must be less than one millionth that of the electron.For each neutrino, there also exists a corresponding antiparticle, called an antineutrino, which also has half-integer spin and no electric charge. They are distinguished from the neutrinos by having opposite signs of lepton number and chirality. To conserve total lepton number, in nuclear beta decay, electron neutrinos appear together with only positrons (anti-electrons) or electron-antineutrinos, and electron antineutrinos with electrons or electron neutrinos.Neutrinos are created by various radioactive decays, including in beta decay of atomic nuclei or hadrons, nuclear reactions such as those that take place in the core of a star or artificially in nuclear reactors, nuclear bombs or particle accelerators, during a supernova, in the spin-down of a neutron star, or when accelerated particle beams or cosmic rays strike atoms. The majority of neutrinos in the vicinity of the Earth are from nuclear reactions in the Sun. In the vicinity of the Earth, about 65 billion (6.5×1010) solar neutrinos per second pass through every square centimeter perpendicular to the direction of the Sun.For study, neutrinos can be created artificially with nuclear reactors and particle accelerators. There is intense research activity involving neutrinos, with goals that include the determination of the three neutrino mass values, the measurement of the degree of CP violation in the leptonic sector (leading to leptogenesis); and searches for evidence of physics beyond the Standard Model of particle physics, such as neutrinoless double beta decay, which would be evidence for violation of lepton number conservation. Neutrinos can also be used for tomography of the interior of the earth.

Pontecorvo–Maki–Nakagawa–Sakata matrix

In particle physics, the Pontecorvo–Maki–Nakagawa–Sakata matrix (PMNS matrix), Maki–Nakagawa–Sakata matrix (MNS matrix), lepton mixing matrix, or neutrino mixing matrix is a unitary mixing matrix which contains information on the mismatch of quantum states of neutrinos when they propagate freely and when they take part in the weak interactions. It is a model of neutrino oscillation. This matrix was introduced in 1962 by Ziro Maki, Masami Nakagawa and Shoichi Sakata, to explain the neutrino oscillations predicted by Bruno Pontecorvo.

Tau neutrino

The tau neutrino or tauon neutrino is a subatomic elementary particle which has the symbol ντ and no net electric charge. Together with the tau, it forms the third generation of leptons, hence the name tau neutrino. Its existence was immediately implied after the tau particle was detected in a series of experiments between 1974 and 1977 by Martin Lewis Perl with his colleagues at the SLAC–LBL group. The discovery of the tau neutrino was announced in July 2000 by the DONUT collaboration (Direct Observation of the Nu Tau).

Warm dark matter

Warm dark matter (WDM) is a hypothesized form of dark matter that has properties intermediate between those of hot dark matter and cold dark matter, causing structure formation to occur bottom-up from above their free-streaming scale, and top-down below their free streaming scale. The most common WDM candidates are sterile neutrinos and gravitinos. The WIMPs (weakly interacting massive particles), when produced non-thermally could be candidates for warm dark matter. In general, however the thermally produced WIMPs are cold dark matter candidates.

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