# Sterile neutrino

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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 (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 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 1015 GeV and less than one 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 neutrinos may be neutral heavy leptons (NHLs), also called heavy neutral leptons (HNLs).

## Motivation

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, even though chirality is not conserved in the propagation of a free particle (a particle that starts out left-handed can evolve a right-handed component). The question, thus, remains: can neutrinos and antineutrinos be differentiated just 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. 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 charge, 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, 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

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 ${\displaystyle \phi }$ acquires its non-zero vacuum expectation value, ${\displaystyle \nu }$, spontaneously breaking its SU(2)L × U(1) symmetry, and thus yielding non-zero Yukawa couplings:

${\displaystyle {\mathcal {L}}(\psi )={\bar {\psi }}(i\partial \!\!\!/)\psi -G{\bar {\psi }}_{L}\phi \psi _{R}}$

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 ${\displaystyle M_{\nu }}$:

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

where ${\displaystyle M_{NHL}}$ is big and ${\displaystyle m_{D}}$ 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:

${\displaystyle m_{\nu }\ll m_{D}\ll M_{NHL}}$

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

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

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 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.[citation needed] 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[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 Liquid Scintillator Neutrino Detector 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.[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 0.7 keV.[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 to 3 eV.[12][not in citation given (See discussion.)] 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]

## References

Notes
References
1. ^ A major physics experiment just detected a particle that shouldn't exist Live Science (2018)
2. ^ 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.
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; Cooper, R. L; Dharmapalan, R; Diaz, A; Djurcic, Z; Finley, D. A; Ford, R; Garcia, F. G; Garvey, G. T; Grange, J; Huang, E. -C; Huelsnitz, W; Ignarra, C; Johnson, R. A; Karagiorgi, G; Katori, T; Kobilarcik, T; Louis, W. C; Mariani, C; Marsh, W; Mills, G. B; Mirabal, J; Monroe, J; Moore, C. D; et al. (2018). "Observation of a Significant Excess of Electron-Like Events in the MiniBooNE Short-Baseline Neutrino Experiment". arXiv:1805.12028.
5. ^ Battison, Leila (2011-09-16). "Dwarf galaxies suggest dark matter theory may be wrong". BBC News. Retrieved 2011-09-18.
6. ^
7. ^ Scientific American: "Dimensional Shortcuts", 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; Butorov, I; Cao, G. F; Cao, J; Chan, Y. L; Chang, J. F; Chang, L. C; Chang, Y; Chasman, C; Chen, H; Chen, Q. Y; Chen, S. M; Chen, X; Chen, X; Chen, Y. X; Chen, Y; Cheng, Y. P; Cherwinka, J. J; Chu, M. C; Cummings, J. P; De Arcos, J; Deng, Z. Y; Ding, Y. Y; Diwan, M. V; et al. (1 October 2014). "Search for a Light Sterile Neutrino at Daya Bay". Phys. Rev. Lett. 113 (14): 141802. arXiv:1407.7259. Bibcode:2014PhRvL.113n1802A. doi:10.1103/PhysRevLett.113.141802.
11. ^ http://www.symmetrymagazine.org/article/daya-bay-discovers-a-mismatch
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.
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