View source for Sterile neutrino

{{Short description|Hypothetical particle that interacts only via gravity}}
{{Infobox Particle
| bgcolour =
| name = Sterile neutrino, right-handed neutrino
| image = 
| caption = 
| num_types = unknown
| composition = [[Elementary particle]]
| statistics = [[Fermionic]]
| group = [[lepton]]
| generation = unknown
| interaction = gravity; other potential unknown interactions
| particle = 
| antiparticle = 
| status = Hypothetical
| theorized = 
| discovered = 
| symbol = 
| mass = unknown
| mean_lifetime = 
| decay_particle = 
| electric_charge = 0
| weak_isospin_3 = 0
| chirality = right-handed
| B-L = depends on L charge assignment 
| X_charge = −5
| color_charge = none
| spin = {{frac|1|2}}
| weak_hypercharge = 0
| num_spin_states = 2
}}
'''Sterile neutrinos''' (or '''inert neutrinos''') are hypothetical [[particles]] (neutral [[lepton]]s – [[neutrino]]s) that interact only via [[gravity]] and not via any of the other [[fundamental interaction]]s of the [[Standard Model]].<ref>{{cite web |title=Sterile neutrinos |series=All things neutrino |url=https://neutrinos.fnal.gov/types/sterile-neutrinos/ |access-date=2021-04-29 |language=en-US}}</ref> The term ''sterile neutrino'' is used to distinguish them from the known, ordinary ''active neutrinos'' in the [[Standard Model]], which carry an [[weak isospin|isospin]] charge of {{sfrac|±|1| 2 }} and engage in the [[weak interaction]]. The term typically refers to [[neutrino]]s with [[Chirality (physics)|right-handed chirality]] (see [[Neutrino#Chirality|right-handed neutrino]]), which may be inserted into the Standard Model. Particles that possess the [[quantum number]]s of sterile neutrinos and masses great enough such that they do not interfere with the current theory of [[Big Bang nucleosynthesis]] are often called '''neutral heavy leptons''' (NHLs) or '''heavy neutral leptons''' (HNLs).<ref>{{cite journal |first1=P.A. |last1=Zyla |display-authors=etal |collaboration=Particle Data Group |year=2020 |url=https://pdg.lbl.gov/2020/listings/rpp2020-list-heavy-neutral-leptons.pdf |title= Review of Particle Physics|journal= Progress of Theoretical and Experimental Physics: Neutral Heavy Leptons, Searches for |volume=2020 |issue=8 |page= 083C01 [1168] |doi=10.1093/ptep/ptaa104}}</ref>

The existence of right-handed neutrinos is theoretically well-motivated, because the known active neutrinos are left-handed and all other known [[fermions]] have been observed with both left and right [[chirality]].<ref name=Boyarsky-Drewes-etal-2019>{{cite journal |last1=Boyarsky |first1=A. |last2=Drewes |first2=M. |last3=Lasserre |first3=T. |last4=Mertens |first4=S. |last5=Ruchayskiy |first5=O. |date=January 2019 |title=Sterile neutrino Dark Matter |journal=Progress in Particle and Nuclear Physics |volume=104 |pages=1–45 |doi=10.1016/j.ppnp.2018.07.004 |arxiv=1807.07938 |bibcode=2019PrPNP.104....1B |s2cid=116613775}}</ref> They could also explain in a natural way the small active [[neutrino mass]]es inferred from [[neutrino oscillation]].<ref name=Boyarsky-Drewes-etal-2019/> The mass of the right-handed neutrinos themselves is unknown and could have any value between {{val|e=15|ul=GeV}} and less than 1&nbsp;eV.<ref name="RHNeutrinosReview2">{{cite journal |last=Drewes |first=Marco |year=2013 |title=The phenomenology of right handed neutrinos |journal=[[International Journal of Modern Physics E]] |volume=22 |issue=8 |pages=1330019–1330593 |arxiv=1303.6912 |bibcode=2013IJMPE..2230019D |doi=10.1142/S0218301313300191 |s2cid=119161526}}</ref> To comply with theories of [[leptogenesis]] and [[dark matter]], there must be ''at least'' 3&nbsp;flavors of sterile neutrinos (if they exist).<ref>{{cite journal |last1=Ibe |first1=Masahiro |last2=Kusenko |first2=Alexander |last3=Yanagida |first3=Tsutomu T. |date=2016-07-10 |title=Why three generations? |journal=Physics Letters B |language=en |volume=758 |pages=365–369 |doi=10.1016/j.physletb.2016.05.025 |issn=0370-2693 |doi-access=free |arxiv=1602.03003 |bibcode=2016PhLB..758..365I}}</ref> This is in contrast to the number of active neutrino types required to ensure the [[electroweak interaction]] is free of anomalies, which must be ''exactly''&nbsp;3: the number of charged leptons and [[quark]] [[Generation (particle physics)|generations]].

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 [[Neutrino oscillations|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 hypothetical [[dark radiation]].<ref name=RHNeutrinosReview2/> In May&nbsp;2018, physicists of the [[MiniBooNE]] experiment reported a stronger neutrino oscillation signal than expected, a possible hint of sterile neutrinos.<ref name=LS-20180601/><ref name=ARX-20180530/> However, results of the [[MicroBooNE]] experiment showed no evidence of sterile neutrinos in October 2021.<ref>{{cite press release |title=MicroBooNE experiment's first results show no hint of a sterile neutrino |date=27 October 2021 |website=news.uchicago.edu |publisher=[[University of Chicago]] News |lang=en |url=https://news.uchicago.edu/story/microboone-experiments-first-results-show-no-hint-sterile-neutrino}}</ref>

== Motivation ==
{{See also|Neutrino#Chirality|Neutrino oscillation|l1=Neutrino: Chirality}}
Experimental results show that all produced and observed neutrinos have left-handed [[Helicity (particle physics)|helicities]] (spin antiparallel to [[momentum]]), and all antineutrinos have right-handed helicities, within the margin of error.<ref name=Boyarsky-Drewes-etal-2019/> In the massless limit, it means that only one of two possible [[Chirality (physics)|chiralities]] is observed for either particle. These are the only helicities (and chiralities) allowed in the Standard Model of particle interactions; particles with the contrary helicities are explicitly excluded from the formulas.<ref>{{cite journal |last=Fonseca |first=Renato M. |date=August 2015 |title=On the chirality of the SM and the fermion content of GUTs |journal=Nuclear Physics&nbsp;B |language=en |volume=897 |pages=757–780 |doi=10.1016/j.nuclphysb.2015.06.012 |doi-access=free |arxiv=1504.03695 |bibcode=2015NuPhB.897..757F}}</ref>

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.<ref>{{cite journal |last1=Fukuda |first1=Y. |last2=Hayakawa |first2=T. |last3=Ichihara |first3=E. |last4=Inoue |first4=K. |last5=Ishihara |first5=K. |last6=Ishino |first6=H. |last7=Itow |first7=Y. |last8=Kajita |first8=T. |last9=Kameda |first9=J. |last10=Kasuga |first10=S. |last11=Kobayashi |first11=K. |date=1998-08-24 |title=Evidence for Oscillation of Atmospheric Neutrinos |journal=Physical Review Letters |language=en |volume=81 |issue=8 |pages=1562–1567 |doi=10.1103/PhysRevLett.81.1562 |doi-access=free |arxiv=hep-ex/9807003 |bibcode=1998PhRvL..81.1562F |issn=0031-9007}}</ref> 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).<ref>{{cite journal |last1=Jentschura |first1=U.D. |last2=Wundt |first2=B.J. |date=2014-07-01 |title=Neutrino helicity reversal and fundamental symmetries |journal=Journal of Physics&nbsp;G: Nuclear and Particle Physics |volume=41 |issue=7 |pages=075201 |doi=10.1088/0954-3899/41/7/075201 |issn=0954-3899 |arxiv=1206.6342 |bibcode=2014JPhG...41g5201J |s2cid=119241784 |url=https://iopscience.iop.org/article/10.1088/0954-3899/41/7/075201}}</ref> Yet all neutrinos have been observed with left-handed ''chirality'', and all antineutrinos right-handed. (See ''{{section link|Chirality (physics)#Chirality and helicity}}'' for the difference.)

Chirality is a fundamental property of particles and ''is'' relativistically invariant: It is the same regardless of the particle's speed and mass in every inertial reference frame.<ref>{{cite journal |last1=Chen |first1=Jing-Yuan |last2=Son |first2=Dam T. |last3=Stephanov |first3=Mikhail A. |last4=Yee |first4=Ho-Ung |last5=Yin |first5=Yi |date=2014-10-30 |title=Lorentz invariance in chiral kinetic theory |journal=Physical Review Letters |volume=113 |issue=18 |pages=182302 |doi=10.1103/PhysRevLett.113.182302 |doi-access=free |pmid=25396362 |arxiv=1404.5963 |bibcode=2014PhRvL.113r2302C |issn=0031-9007 |language=en}}</ref> However, a particle with mass that starts out with left-handed chirality can develop a right-handed component as it travels – unless it is massless, chirality is ''not'' conserved during the propagation of a free particle through space (nominally, through interaction with the [[Higgs boson|Higgs field]]).

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?

== Properties ==
Such particles would belong to a [[singlet state|singlet]] [[group representation|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]], zero [[color charge]], although they are conventionally represented to have a{{nobr| {{mvar|[[B-L|B &minus; L]]}} }}quantum number of &minus;1.<ref>{{cite journal |last1=Das |first1=Arindam |last2=Dev |first2=P.S. Bhupal |last3=Okada |first3=Nobuchika |date=2019-12-10 |title=Long-lived TeV-scale right-handed neutrino production at the LHC in gauged U(1)X model |journal=Physics Letters&nbsp;B |volume=799 |pages=135052 |doi=10.1016/j.physletb.2019.135052 |doi-access=free |issn=0370-2693 |arxiv=1906.04132 |bibcode=2019PhLB..79935052D |language=en}}</ref> If the Standard Model is embedded in a hypothetical [[SO(10)]] [[grand unified theory]], they can be assigned an [[X (charge)|X&nbsp;charge]] of &minus;5. The left-handed anti-neutrino has a{{nobr| {{mvar|B &minus; L}} }}of +1 and an X&nbsp;charge of +5.

Due to the lack of electric charge, [[hypercharge]], and color charge, sterile neutrinos would not interact via the [[electromagnetism|electromagnetic]], weak, or [[strong interaction|strong]] interactions, making them extremely difficult to detect. They have [[Yukawa interaction]]s with ordinary [[leptons]] and [[Higgs boson]]s, which via the [[Higgs mechanism]] leads to mixing with ordinary neutrinos.

In experiments involving energies larger than their mass, sterile neutrinos would participate in all processes in which ordinary neutrinos take part, but with a quantum mechanical probability that is suppressed by a small mixing angle. That makes it possible to produce them in experiments, if they are light enough to be within the reach of current particle accelerators.

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 boson|gauge interactions]] which are extremely suppressed at ordinary energies because their SO(10)-derived [[gauge boson]] is extremely massive. They do not appear at all in some other [[Grand Unified Theory|Grand Unified Theories]], 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 [[Standard Model (mathematical formulation)#Mass terms|Dirac mass terms]] in the Standard Model's [[Lagrangian (field theory)|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 [[Special unitary group|'''SU'''(2)]] doublet Higgs field <math>\phi</math> acquires its non-zero vacuum expectation value, <math>\nu</math>, [[spontaneous symmetry breaking|spontaneously breaking]] its SU(2){{sub|L}} &times; U(1) symmetry, and thus yielding non-zero Yukawa couplings:
: <math>\mathcal{L}(\psi) = 
\bar{\psi}(i\partial\!\!\!/)\psi - G \bar\psi_L \phi \psi_R</math>

Such is the case for charged leptons, like the electron, but within the Standard Model the right-handed neutrino does not exist. So absent the sterile right chiral neutrinos to pair up with the left chiral neutrinos, even with Yukawa coupling the active neutrinos remain massless. In other words, there are no mass-generating terms for neutrinos under the Standard Model: For each generation, the model only contains a left-handed neutrino and its antiparticle, a right-handed antineutrino, each of which is produced in weak [[Quantum state|eigenstates]] during weak interactions; the "sterile" neutrinos are omitted. (See [[Standard Model (mathematical formulation)#Neutrino masses|neutrino masses in the Standard Model]] for a detailed explanation.)

In the [[seesaw mechanism]], the model is extended to include the missing right-handed neutrinos and left-handed antineutrinos; one of the [[Eigenvalues and eigenvectors|eigenvectors]] of the neutrino mass matrix is then hypothesized to be remarkably heavier than the other.

A sterile (right-chiral) neutrino would have the same [[weak hypercharge]], weak [[isospin]], and electric charge as its antiparticle, because all of these are zero and hence are unaffected by [[charge conjugation|sign reversal]].{{efn|
And as with all other particle / anti-particle pairs, the sterile right-chiral neutrino and left-chiral anti-neutrino would also have identical, non-zero mass. Chirality, lepton-number, and flavor (if any) are the only quantum numbers that distinguish a sterile neutrino from a sterile antineutrino. For any charged particle, for example the [[electron]], this is not the case: Its antiparticle, the [[positron]], has opposite electric charge, opposite weak isospin, and opposite chirality, among other opposite charges. Similarly, an [[up quark]] has a charge of {{sfrac|+|2|3}} and, for example, a color charge of red, while its antiparticle has an electric charge of {{sfrac|&minus;|2|3}} and in this example 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 [[real neutral particle|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]].<ref>{{cite journal |last=Rodejohann |first=Werner |date=September 2011 |title=Neutrino-less double beta decay and particle physics |journal=International Journal of Modern Physics&nbsp;E |volume=20 |issue=9 |pages=1833–1930 |doi=10.1142/S0218301311020186 |issn=0218-3013 |arxiv=1106.1334 |bibcode=2011IJMPE..20.1833R |s2cid=119102859 |url=https://www.worldscientific.com/doi/abs/10.1142/S0218301311020186 |lang=en}}</ref> 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 [[C-symmetry|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 fermion|Majorana]] neutrino field is an eigenstate of the CP transformation". Consequently, Majorana and Dirac neutrinos would behave differently under CP transformations (actually [[Lorentz transformations|Lorentz]] and [[CPT symmetry|CPT]] transformations). Also, a massive Dirac neutrino would have nonzero [[magnetic dipole moment|magnetic]] and [[electric dipole moment]]s, 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 be inserted into the mass [[Lagrangian (field theory)|Lagrangian]].

=== Seesaw mechanism ===
{{Main|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.<ref>{{cite conference |last=Mohapatra |first=R.N. |date=April 2005 |title=Seesaw mechanism and its implications |conference=Seesaw 25 |lang=en |location=Institut Henri Poincaré, Paris, FR |publisher=World Scientific |pages=29–44 |doi=10.1142/9789812702210_0003 |isbn=978-981-256-111-4 |arxiv=hep-ph/0412379 |bibcode=2005icsm.conf...29M |s2cid=2709571}}</ref>

Both left-handed and right-handed neutrinos could then have mass and handedness which are no longer exactly preserved (thus "left-handed neutrino" would mean that the state is ''mostly'' left and "right-handed neutrino" would mean ''mostly'' right-handed). To get the neutrino mass eigenstates, we have to diagonalize the general mass matrix <math>\ M_{\nu}:</math>
: <math>M_{\nu} \approx \begin{pmatrix}
                           0           &  m_\text{D} \\
                           m_\text{D}  &  M_\text{NHL}
                        \end{pmatrix}</math>
where <math>\ M_\text{NHL}\ ,</math> is the neutral heavy lepton's mass, which is big, and <math>\ m_\text{D}\ </math> are intermediate-size mass terms, which interconnect the sterile and active neutrino masses. The matrix nominally assigns active neutrinos zero mass, but the <math>\ m_\text{D}\ </math> terms provide a route for some small part of the sterile neutrinos' enormous mass, <math>\ M_\text{NHL}\ ,</math> to "leak into" the active neutrinos.

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:

: <math>m_\nu \ll m_\text{D} \ll M_\text{NHL}\ .</math>

According to GUTs and left-right models, the right-handed neutrino is extremely heavy: <math display="inline">M_\text{NHL} \sim 10^5 \ldots 10^{12} \text{ GeV },</math> while the smaller eigenvalue is approximately given by

: <math>m_\nu \approx \frac{m_\text{D}^2}{M_\text{NHL}}\ .</math><ref>{{cite news |last=Rodejohann |first=Werner |date=1 May 2021 |title=Sterile neutrinos from the low energy to the GUT scale |url=https://indico.cern.ch/event/176696/contributions/1442190/attachments/229763/321468/Rodejohann_CERN-sterile-neutrino-TH-review.pdf }}</ref>

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.

== Sterile neutrinos as dark matter ==
{{See also|Dark matter}}For a particle to be considered a dark matter candidate, it must have non-zero mass and no [[Electromagnetism|electromagnetic]] charge.<ref>{{cite web |title=Dark matter |website=[[CERN]] |url=https://home.cern/science/physics/dark-matter |access-date=2021-04-29 |language=en}}</ref> Naturally, neutrinos and neutrino-like particles are of interest in the search for dark matter because they possess both these properties. Observations suggest that there is more [[cold dark matter]] (non-relativistic) than [[hot dark matter]] (relativistic). The active neutrinos of the Standard Model, having very low mass (and therefore very high speeds) are therefore unlikely to account for all dark matter.<ref>{{cite journal |last=Ibarra |first=Alejandro |date=2015-07-15 |title=Neutrinos and dark matter |journal=AIP Conference Proceedings |volume=1666 |issue=1 |page=140004 |doi=10.1063/1.4915588 |bibcode=2015AIPC.1666n0004I |issn=0094-243X |doi-access=free }}</ref>

Since no bounds on the mass of sterile neutrinos are known, the possibility that the sterile neutrino is dark matter has not yet been ruled out, as it has for active neutrinos. If dark matter consists of sterile neutrinos then certain constraints can be applied to their properties. Firstly, in order to produce the structure of the universe observed today the mass of the sterile neutrino would need to be on the [[keV]] scale, based on parameter space of the remaining [[supersymmetry|supersymmetric models]] that have not yet been excluded by experiment.<ref>
{{cite journal
 |last=Merle |first=Alexander
 |date=August 2013
 |title=keV neutrino model building
 |journal=International Journal of Modern Physics&nbsp;D
 |volume=22  |issue=10  |page=1330020
 |doi=10.1142/S0218271813300206
 |issn=0218-2718  |arxiv=1302.2625  |bibcode=2013IJMPD..2230020M
 |s2cid=118550598  |language=en
 |url=https://www.worldscientific.com/doi/abs/10.1142/S0218271813300206
}}
</ref>
Secondly, while it is not required that dark matter be stable, the lifetime of the particles must be longer than the current age of the universe. This places an upper bound on the strength of the mixing between sterile and active neutrinos in the seesaw mechanism.<ref>
{{cite journal
 |first1=A. |last1=Boyarsky      |first2=M. |last2=Drewes 
 |first3=T. |last3=Lasserre      |first4=S. |last4=Mertens
 |first5=O. |last5=Ruchayskiy
 |date=January 2019
 |title=Sterile neutrino dark matter
 |journal=Progress in Particle and Nuclear Physics
 |volume=104 |pages=1–45
 |doi=10.1016/j.ppnp.2018.07.004   |arxiv=1807.07938
 |s2cid=116613775   |bibcode=2019PrPNP.104....1B   |language=en
 |url=https://linkinghub.elsevier.com/retrieve/pii/S0146641018300711
}}
</ref>
From what is known about the particle thus far, the sterile neutrino is a promising dark matter candidate, but as with every other proposed dark matter particle, it has yet to be confirmed to exist.

== 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 [[L3 experiment|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.<ref name=bbcwdm>
{{cite news
 |last=Battison |first=Leila
 |date=2011-09-16
 |title=Dwarf galaxies suggest dark matter theory may be wrong
 |website=[[BBC News]]
 |url=https://www.bbc.co.uk/news/science-environment-14948730
 |access-date=2011-09-18  |df=dmy-all
}}
</ref>
[[File:MiniBooNE.jpg|thumb|The MiniBooNE detector (interior shown) at Fermilab was created to measure the oscillation of neutrinos.]]
Sterile neutrinos may mix with ordinary neutrinos via a [[Dirac mass]] after [[electroweak symmetry breaking]], in analogy to [[quarks]] and charged leptons.<ref>
{{cite journal
 |last1=Gorbunov |first1=Dmitry
 |last2=Panin    |first2=Alexander
 |date=2014-01-31  |df=dmy-all
 |title=Minimal active-sterile neutrino mixing in seesaw type&nbsp;I mechanism with sterile neutrinos at GeV scale
 |journal=[[Physical Review D]]
 |volume=89  |issue=1  |page=017302
 |doi=10.1103/PhysRevD.89.017302  |issn=1550-7998
 |arxiv=1312.2887  |s2cid=119201012
 |bibcode=2014PhRvD..89a7302G  |lang=en
}}
</ref> Sterile neutrinos and (in more-complicated models) ordinary neutrinos may also have [[Majorana equation|Majorana mass]]es. 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 GUT scale seesaw models the heavy neutrinos can be as heavy as the [[GUT scale]] ({{val|p=≈|e=15|u=GeV}}).<ref>
{{cite journal
 |last=Shakya |first=Bibhushan
 |date=2016-02-28  |df=dmy-all
 |title=Sterile neutrino dark matter from freeze-in
 |journal=[[Modern Physics Letters A]]
|volume=31 |issue=6 |page=1630005
 |doi=10.1142/S0217732316300056 |issn=0217-7323
 |arxiv=1512.02751 |bibcode=2016MPLA...3130005S
 |s2cid=119198719 |lang=en
}}
</ref> In other models, such as the νMSM model where their masses are in the keV to GeV range, they could be lighter than the [[W-boson|weak gauge bosons W and Z]].<ref>
{{cite conference
 |last=Gorbunov  |first=Dmitry
 |date=2016-03-16  |df=dmy-all
 |title=nuMSM: The model, its predictions and experimental tests
 |conference=European Physical Society Conference on High Energy Physics — PoS (EPS-HEP2015)
 |volume=234  |page=092
 |location=Vienna, Austria
 |publisher=Sissa Medialab
 |doi=10.22323/1.234.0092 |doi-access=free
 |url=https://pos.sissa.it/234/092
 |lang=en
}}
</ref>
A light (with the mass {{val|p=≈|1|u=eV}}) sterile neutrino was suggested as a possible explanation of the results of the [[Liquid Scintillator Neutrino Detector]] experiment. On 11&nbsp;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.<ref>
{{cite press release
 |title=First results
 |department=Booster Neutrino Experiment (BooNE)
 |publisher=[[Fermilab|Fermi National Accelerator Laboratory (Fermilab)]]
 |url=http://www-boone.fnal.gov/publicpages/First_Results.pdf
}}
</ref>
More-recent results and analysis have provided some support for the existence of the sterile neutrino.<ref>
{{cite journal
 |first1=E.  |last1=Bulbul        |first2=M.   |last2=Markevitch
 |first3=A.  |last3=Foster        |first4=R.K. |last4=Smith
 |first5=M.  |last5=Loewenstein   |first6=S.W. |last6=Randall
 |year=2014
 |title=Detection of an unidentified emission line in the stacked X-ray spectrum of galaxy clusters
 |journal=[[The Astrophysical Journal]]
 |volume=789  |issue=1  |page=13
 |arxiv=1402.2301  |bibcode=2014ApJ...789...13B
 |doi=10.1088/0004-637X/789/1/13|s2cid=118468448
}}
</ref>

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&nbsp;eV.<ref>{{cite press release |author=Lasserre, Th. |date=April 2012 |title=The reactor antineutrino anomaly |website=irfu.cea.fr |lang=en |url=http://irfu.cea.fr/en/Phocea/Vie_des_labos/Ast/ast_visu.php?id_ast=3045}}</ref> [[Daya Bay Reactor Neutrino Experiment|Daya Bay]] has also searched for a light sterile neutrino and excluded some mass regions.<ref>
{{cite journal
 |last1=An        |first1=F.P.      |last2=Balantekin |first2=A.B.
 |last3=Band      |first3=H.R.      |last4=Beriguete |first4=W.
 |last5=Bishai    |first5=M.        |last6=Blyth     |first6=S.
 |last7=Butorov   |first7=I.        |last8=Cao       |first8=G.F.
 |last9=Cao       |first9=J.        |last10=Chan     |first10=Y.L.
 |last11=Chang    |first11=J.F.     |last12=Chang    |first12=L.C.
 |last13=Chang    |first13=Y.       |last14=Chasman  |first14=C.
 |last15=Chen     |first15=H.       |last16=Chen     |first16=Q.Y.
 |last17=Chen     |first17=S.M.     |last18=Chen     |first18=X.
 |last19=Chen     |first19=X.       |last20=Chen     |first20=Y.X.
 |last21=Chen     |first21=Y.       |last22=Cheng    |first22=Y.P.
 |last23=Cherwinka |first23=J.J.    |last24=Chu      |first24=M.C.
 |last25=Cummings |first25=J.P.     |last26=de&nbsp;Arcos |first26=J.
 |last27=Deng     |first27=Z.Y.     |last28=Ding     |first28=Y.Y.
 |last29=Diwan    |first29=M.V.     |last30=Draeger  |first30=E.
 |display-authors=6
 |date=October 2014
 |title=Search for a light sterile neutrino at Daya Bay
 |journal=[[Physical Review Letters]]
 |volume=113  |issue=14  |page=141802
 |doi=10.1103/PhysRevLett.113.141802
 |bibcode=2014PhRvL.113n1802A
 |pmid=25325631  |arxiv=1407.7259
 |s2cid=10500157
}}
</ref>
Daya Bay collaboration measured the anti-neutrino energy spectrum, and found that anti-neutrinos at an energy of around 5&nbsp;MeV are in excess relative to theoretical expectations. It also recorded 6% missing anti-neutrinos.<ref>
{{cite news
 |last=Jepsen |first=Kathryn
 |date=2016-02-12  |df=dmy-all
 |title=Daya Bay discovers a mismatch
 |journal=[[Symmetry (journal)|Symmetry]]
 |url=http://www.symmetrymagazine.org/article/daya-bay-discovers-a-mismatch
 |access-date=2022-12-19
}}
</ref>
This could suggest either that sterile neutrinos exist or that our understanding of some other aspect of neutrinos is incomplete.

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&nbsp;eV.<ref>
{{cite journal
 |last1=Ade  |first1=P.A.R.
 |display-authors=etal
 |collaboration=[[Planck (spacecraft)|Planck]] collaboration
 |year=2013
 |title=Planck 2013 results. XVI.&nbsp;Cosmological parameters
 |journal=[[Astronomy & Astrophysics]]
 |volume=571  |page=A16
 |bibcode=2014A&A...571A..16P   |arxiv=1303.5076
 |doi=10.1051/0004-6361/201321591  |s2cid=118349591
}}
</ref>{{Failed verification|date=June 2018|talk=Planck_result_summarized_inaccurately}} In 2016, scientists at the [[IceCube Neutrino Observatory]] did not find any evidence for the sterile neutrino.<ref>
{{cite news
 |last=Castelvecchi |first=Davide
 |date=8 August 2016
 |title=Icy telescope throws cold water on sterile neutrino theory
 |journal=[[Nature (journal)|Nature]]
 |s2cid=125498830  |doi=10.1038/nature.2016.20382
 |url=http://www.nature.com/news/icy-telescope-throws-cold-water-on-sterile-neutrino-theory-1.20382#/b1
 |access-date=12 August 2016
}}
</ref>
However, in May&nbsp;2018, physicists of the MiniBooNE experiment reported a stronger neutrino oscillation signal than expected, a possible hint of sterile neutrinos.<ref name=LS-20180601>
{{cite news
 |last=Letzter |first=Rafi
 |date=1 June 2018
 |title=A major physics experiment just detected a particle that shouldn't exist
 |website=[[LiveScience]]
 |url=https://www.livescience.com/62721-sterile-neutrino-detected-fermilab.html
 |access-date=3 June 2018
}}
</ref><ref name=ARX-20180530>
{{cite journal
 |last1=Aguilar-Arevalo |first1=A.A.    |last2=Brown    |first2=B.C.
 |last3=Bugel     |first3=L.            |last4=Cheng    |first4=G.
 |last5=Conrad    |first5=J.M.          |last6=Cooper   |first6=R.L.
 |last7=Dharmapalan |first7=R.          |last8=Diaz     |first8=A.
 |last9=Djurcic   |first9=Z.            |last10=Finley  |first10=D.A.
 |last11=Ford     |first11=R.           |last12=Garcia  |first12=F.G.
 |last13=Garvey   |first13=G.T.         |last14=Grange  |first14=J.
 |last15=Huang    |first15=E.-C.        |last16=Huelsnitz |first16=W.
 |last17=Ignarra  |first17=C.           |last18=Johnson |first18=R.A.
 |last19=Karagiorgi |first19=G.         |last20=Katori  |first20=T.
 |last21=Kobilarcik |first21=T.         |last22=Louis   |first22=W.C.
 |last23=Mariani  |first23=C.           |last24=Marsh   |first24=W.
 |last25=Mills    |first25=G.B.         |last26=Mirabal |first26=J.
 |last27=Monroe   |first27=J.           |last28=Moore   |first28=C.D.
 |last29=Mousseau |first29=J.   |display-authors=6
 |collaboration=[[MiniBooNE]] collaboration
 |year=2018
 |title=Observation of a significant excess of electron-like events in the MiniBooNE short-baseline neutrino experiment
 |journal=[[Physical Review Letters]]
 |volume=121  |issue=22  |page=221801
 |doi=10.1103/PhysRevLett.121.221801
 |pmid=30547637  |arxiv=1805.12028  |s2cid=53999758
 |bibcode=2018PhRvL.121v1801A
}}
</ref>
Since then, in October&nbsp;2021, the [[MicroBooNE]] experiment's first results showed no hints of sterile neutrinos, rather finding the results aligning with the Standard Model's three neutrino flavours.<ref>
{{cite press release
 |title=MicroBooNE experiment's first results show no hint of a sterile neutrino
 |date=2021-10-27  |df=dmy-all
 |place=Batavia, IL
 |publisher=[[Fermi National Accelerator Laboratory]]
 |url=https://news.fnal.gov/2021/10/microboone-experiments-first-results-show-no-hint-of-a-sterile-neutrino/
 |access-date=2021-11-13  |lang=en-US
}}
</ref> This result had not found an explanation for MiniBooNE's anomalous results, however.

In June&nbsp;2022, the [[SAGE (Soviet–American Gallium Experiment)#Baksan Experiment on Sterile Transitions (BEST)|BEST experiment]] released two papers observing a 20–24% deficit in the production of the isotope germanium expected from the reaction {{nowrap|<sup>71</sup>Ga + &nu;<sub>e</sub> → e<sup>−</sup> + <sup>71</sup>Ge}}. The so-called "Gallium anomaly" suggests that a sterile neutrino explanation could be consistent with the data.<ref>
{{cite press release
 |publisher=[[Los Alamos National Laboratory]]
 |date=2022-06-18  |df=dmy-all
 |title=Deep underground experiment results confirm anomaly: Possible new fundamental physics
 |website=SciTechDaily
 |url=https://scitechdaily.com/deep-underground-experiment-results-confirm-anomaly-possible-new-fundamental-physics/
 |access-date=2022-06-22
 |lang=en-us
}}
</ref><ref>
{{cite journal
 |last1=Barinov  |first1=V.V.       |last2=Cleveland |first2=B.T.
 |last3=Danshin  |first3=S.N.       |last4=Ejiri     |first4=H.
 |last5=Elliott  |first5=S.R.       |last6=Frekers   |first6=D.
 |last7=Gavrin   |first7=V. N.      |last8=Gorbachev |first8=V.V.
 |last9=Gorbunov |first9=D.S.       |last10=Haxton   |first10=W.C.
 |last11=Ibragimova |first11=T.V. |display-authors=6
 |date=2022-06-09  |df=dmy-all
 |title=Results from the Baksan experiment on sterile transitions (BEST)
 |journal=[[Physical Review Letters]]
 |volume=128  |issue=23  |page=232501
 |doi=10.1103/PhysRevLett.128.232501 |pmid=35749172
 |arxiv=2109.11482 |bibcode=2022PhRvL.128w2501B
 |s2cid=237605431
}}
</ref><ref>
{{cite journal
 |last1=Barinov    |first1=V.V.        |last2=Danshin    |first2=S.N.
 |last3=Gavrin     |first3=V.N.        |last4=Gorbachev  |first4=V.V.
 |last5=Gorbunov   |first5=D.S.        |last6=Ibragimova |first6=T.V.
 |last7=Kozlova    |first7=Yu.P.       |last8=Kravchuk   |first8=L.V.
 |last9=Kuzminov   |first9=V.V.   |last10=Lubsandorzhiev |first10=B.K.
 |last11=Malyshkin |first11=Yu.M. |display-authors=6
 |date=2022-06-09  |df=dmy-all
 |title=Search for electron-neutrino transitions to sterile states in the BEST experiment
 |journal=[[Physical Review C]]
 |volume=105  |issue=6  |page=065502
 |doi=10.1103/PhysRevC.105.065502  |arxiv=2201.07364
 |bibcode=2022PhRvC.105f5502B  |s2cid=246035834
}}
</ref>

In January&nbsp;2023, the [[STEREO experiment]] published its final result, reporting the most precise measurement of the antineutrino energy spectrum associated with the fission of [[uranium-235]]. The data is consistent with the Standard Model and rejects the hypothesis of a light sterile neutrino with a mass of around 1&nbsp;eV.<ref>
{{cite journal
 |first1=H.  |last1=Almazán         |first2=L.  |last2=Bernard
 |first3=A.  |last3=Blanchet        |first4=A.  |last4=Bonhomme
 |first5=C.  |last5=Buck            |first6=A.  |last6=Chalil
 |first7=P.  |last7=del Amo Sanchez |first8=I.  |last8=el Atmani
 |first9=L.  |last9=Labit           |first10=J. |last10=Lamblin
 |first11=A. |last11=Letourneau     |first12=D. |last12=Lhuillier
 |first13=M. |last13=Licciardi      |first14=M. |last14=Lindner
 |first15=T. |last15=Materna        |first16=H. |last16=Pessard
 |first17=J.-S. |last17=Réal        |first18=J.-S. |last18=Ricol
 |first19=C. |last19=Roca           |first20=R. |last20=Rogly
 |first21=T. |last21=Salagnac       |first22=V. |last22=Savu
 |first23=S. |last23=Schoppmann     |first24=T. |last24=Soldner
 |first25=A. |last25=Stutz          |first26=M. |last26=Vialat
 |display-authors=6
 |collaboration=The STEREO Collaboration
 |date=2023-01-12  |df=dmy-all
 |title=STEREO neutrino spectrum of <sup>235</sup>U fission rejects sterile neutrino hypothesis
 |journal=[[Nature (journal)|Nature]]
 |volume=613  |issue=7943  |pages=257–261
 |doi=10.1038/s41586-022-05568-2  |arxiv=2210.07664
 |pmid=36631644  |bibcode=2023Natur.613..257S  |s2cid=255747792
 |url=https://www.nature.com/articles/s41586-022-05568-2
}}
</ref>

In 2023 results of searches by the CMS set new limits for sterile neutrinos with masses of 2–3&nbsp;GeV.<ref>
{{cite web
 |title=Search for long-lived heavy neutral leptons decaying in the CMS muon detectors in proton-proton collisions at {{nobr|{{big|{{mvar|s}}}}{{sup|0.5}} {{=}} 13 TeV}}
 |website=inspirehep.net
 |url=https://inspirehep.net/literature/2680045
 |access-date=2023-08-05
}}
</ref>

== See also ==
* [[List of particles#Hypothetical particles|List of hypothetical particles]] 
* [[MiniBooNE]] at Fermilab
* [[WISP (quantum mechanics)|Weakly Interacting Slender Particle]]

== Footnotes ==
{{notelist}}

== References ==
{{reflist|25em}}

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* {{cite journal
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{{refend}}

== External links ==
* {{cite web
 |series=Neutrino unbound
 |title=Sterile neutrinos
 |website=www.nu.to.infn.it
 |url=http://www.nu.to.infn.it/new/Sterile_Neutrinos/
 |archive-url=https://web.archive.org/web/20160624023856/http://www.nu.to.infn.it/new/Sterile_Neutrinos/
 |archive-date=2016-06-24 |df=dmy-all
}}
* {{cite web
 |title=The NuTeV&nbsp;experiment at Fermilab
 |publisher=[[Fermi National Accelerator Laboratory]]
 |url=http://www-e815.fnal.gov/
}}
* {{cite web
 |title=The L3&nbsp;experiment at CERN
 |publisher=[[CERN]]
 |url=http://l3.web.cern.ch/l3/
}}
* {{cite magazine
 |title=Experiment nixes fourth neutrino
 |date=April 2007
 |magazine=[[Scientific American]]
 |url=http://www.sciam.com/article.cfm?articleid=E73C8DC4-E7F2-99DF-3A9288CB19A810BB&chanId=sa026
}}

{{Particles}}
{{Dark matter}}

{{DEFAULTSORT:Sterile Neutrino}}
[[Category:Neutrinos]]
[[Category:Hypothetical elementary particles]]
[[Category:Dark matter]]