Sterile neutrinos (or inert neutrinos) are
hypothetical particles (neutral leptons – neutrinos)
that interact only via gravity and do not
interact via any of the fundamental interactions
of the Standard Model. The term sterile neutrino
is used to distinguish them from the known
active neutrinos in the Standard Model, which
are charged under the weak interaction.
This term usually refers to neutrinos with
right-handed chirality (see right-handed neutrino),
which may be added to the Standard Model.
Occasionally it is used in a general sense
for any neutral fermion, instead of the more
cautiously vague name neutral heavy leptons
(NHLs) or heavy neutral leptons (HNLs).
The existence of right-handed neutrinos is
theoretically well-motivated, as all other
known fermions have been observed with both
left and right chirality, and they can explain
the observed active neutrino masses in a natural
way. The mass of the right-handed neutrinos
themselves is unknown and could have any value
between 1015 GeV and less than 1 eV.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. In
May 2018, physicists of the MiniBooNE experiment
reported a stronger neutrino oscillation signal
than expected, a possible hint of sterile
neutrinos.
== 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. Although note that a particle with
mass that starts out left-handed can develop
a right-handed component as it travels – chirality
is not conserved in the propagation of a free
particle.
The question, thus, remains: Do neutrinos
and antineutrinos differ only in their chirality?
Or do exotic right-handed neutrinos and left-handed
antineutrinos exist as separate particles
from the common left-handed neutrinos and
right-handed antineutrinos?
== 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 electric charge, hypercharge,
and color, sterile neutrinos would not interact
electromagnetically, weakly, or strongly,
making them extremely difficult to detect.
They have Yukawa interactions with ordinary
leptons and Higgs bosons, which via the Higgs
mechanism lead to mixing with ordinary neutrinos.
In experiments involving energies larger than
their mass they would participate in all processes
in which ordinary neutrinos take part, but
with a quantum mechanical probability that
is suppressed by the small mixing angle. That
makes it possible to produce them in experiments
if they are light enough.
They would also interact gravitationally due
to their mass, 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
ϕ
{\displaystyle \phi }
acquires its non-zero vacuum expectation value,
ν
{\displaystyle \nu }
, spontaneously breaking its SU(2)L × U(1)
symmetry, and thus yielding non-zero Yukawa
couplings:
L
(
ψ
)
=
ψ
¯
(
i
∂
/
)
ψ
−
G
ψ
¯
L
ϕ
ψ
R
{\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 +​
2⁄3 and (for example) a color charge of
red, while its antiparticle has an electric
charge of −​ 2⁄3 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
M
ν
{\displaystyle M_{\nu }}
:
M
ν
=
(
0
m
D
m
D
M
N
H
L
)
{\displaystyle M_{\nu }={\begin{pmatrix}0&m_{D}\\m_{D}&M_{NHL}\end{pmatrix}}}
where
M
N
H
L
{\displaystyle M_{NHL}}
is big and
m
D
{\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:
m
ν
≪
m
D
≪
M
N
H
L
{\displaystyle m_{\nu }\ll m_{D}\ll M_{NHL}}
According to GUTs and left-right models, the
right-handed neutrino is extremely heavy:
MNHL ≈ 105–1012 GeV, while the smaller
eigenvalue is approximately equal to
m
ν
≈
m
D
2
M
N
H
L
{\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.Sterile neutrinos may mix with ordinary
neutrinos via a Dirac mass after electroweak
symmetry breaking, in analogy to quarks and
charged leptons.
Sterile neutrinos and (in more-complicated
models) ordinary neutrinos may also have Majorana
masses. In the type 1 seesaw mechanism both
Dirac and Majorana masses are used to drive
ordinary neutrino masses down and make the
sterile neutrinos much heavier than the Standard
Model's interacting neutrinos. In some models
the heavy neutrinos can be as heavy as the
GUT scale (≈1015 GeV). In other models they
could be lighter than the weak gauge bosons
W and Z as in the so-called νMSM model where
their masses are between GeV and keV. A light
(with the mass ≈1 eV) sterile neutrino was
suggested as a possible explanation of the
results of the Liquid Scintillator Neutrino
Detector experiment.
On 11 April 2007, researchers at the MiniBooNE
experiment at Fermilab announced that they
had not found any evidence supporting the
existence of such a sterile neutrino. More-recent
results and analysis have provided some support
for the existence of the sterile neutrino.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. Sterile neutrinos
are also candidates for dark radiation. Daya
Bay has also searched for a light sterile
neutrino and excluded some mass regions. 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. This could
suggest that sterile neutrinos exist or that
our understanding of neutrinos is not complete.
The number of neutrinos and the masses of
the particles can have large-scale effects
that shape the appearance of the cosmic microwave
background. The total number of neutrino species,
for instance, affects the rate at which the
cosmos expanded in its earliest epochs: more
neutrinos means a faster expansion. The Planck
Satellite 2013 data release is compatible
with the existence of a sterile neutrino.
The implied mass range is from 0–3 eV. In
2016, scientists at the IceCube Neutrino Observatory
did not find any evidence for the sterile
neutrino. However, in May 2018, physicists
of the MiniBooNE experiment reported a stronger
neutrino oscillation signal than expected,
a possible hint of sterile neutrinos.
== See also ==
MiniBooNE at Fermilab
== Notes
