# Sterile neutrino

Composition Elementary particle Fermionic unknown gravity; other potential unknown interactions Hypothetical unknown unknown 0 none 1/2 2 0 0 right handed depends on L charge assignment −5

Sterile neutrinos[nb 1] are hypothetical particles that do not interact via any of the fundamental interactions of the Standard Model except gravity. The term sterile neutrino usually refers to neutrinos with right handed chirality (see right-handed neutrino), which may be added to the Standard Model, to distinguish them from the known active neutrinos in the Standard Model, which are charged under the weak interaction. Occasionally it is used in a more general sense for any neutral fermion. The existence of right handed neutrinos is theoretically well-motivated, as all other known fermions have been observed with 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 $10^{15}$ GeV and less than one eV.[1] The number of sterile neutrino types is unknown. 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. They can be produced in the laboratory, either by mixing between active and sterile neutrinos or in high energy particle collisions, if their mass is smaller than the energies of particles in the experiment. 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.[1]

## Motivation

Experimental results show that (nearly) all produced and observed neutrinos have left-handed helicities (spins antiparallel to momenta), 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?

## Properties

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 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 charge, 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).

### Mass

Under the Standard Model, particle masses are generated by the Higgs mechanism, wherein the SU(2)L × U(1) symmetry of the vacuum is spontaneously broken. In the Higgs mechanism, a doublet of scalar Higgs fields, or Higgs bosons, interact with other particles. Via the process of spontaneous symmetry breaking, the Higgs field develops a vacuum expectation value, $\phi$, and in the Lagrangian for neutrino wave functions, a massive Dirac field appears:

$\mathcal{L}(\psi) = \bar{\psi}(i\partial\!\!\!/-m)\psi - g\bar\psi_L \phi \psi_R$

where m is the positive, real mass term.

Such is the case for charged leptons, such as the electron; but, the Standard Model does not have 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. Consequently, it is not possible to form mass terms for neutrinos under the Standard Model: the model 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.

#### 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 fermion, and would be the first of its kind. The concept of the Majorana particle was first introduced by Ettore Majorana in 1937. Examples for bosons 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.[nb 2] 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 moments, 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 neutrinos 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 isosinglet 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:

$m_{\nu} = \begin{pmatrix}0&m_D\\m_D&M_{NHL}\end{pmatrix}$

where $M_{NHL}$ is big and $m_D$ 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:

$m_{\nu} << m_D << M_{NHL}$

According to GUTs and left-right models, the right-handed neutrino is extremely heavy: MNHL1051012 GeV, while the smaller eigenvalue is approximately equal to

$m_{\nu} \approx \frac{m_D^2}{M_{NHL}}$

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 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.[2]

Sterile neutrinos may mix with ordinary neutrinos via a Dirac mass[citation needed][clarification needed]. Sterile neutrinos and ordinary neutrinos may also have Majorana masses. In certain models[which?], 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[which?] the heavy neutrinos can be as heavy as the GUT scale (≈1015 GeV). In other models[which?] 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 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.[3] More recent results and analysis have provided some support for the existence of the sterile neutrino.[4][5][6] Two separate detectors near a nuclear reactor in France found 3% of anti neutrinos missing. They suggested the existence of a 4th neutrino of mass 0.7 Kev.[7] Sterile neutrinos are also candidates for dark radiation.

The number of neutrinos and the masses of the particles can have large-scale effects that shape the appearance of the CMB. 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 found no evidence of neutrino-like particles.[8]

• LSND (Liquid Scintillator Neutrino Detector at LANL)
• MiniBooNE at Fermilab

## References

Notes
1. ^ In scientific literature, these particles are also variously referred to as right-handed neutrinos or inert neutrinos.
2. ^ 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.
References
1. ^ a b Marco Drewes (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.
2. ^ Battison, Leila (2011-09-16). "Dwarf galaxies suggest dark matter theory may be wrong". BBC News. Retrieved 2011-09-18.
3. ^
4. ^ Scientific American: "Dimensional Shortcuts", August 2007
5. ^ Aguilar-Arevalo, A. A.; et al. (MiniBooNE Collaboration) (2010). "Event Excess in the MiniBooNE Search for νμνe Oscillations". Physical Review Letters 105 (18): 181801. arXiv:1007.1150. Bibcode:2010PhRvL.105r1801A. doi:10.1103/PhysRevLett.105.181801.
6. ^ Loewenstein, M.; Kusenko, A. (2010). "Dark Matter Search Using Chandra Observations of Willman 1 and a Spectral Feature Consistent with a Decay Line of a 5 keV Sterile Neutrino". The Astrophysical Journal 714 (1): 652. arXiv:0912.0552. Bibcode:2010ApJ...714..652L. doi:10.1088/0004-637X/714/1/652.
7. ^ The Reactor Antineutrino Anomaly
8. ^ Ade, P.A.R.; et al. (Planck Collaboration) (2013). "Planck 2013 results. XVI. Cosmological parameters". arXiv:1303.5076 [astro-ph.CO].
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