Sterile neutrinos are hypothetical
particles 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, 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.
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. 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.
Sterile neutrinos may be Neutral Heavy
Leptons.
Motivation
Experimental results show that all
produced and observed neutrinos have
left-handed helicities, 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 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.
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. 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
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 
acquires its non-zero vacuum expectation
value, , spontaneously breaking its
SU(2)L × U(1) symmetry, and thus
yielding non-zero Yukawa couplings:
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 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 are
observed in the quark sector, where the
top and bottom masses differ by a factor
40.
Unlike for the left-handed neutrino, a
Majorana mass term can be added for a
sterile neutrino without violating local
symmetries 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. 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, 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.
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
no 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. 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 and left-right
symmetrical models predict the following
relation:
According to GUTs and left-right models,
the right-handed neutrino is extremely
heavy: MNHL ≈
00000000000♠105—7002160217648699999♠1012
GeV, 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.
Detection attempts
The production and decay of sterile
neutrinos could happen through the
mixing with virtual neutrinos. There
were several experiments set up to
discover or observe NHLs, for example
the NuTeV 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.
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 ordinary neutrinos
may also have Majorana masses. In 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. 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 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.
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 4th 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.
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
found no evidence of additional
neutrino-like particles.
See also
MiniBooNE at Fermilab
References
Notes
References
Bibliography
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Bibcode:2013IJMPD..2230020M.
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Bibcode:1999PhRvL..83.4943V.
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External links
The NuTeV experiment at Fermilab
The L3 Experiment at CERN
Experiment Nixes Fourth Neutrino
