Sterile neutrino
Encyclopedia
Sterile neutrinosIn scientific literature, these particles are also variously referred to as right-handed neutrinos, inert neutrinos, heavy neutrinos, or neutral heavy leptons (NHL). are a hypothetical type of neutrino
that do not interact via any of the fundamental interaction
s of the Standard Model
except gravity. It is a right-handed neutrino or left-handed anti-neutrino predicted by some extensions to the Standard ModelSee: Grand Unification Theory
that may explain other phenomena, such as neutrino mixing, in which these particles may participate, and the large difference in mass between neutrinos and the charged leptons. The search for these particles is an active area of particle physics
.
), 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; the Standard Model predicts only these neutrinos exist.
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 reference frame. The question, thus, remains: can neutrinos and antineutrinos be differentiated only by chirality? or do right-handed neutrinos and left-handed antineutrinos exist as separate particles?
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 and 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 charges, sterile neutrinos would not interact electromagnetically
, weakly, or strongly, making them extremely difficult to detect. They would interact gravitationally due to their mass, however, and if they are heavy enough, they 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).
. In the Higgs mechanism, a doublet of scalar Higgs fields
(or Higgs boson
s), interact with other particles. In the process of spontaneous symmetry breaking
, the Higgs field develops a vacuum expectation value,
, and in the Lagrangian
for neutrino wave functions, a massive Dirac field appears:
where m is the positive, real
mass term.
That is the case for the charged leptons, such as the electron, but the Standard Model does not have a corresponding Dirac mass terms for neutrinos. Weak interactions couple only to the left-handed currents, thus, right-handed neutrinos are not present in the Standard Model Lagrangian. As the result it is not possible to form mass terms for neutrino in the Standard Model: it only predicts a left-handed neutrino and its antiparticle, a right-handed antineutrino, for each generation, produced in chiral eigenstates in weak interactions.
The assumption of a different mass for sterile neutrinos, which is predicted to be significantly heavier than their normal counterparts, arises from a question of what forms the difference between a particle and its antiparticle. For any charged particle, for example the electron, this is simple to answer: its antiparticle, the positron
, has opposite electric charge, among other opposite charges. Similarly, an up quark
has a charge of +⅔ and (for example) a color charge of red, while its antiparticle has an electric charge of -⅔ and a color charge of anti-red.
For the uncharged neutrinos, the answer is less clear. The Standard Model's massless neutrinos only differ from their antiparticles by their chirality, and thus, their helicity, but since neutrinos have been observed to have mass, there may be physics outside the Standard Model, and this opens the door for two different possibilities of the nature of neutrino mass: Majorana or Dirac.
, and would be the first of its kind. The concept of the Majorana particle was first introduced by Ettore Majorana
in 1937. Examples for boson
s are the neutral pion
, the photon
, and the Z boson which are identical to their antiparticles. If this were the case, the massive neutrino is its own antiparticle
, and could annihilate with another neutrino, possibly allowing neutrinoless double beta decay, and the sterile neutrino would need to differ from the neutrino by something other than its handedness.
However, if we assume that a particle must be different in some way from its antiparticle, then the neutrino is a Dirac fermion
. All known fermions are Dirac fermions; an example is the neutron
which has no electric charge but is different from its antiparticle due to its quark
composition.A neutron
is composed of one up quark
and two down quarks, whereas an antineutron
is composed of one up anti-quark and two down anti-quarks. The neutral kaon
, a boson, is also a Dirac particle in a sense.
To put this in mathematical terms, we have to make use of the transformation properties of particles. We define a Majorana field as an eigenstate of charge conjugation. This definition is only for free fields, and must be generalized to the interacting field. Neutrinos interact only via the weak interactions, which are not invariant to 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). The distinction between Majorana and Dirac neutrinos is not only theoretical; a massive Dirac neutrino would have nonzero magnetic and electric dipole moment
s, which could be observed experimentally, whereas a Majorana neutrino would not.
The Majorana and Dirac particles are different only if their rest mass is not zero. If the neutrino has no mass and travels at the speed of light, then the Lorentz transformation to a faster moving frame is not possible. The difference between the types disappears smoothly. For Dirac neutrinos, the dipole moments are proportional to mass and would vanish for a massless particle. Both Majorana and Dirac mass terms however will appear in the mass lagrangian if neutrino have mass, which we now know to be the case.
The suggestion that a neutrino could be a Majorana particle leads to the possible explanation of the negligible neutrino mass in comparison with the masses of other Standard Model fermions.
and does not couple to any fermions or bosons directly. Both neutrinos have mass and the 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 M:
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: , 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.
or LEP-l3 at CERN
. They all lead 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.
Sterile neutrinos may mix with ordinary neutrinos via a Dirac mass
.
Sterile neutrinos and ordinary neutrinos may also have Majorana masses. In certain models, both Dirac and Majorana masses are used in a seesaw mechanism
, which drives ordinary neutrino masses down and makes the sterile neutrinos much heavier than the Standard Model interacting neutrinos. In some models the heavy neutrinos can be as heavy as the GUT scale . 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 ) sterile neutrino was suggested as a possible explanation of the results of the LSND
experiment.
On April 11, 2007, researchers at the MiniBooNE
experiment at Fermilab
announced that they had not found any evidence supporting the existence of such a sterile neutrino. More recent results and analysis have provided some support for the existence of the sterile neutrino.
Neutrino
A neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a half-integer spin, chirality and a disputed but small non-zero mass. It is able to pass through ordinary matter almost unaffected...
that do not interact via any of the fundamental interaction
Fundamental interaction
In particle physics, fundamental interactions are the ways that elementary particles interact with one another...
s of the Standard Model
Standard Model
The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...
except gravity. It is a right-handed neutrino or left-handed anti-neutrino predicted by some extensions to the Standard ModelSee: Grand Unification Theory
Grand unification theory
The term Grand Unified Theory, often abbreviated as GUT, refers to any of several similar candidate models in particle physics in which at high-energy, the three gauge interactions of the Standard Model which define the electromagnetic, weak, and strong interactions, are merged into one single...
that may explain other phenomena, such as neutrino mixing, in which these particles may participate, and the large difference in mass between neutrinos and the charged leptons. The search for these particles is an active area of particle physics
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...
.
Motivation
Experimental results show that (nearly) all produced and observed neutrinos have left-handed helicities (spins antiparallel to momentaMomentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...
), 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
Chirality (physics)
A chiral phenomenon is one that is not identical to its mirror image . The spin of a particle may be used to define a handedness for that particle. A symmetry transformation between the two is called parity...
is observed for either particle. These are the only helicities (and chiralities) included in the Standard Model of particle interactions; the Standard Model predicts only these neutrinos exist.
Recent experiments such as neutrino oscillation
Neutrino oscillation
Neutrino oscillation is a quantum mechanical phenomenon predicted by Bruno Pontecorvowhereby a neutrino created with a specific lepton flavor can later be measured to have a different flavor. The probability of measuring a particular flavor for a neutrino varies periodically as it propagates...
, 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
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....
(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 reference frame. The question, thus, remains: can neutrinos and antineutrinos be differentiated only by chirality? or do right-handed neutrinos and left-handed antineutrinos exist as separate particles?
Properties
Such particles would belong to a singlet representationGroup representation
In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group operation can be represented by matrix multiplication...
with respect to the strong interaction
Strong interaction
In particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a non-contact force...
and the weak interaction
Weak interaction
Weak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...
, having zero electric charge
Electric charge
Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...
, zero weak hypercharge
Weak hypercharge
The weak hypercharge in particle physics is a conserved quantum number relating the electrical charge and the third component of weak isospin, and is similar to the Gell-Mann–Nishijima formula for the hypercharge of strong interactions...
, zero 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...
, and, as with the other leptons, no color
Color charge
In particle physics, color charge is a property of quarks and gluons that is related to the particles' strong interactions in the theory of quantum chromodynamics . Color charge has analogies with the notion of electric charge of particles, but because of the mathematical complications of QCD,...
, although they do have a B-L
B-L
In high energy physics, B − L is the difference between the baryon number and the lepton number .-Details:...
of -1 and an X charge
X (charge)
In particle physics, the X-charge is a conserved quantum number associated with the SO grand unification theory....
of -5. The left-handed anti-neutrino has a B-L
B-L
In high energy physics, B − L is the difference between the baryon number and the lepton number .-Details:...
of 1 and an X charge
X (charge)
In particle physics, the X-charge is a conserved quantum number associated with the SO grand unification theory....
of 5.
Due to the lack of charges, sterile neutrinos would not interact electromagnetically
Electromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
, weakly, or strongly, making them extremely difficult to detect. They would interact gravitationally due to their mass, however, and if they are heavy enough, they could explain cold dark matter
Cold dark matter
Cold dark matter is the improvement of the big bang theory that contains the additional assumption that most of the matter in the Universe consists of material that cannot be observed by its electromagnetic radiation and whose constituent particles move slowly...
or warm dark matter
Warm dark matter
Warm dark matter 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...
. In some grand unification theories
Grand unification theory
The term Grand Unified Theory, often abbreviated as GUT, refers to any of several similar candidate models in particle physics in which at high-energy, the three gauge interactions of the Standard Model which define the electromagnetic, weak, and strong interactions, are merged into one single...
, such as SO(10), they also interact via gauge interactions
Gauge boson
In particle physics, gauge bosons are bosonic particles that act as carriers of the fundamental forces of nature. More specifically, elementary particles whose interactions are described by gauge theory exert forces on each other by the exchange of gauge bosons, usually as virtual particles.-...
which are extremely suppressed at ordinary energies because their gauge boson
Gauge boson
In particle physics, gauge bosons are bosonic particles that act as carriers of the fundamental forces of nature. More specifically, elementary particles whose interactions are described by gauge theory exert forces on each other by the exchange of gauge bosons, usually as virtual particles.-...
is extremely massive. They do not appear at all in some other GUTs, such as the Georgi-Glashow model
Georgi-Glashow model
In particle physics, the Georgi–Glashow model is a particular grand unification theory proposed by Howard Georgi and Sheldon Glashow in 1974. In this model the standard model gauge groups SU×SU×U are combined into a single simple gauge group -- SU...
(i.e. all its SU(5) charges or quantum numbers are zero).
Mass
In the Standard Model, particle masses are generated by the spontaneous breaking of the SU(2)L × U(1) symmetry of the vacuum, which is commonly called the Higgs mechanismHiggs mechanism
In particle physics, the Higgs mechanism is the process in which gauge bosons in a gauge theory can acquire non-vanishing masses through absorption of Nambu-Goldstone bosons arising in spontaneous symmetry breaking....
. In the Higgs mechanism, a doublet of scalar Higgs fields
Higgs boson
The Higgs boson is a hypothetical massive elementary particle that is predicted to exist by the Standard Model of particle physics. Its existence is postulated as a means of resolving inconsistencies in the Standard Model...
(or Higgs boson
Higgs boson
The Higgs boson is a hypothetical massive elementary particle that is predicted to exist by the Standard Model of particle physics. Its existence is postulated as a means of resolving inconsistencies in the Standard Model...
s), interact with other particles. In the process of spontaneous symmetry breaking
Spontaneous symmetry breaking
Spontaneous symmetry breaking is the process by which a system described in a theoretically symmetrical way ends up in an apparently asymmetric state....
, the Higgs field develops a vacuum expectation value,
, and in the LagrangianLagrangian
The Lagrangian, L, of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics by Irish mathematician William Rowan Hamilton known as...
for neutrino wave functions, a massive Dirac field appears:
where m is the positive, real
Real number
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...
mass term.
That is the case for the charged leptons, such as the electron, but the Standard Model does not have a corresponding Dirac mass terms for neutrinos. Weak interactions couple only to the left-handed currents, thus, right-handed neutrinos are not present in the Standard Model Lagrangian. As the result it is not possible to form mass terms for neutrino in the Standard Model: it only predicts a left-handed neutrino and its antiparticle, a right-handed antineutrino, for each generation, produced in chiral eigenstates in weak interactions.
The assumption of a different mass for sterile neutrinos, which is predicted to be significantly heavier than their normal counterparts, arises from a question of what forms the difference between a particle and its antiparticle. For any charged particle, for example the electron, this is simple to answer: its antiparticle, the positron
Positron
The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...
, has opposite electric charge, among other opposite charges. Similarly, an up quark
Up quark
The up quark or u quark is the lightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the down quark, forms the neutrons and protons of atomic nuclei...
has a charge of +⅔ and (for example) a color charge of red, while its antiparticle has an electric charge of -⅔ and a color charge of anti-red.
For the uncharged neutrinos, the answer is less clear. The Standard Model's massless neutrinos only differ from their antiparticles by their chirality, and thus, their helicity, but since neutrinos have been observed to have mass, there may be physics outside the Standard Model, and this opens the door for two different possibilities of the nature of neutrino mass: Majorana or Dirac.
Majorana or Dirac?
If we assume that a particle need not be different in some way from its antiparticle, then the neutrino would be a Majorana fermionMajorana fermion
In physics, a Majorana fermion is a fermion which is its own anti-particle. The term is used in opposition to Dirac fermion, which describes particles that differ from their antiparticles...
, and would be the first of its kind. The concept of the Majorana particle was first introduced by Ettore Majorana
Ettore Majorana
Ettore Majorana was an Italian theoretical physicist who began work on neutrino masses. He disappeared suddenly in mysterious circumstances. He is noted for the eponymous Majorana equation and for Majorana fermions.-Gifted in mathematics:Majorana was born in Catania, Sicily...
in 1937. Examples for boson
Boson
In particle physics, bosons are subatomic particles that obey Bose–Einstein statistics. Several bosons can occupy the same quantum state. The word boson derives from the name of Satyendra Nath Bose....
s are the neutral pion
Pion
In particle physics, a pion is any of three subatomic particles: , , and . Pions are the lightest mesons and they play an important role in explaining the low-energy properties of the strong nuclear force....
, the photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
, and the Z boson which are identical to their antiparticles. If this were the case, the massive neutrino is its own antiparticle
Real neutral particle
In particle physics, a real neutral particle is an elementary particle that is its own antiparticle. Known examples include photons, Z bosons, and neutral pions; along with the hypothetical Higgs bosons, neutralinos, sterile neutrinos, and gravitons .The electromagnetic charge, weak charge, and...
, and could annihilate with another neutrino, possibly allowing neutrinoless double beta decay, and the sterile neutrino would need to differ from the neutrino by something other than its handedness.
However, if we assume that a particle must be different in some way from its antiparticle, then the neutrino is a Dirac fermion
Dirac fermion
In particle physics, a Dirac fermion is a fermion which is not its own anti-particle. It is named for Paul Dirac. All fermions in the standard model, except possibly neutrinos, are Dirac fermions...
. All known fermions are Dirac fermions; an example is the neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...
which has no electric charge but is different from its antiparticle due to its quark
Quark
A quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
composition.A neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...
is composed of one up quark
Up quark
The up quark or u quark is the lightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the down quark, forms the neutrons and protons of atomic nuclei...
and two down quarks, whereas an antineutron
Antineutron
The antineutron is the antiparticle of the neutron with symbol . It differs from the neutron only in that some of its properties have equal magnitude but opposite sign. It has the same mass as the neutron, and no net electric charge, but has opposite baryon number...
is composed of one up anti-quark and two down anti-quarks. The neutral kaon
Kaon
In particle physics, a kaon is any one of a group of four mesons distinguished by the fact that they carry a quantum number called strangeness...
, a boson, is also a Dirac particle in a sense.
To put this in mathematical terms, we have to make use of the transformation properties of particles. We define a Majorana field as an eigenstate of charge conjugation. This definition is only for free fields, and must be generalized to the interacting field. Neutrinos interact only via the weak interactions, which are not invariant to charge conjugation (C), so an interacting Majorana neutrino cannot be an eigenstate of C. The generalized definition is: "a Majorana
Majorana
Majorana may refer to:* Majorana equation, a relativistic wave equation* Majorana fermion, a concept in particle physics* Majorana spinor, a concept in quantum field theory* Origanum majorana, a somewhat cold-sensitive perennial herb...
neutrino field is an eigenstate of the CP transformation".
Consequently, Majorana and Dirac neutrinos would behave differently under CP transformations (actually Lorentz and CPT
CPT symmetry
CPT symmetry is a fundamental symmetry of physical laws under transformations that involve the inversions of charge, parity, and time simultaneously.-History:...
transformations). The distinction between Majorana and Dirac neutrinos is not only theoretical; a massive Dirac neutrino would have nonzero magnetic and electric dipole moment
Electric dipole moment
In physics, the electric dipole moment is a measure of the separation of positive and negative electrical charges in a system of charges, that is, a measure of the charge system's overall polarity with SI units of Coulomb-meter...
s, which could be observed experimentally, whereas a Majorana neutrino would not.
The Majorana and Dirac particles are different only if their rest mass is not zero. If the neutrino has no mass and travels at the speed of light, then the Lorentz transformation to a faster moving frame is not possible. The difference between the types disappears smoothly. For Dirac neutrinos, the dipole moments are proportional to mass and would vanish for a massless particle. Both Majorana and Dirac mass terms however will appear in the mass lagrangian if neutrino have mass, which we now know to be the case.
The suggestion that a neutrino could be a Majorana particle leads to the possible explanation of the negligible neutrino mass in comparison with the masses of other Standard Model fermions.
Seesaw mechanism
If the neutrino is a Majorana particle, then we may assume that besides the left-handed neutrino, which couples to its family charged lepton in weak charged currents, there is also a right-handed sterile neutrino partner "NHL", which is a weak isosingletWeak 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...
and does not couple to any fermions or bosons directly. Both neutrinos have mass and the 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 M:
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: , while the smaller eigenvalue is approximately equal to
This is the seesaw mechanism
Seesaw mechanism
In theoretical physics, the seesaw mechanism is a mechanism within grand unification theory, and in particular in theories of neutrino masses and neutrino oscillation, where it can be used to explain the smallness of observed neutrino masses relative to those of quarks and leptons.There are several...
: 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 FermilabFermilab
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...
or LEP-l3 at CERN
CERN
The European Organization for Nuclear Research , known as CERN , is an international organization whose purpose is to operate the world's largest particle physics laboratory, which is situated in the northwest suburbs of Geneva on the Franco–Swiss border...
. They all lead to establishing limits to observation, rather than actual observation of those particles. If they are indeed a constituent of dark matter, sensitive X-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...
detectors would be needed to observe the radiation emitted by their decays.
Sterile neutrinos may mix with ordinary neutrinos via a Dirac mass
Dirac equation
The Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928. It provided a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity, and...
.
Sterile neutrinos and ordinary neutrinos may also have Majorana masses. In certain models, both Dirac and Majorana masses are used in a seesaw mechanism
Seesaw mechanism
In theoretical physics, the seesaw mechanism is a mechanism within grand unification theory, and in particular in theories of neutrino masses and neutrino oscillation, where it can be used to explain the smallness of observed neutrino masses relative to those of quarks and leptons.There are several...
, which drives ordinary neutrino masses down and makes the sterile neutrinos much heavier than the Standard Model interacting neutrinos. In some models the heavy neutrinos can be as heavy as the GUT scale . 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 ) sterile neutrino was suggested as a possible explanation of the results of the LSND
LSND
The Liquid Scintillator Neutrino Detector was a scintillation counter at Los Alamos National Laboratory that measured the number of neutrinos being produced by an accelerator neutrino source...
experiment.
On April 11, 2007, researchers at the MiniBooNE
MiniBooNE
MiniBooNE is an experiment at Fermilab designed to observe neutrino oscillations . A neutrino beam consisting primarily of muon neutrinos is directed at a detector filled with 800 tons of mineral oil and lined with 1,280 photomultiplier tubes...
experiment at 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...
announced that they had not found any evidence supporting the existence of such a sterile neutrino. More recent results and analysis have provided some support for the existence of the sterile neutrino.