A neutrino ( or ) (denoted by the Greek letter
ν) is a fermion (an elementary particle with
half-integer spin) that interacts only via
the weak subatomic force and gravity. The
mass of the neutrino is much smaller than
that of the other known elementary particles.
Although only differences of squares of the
three mass values are known as of 2016, cosmological
observations imply that the sum of the three
masses must be less than one millionth that
of the electron. The neutrino is so named
because it is electrically neutral and because
its rest mass is so small (-ino) that it was
long thought to be zero. The weak force has
a very short range, gravity is extremely weak
on the subatomic scale, and neutrinos, as
leptons, do not participate in the strong
interaction. Thus, neutrinos typically pass
through normal matter unimpeded and undetected.Weak
interactions create neutrinos in one of three
leptonic flavors: electron neutrinos (νe),
muon neutrinos (νμ), or tau neutrinos (ντ),
in association with the corresponding charged
lepton. Although neutrinos were long believed
to be massless, it is now known that there
are three discrete neutrino masses with different
tiny values, but they do not correspond uniquely
to the three flavors. A neutrino created with
a specific flavor is in an associated specific
quantum superposition of all three mass states.
As a result, neutrinos oscillate between different
flavors in flight. For example, an electron
neutrino produced in a beta decay reaction
may interact in a distant detector as a muon
or tau neutrino.For each neutrino, there also
exists a corresponding antiparticle, called
an antineutrino, which also has half-integer
spin and no electric charge. They are distinguished
from the neutrinos by having opposite signs
of lepton number and chirality. To conserve
total lepton number, in nuclear beta decay,
electron neutrinos appear together with only
positrons (anti-electrons) or electron-antineutrinos,
and electron antineutrinos with electrons
or electron neutrinos.Neutrinos are created
by various radioactive decays, including in
beta decay of atomic nuclei or hadrons, nuclear
reactions such as those that take place in
the core of a star or artificially in nuclear
reactors, nuclear bombs or particle accelerators,
during a supernova, in the spin-down of a
neutron star, or when accelerated particle
beams or cosmic rays strike atoms. The majority
of neutrinos in the vicinity of the Earth
are from nuclear reactions in the Sun. In
the vicinity of the Earth, about 65 billion
(6.5×1010) solar neutrinos per second pass
through every square centimeter perpendicular
to the direction of the Sun.For study, neutrinos
can be created artificially with nuclear reactors
and particle accelerators. There is intense
research activity involving neutrinos, with
goals that include the determination of the
three neutrino mass values, the measurement
of the degree of CP violation in the leptonic
sector (leading to leptogenesis); and searches
for evidence of physics beyond the Standard
Model of particle physics, such as neutrinoless
double beta decay, which would be evidence
for violation of lepton number conservation.
Neutrinos can also be used for tomography
of the interior of the earth.
== History ==
=== 
Pauli's proposal ===
The neutrino was postulated first by Wolfgang
Pauli in 1930 to explain how beta decay could
conserve energy, momentum, and angular momentum
(spin). In contrast to Niels Bohr, who proposed
a statistical version of the conservation
laws to explain the observed continuous energy
spectra in beta decay, Pauli hypothesized
an undetected particle that he called a "neutron",
using the same -on ending employed for naming
both the proton and the electron. He considered
that the new particle was emitted from the
nucleus together with the electron or beta
particle in the process of beta decay.James
Chadwick discovered a much more massive neutral
nuclear particle in 1932 and named it a neutron
also, leaving two kinds of particles with
the same name. Earlier (in 1930) Pauli had
used the term "neutron" for both the neutral
particle that conserved energy in beta decay,
and a presumed neutral particle in the nucleus;
initially he did not consider these two neutral
particles as distinct from each other. The
word "neutrino" entered the scientific vocabulary
through Enrico Fermi, who used it during a
conference in Paris in July 1932 and at the
Solvay Conference in October 1933, where Pauli
also employed it. The name (the Italian equivalent
of "little neutral one") was jokingly coined
by Edoardo Amaldi during a conversation with
Fermi at the Institute of Physics of via Panisperna
in Rome, in order to distinguish this light
neutral particle from Chadwick's heavy neutron.In
Fermi's theory of beta decay, Chadwick's large
neutral particle could decay to a proton,
electron, and the smaller neutral particle
(now called an electron antineutrino):
n0 → p+ + e− + νeFermi's paper, written
in 1934, unified Pauli's neutrino with Paul
Dirac's positron and Werner Heisenberg's neutron–proton
model and gave a solid theoretical basis for
future experimental work. The journal Nature
rejected Fermi's paper, saying that the theory
was "too remote from reality". He submitted
the paper to an Italian journal, which accepted
it, but the general lack of interest in his
theory at that early date caused him to switch
to experimental physics.By 1934 there was
experimental evidence against Bohr's idea
that energy conservation is invalid for beta
decay: At the Solvay conference of that year,
measurements of the energy spectra of beta
particles (electrons) were reported, showing
that there is a strict limit on the energy
of electrons from each type of beta decay.
Such a limit is not expected if the conservation
of energy is invalid, in which case any amount
of energy would be statistically available
in at least a few decays. The natural explanation
of the beta decay spectrum as first measured
in 1934 was that only a limited (and conserved)
amount of energy was available, and a new
particle was sometimes taking a varying fraction
of this limited energy, leaving the rest for
the beta particle. Pauli made use of the occasion
to publicly emphasize that the still-undetected
"neutrino" must be an actual particle.
=== Direct detection ===
In 1942, Wang Ganchang first proposed the
use of beta capture to experimentally detect
neutrinos. In the 20 July 1956 issue of Science,
Clyde Cowan, Frederick Reines, F. B. Harrison,
H. W. Kruse, and A. D. McGuire published confirmation
that they had detected the neutrino, a result
that was rewarded almost forty years later
with the 1995 Nobel Prize.In this experiment,
now known as the Cowan–Reines neutrino experiment,
antineutrinos created in a nuclear reactor
by beta decay reacted with protons to produce
neutrons and positrons:
νe + p+ → n0 + e+The positron quickly finds
an electron, and they annihilate each other.
The two resulting gamma rays (γ) are detectable.
The neutron can be detected by its capture
on an appropriate nucleus, releasing a gamma
ray. The coincidence of both events – positron
annihilation and neutron capture – gives
a unique signature of an antineutrino interaction.
In February 1965, the first neutrino found
in nature was identified in one of South Africa's
gold mines by a group which included Friedel
Sellschop. The experiment was performed in
a specially prepared chamber at a depth of
3 km in the ERPM mine near Boksburg. A plaque
in the main building commemorates the discovery.
The experiments also implemented a primitive
neutrino astronomy and looked at issues of
neutrino physics and weak interactions.
=== Neutrino flavor ===
The antineutrino discovered by Cowan and Reines
is the antiparticle of the electron neutrino.
In 1962, Leon M. Lederman, Melvin Schwartz
and Jack Steinberger showed that more than
one type of neutrino exists by first detecting
interactions of the muon neutrino (already
hypothesised with the name neutretto), which
earned them the 1988 Nobel Prize in Physics.
When the third type of lepton, the tau, was
discovered in 1975 at the Stanford Linear
Accelerator Center, it too was expected to
have an associated neutrino (the tau neutrino).
First evidence for this third neutrino type
came from the observation of missing energy
and momentum in tau decays analogous to the
beta decay leading to the discovery of the
electron neutrino. The first detection of
tau neutrino interactions was announced in
2000 by the DONUT collaboration at Fermilab;
its existence had already been inferred by
both theoretical consistency and experimental
data from the Large Electron–Positron Collider.
=== Solar neutrino problem ===
In the 1960s, the now-famous Homestake experiment
made the first measurement of the flux of
electron neutrinos arriving from the core
of the Sun and found a value that was between
one third and one half the number predicted
by the Standard Solar Model. This discrepancy,
which became known as the solar neutrino problem,
remained unresolved for some thirty years,
while possible problems with both the experiment
and the solar model were investigated, but
none could be found. Eventually it was realized
that both were correct, but rather it was
the neutrinos themselves that were far more
interesting than expected. It was postulated
that the three neutrinos had nonzero and slightly
but indistinguishably different masses, and
could therefore oscillate into undetectable
flavors on their flight to the Earth. This
hypothesis was investigated by a new series
of experiments, thereby opening a new major
field of research that still continues. Eventual
confirmation of the phenomenon of neutrino
oscillation led to two Nobel prizes, to Raymond
Davis, Jr., who conceived and led the Homestake
experiment, and to Art McDonald, who led the
SNO experiment, which could detect all of
the neutrino flavors and found no deficit.
=== Oscillation ===
A practical method for investigating neutrino
oscillations was first suggested by Bruno
Pontecorvo in 1957 using an analogy with kaon
oscillations; over the subsequent 10 years
he developed the mathematical formalism and
the modern formulation of vacuum oscillations.
In 1985 Stanislav Mikheyev and Alexei Smirnov
(expanding on 1978 work by Lincoln Wolfenstein)
noted that flavor oscillations can be modified
when neutrinos propagate through matter. This
so-called Mikheyev–Smirnov–Wolfenstein
effect (MSW effect) is important to understand
because many neutrinos emitted by fusion in
the Sun pass through the dense matter in the
solar core (where essentially all solar fusion
takes place) on their way to detectors on
Earth.
Starting in 1998, experiments began to show
that solar and atmospheric neutrinos change
flavors (see Super-Kamiokande and Sudbury
Neutrino Observatory). This resolved the solar
neutrino problem: the electron neutrinos produced
in the Sun had partly changed into other flavors
which the experiments could not detect.
Although individual experiments, such as the
set of solar neutrino experiments, are consistent
with non-oscillatory mechanisms of neutrino
flavor conversion, taken altogether, neutrino
experiments imply the existence of neutrino
oscillations. Especially relevant in this
context are the reactor experiment KamLAND
and the accelerator experiments such as MINOS.
The KamLAND experiment has indeed identified
oscillations as the neutrino flavor conversion
mechanism involved in the solar electron neutrinos.
Similarly MINOS confirms the oscillation of
atmospheric neutrinos and gives a better determination
of the mass squared splitting. Takaaki Kajita
of Japan and Arthur B. McDonald of Canada
received the 2015 Nobel Prize for Physics
for their landmark finding, theoretical and
experimental, that neutrinos can change flavors.
=== Cosmic neutrinos ===
Raymond Davis, Jr. and Masatoshi Koshiba were
jointly awarded the 2002 Nobel Prize in Physics.
Both conducted pioneering work on solar neutrino
detection, and Koshiba's work also resulted
in the first real-time observation of neutrinos
from the SN 1987A supernova in the nearby
Large Magellanic Cloud. These efforts marked
the beginning of neutrino astronomy.SN 1987A
represents the only verified detection of
neutrinos from a supernova.
== Properties and reactions ==
The neutrino has half-integer spin (½ ħ)
and is therefore a fermion. Also being leptons,
neutrinos have been observed to interact through
only the weak force, although it is assumed
that they also interact gravitationally.
=== Flavor, mass, and their mixing ===
Weak interactions create neutrinos in one
of three leptonic flavors: electron neutrinos
(νe), muon neutrinos (νμ), or tau neutrinos
(ντ), in association with the corresponding
electron, muon, and tau charged leptons, respectively.Although
neutrinos were long believed to be massless,
it is now known that there are also three
discrete neutrino masses, but they don't correspond
uniquely to the three flavors. Although only
differences of squares of the three mass values
are known as of 2016, experiments have shown
that these masses are tiny in magnitude. From
cosmological measurements, it has been calculated
that the sum of the three neutrino masses
must be less than one millionth that of the
electron.More formally, neutrino flavor eigenstates
are not the same as the neutrino mass eigenstates
(simply labelled 1, 2, 3). As of 2016, it
is not known which of these three is the heaviest.
In analogy with the mass hierarchy of the
charged leptons, the configuration with mass
2 being lighter than mass 3 is conventionally
called the "normal hierarchy", while in the
"inverted hierarchy", the opposite would hold.
Several major experimental efforts are underway
to help establish which is correct.A neutrino
created in a specific flavor eigenstate is
in an associated specific quantum superposition
of all three mass eigenstates. This is possible
because the three masses differ so little
that they cannot be experimentally distinguished
within any practical flight path, due to the
uncertainty principle. The proportion of each
mass state in the produced pure flavor state
has been found to depend strongly on that
flavor. The relationship between flavor and
mass eigenstates is encoded in the PMNS matrix.
Experiments have established values for the
elements of this matrix.The existence of a
neutrino mass allows the possibility of a
tiny neutrino magnetic moment, in which case
neutrinos could interact electromagnetically
as well; no such interaction has been discovered.
=== Flavor oscillations ===
Neutrinos oscillate between different flavors
in flight. For example, an electron neutrino
produced in a beta decay reaction may interact
in a distant detector as a muon or tau neutrino,
as defined by the flavor of the charged lepton
produced in the detector. This oscillation
occurs because the three mass state components
of the produced flavor travel at slightly
different speeds, so that their quantum mechanical
wave packets develop relative phase shifts
that change how they combine to produce a
varying superposition of three flavors. Each
flavor component thereby oscillates sinusoidally
as the neutrino travels, with the flavors
varying in relative strengths. The relative
flavor proportions when the neutrino interacts
represent the relative probabilities for that
flavor of interaction to produce the corresponding
flavor of charged lepton.There are other possibilities
in which neutrino could oscillate even if
they were massless. If Lorentz symmetry were
not an exact symmetry, neutrinos could experience
Lorentz-violating oscillations.
=== Mikheyev–Smirnov–Wolfenstein effect
===
Neutrinos traveling through matter, in general,
undergo a process analogous to light traveling
through a transparent material. This process
is not directly observable because it does
not produce ionizing radiation, but gives
rise to the MSW effect. Only a small fraction
of the neutrino's energy is transferred to
the material.
=== Antineutrinos ===
For each neutrino, there also exists a corresponding
antiparticle, called an antineutrino, which
also has no electric charge and half-integer
spin. They are distinguished from the neutrinos
by having opposite signs of lepton number
and opposite chirality. As of 2016, no evidence
has been found for any other difference. In
all observations so far of leptonic processes
(despite extensive and continuing searches
for exceptions), there is no overall change
in lepton number; for example, if total lepton
number is zero in the initial state, electron
neutrinos appear in the final state together
with only positrons (anti-electrons) or electron-antineutrinos,
and electron antineutrinos with electrons
or electron neutrinos.Antineutrinos are produced
in nuclear beta decay together with a beta
particle, in which, e.g., a neutron decays
into a proton, electron, and antineutrino.
All antineutrinos observed thus far possess
right-handed helicity (i.e. only one of the
two possible spin states has ever been seen),
while neutrinos are left-handed. Nevertheless,
as neutrinos have mass, their helicity is
frame-dependent, so it is the related frame-independent
property of chirality that is relevant here.
Antineutrinos were first detected as a result
of their interaction with protons in a large
tank of water. This was installed next to
a nuclear reactor as a controllable source
of the antineutrinos (See: Cowan–Reines
neutrino experiment).
Researchers around the world have begun to
investigate the possibility of using antineutrinos
for reactor monitoring in the context of preventing
the proliferation of nuclear weapons.
=== Majorana mass ===
Because antineutrinos and neutrinos are neutral
particles, it is possible that they are the
same particle. Particles that have this property
are known as Majorana particles, after the
Italian physicist Ettore Majorana who first
proposed the concept. For the case of neutrinos
this theory has gained popularity as it can
be used, in combination with the seesaw mechanism,
to explain why neutrino masses are so small
compared to those of the other elementary
particles, such as electrons or quarks. Majorana
neutrinos have the property that the neutrino
and antineutrino could be distinguished only
by chirality; what experiments observe as
a difference between the neutrino and antineutrino
could simply be due to one particle with two
possible chiralities.
It is not yet known whether neutrinos are
Majorana or Dirac particles; it is possible
to test this property experimentally. For
example, if neutrinos are indeed Majorana
particles, then lepton-number violating processes
such as neutrinoless double beta decay would
be allowed, while they would not if neutrinos
are Dirac particles. Several experiments have
been and are being conducted to search for
this process, e.g. GERDA. and SNO+. The cosmic
neutrino background is also a probe of whether
neutrinos are Majorana particles, since there
should be a different number of cosmic neutrinos
detected in either the Dirac or Majorana case.
=== Nuclear reactions ===
Neutrinos can interact with a nucleus, changing
it to another nucleus. This process is used
in radiochemical neutrino detectors. In this
case, the energy levels and spin states within
the target nucleus have to be taken into account
to estimate the probability for an interaction.
In general the interaction probability increases
with the number of neutrons and protons within
a nucleus.It is very hard to uniquely identify
neutrino interactions among the natural background
of radioactivity. For this reason, in early
experiments a special reaction channel was
chosen to facilitate the identification: the
interaction of an antineutrino with one of
the hydrogen nuclei in the water molecules.
A hydrogen nucleus is a single proton, so
simultaneous nuclear interactions, which would
occur within a heavier nucleus, don't need
to be considered for the detection experiment.
Within a cubic metre of water placed right
outside a nuclear reactor, only relatively
few such interactions can be recorded, but
the setup is now used for measuring the reactor's
plutonium production rate.
=== Induced fission ===
Very much like neutrons do in nuclear reactors,
neutrinos can induce fission reactions within
heavy nuclei. So far, this reaction has not
been measured in a laboratory, but is predicted
to happen within stars and supernovae. The
process affects the abundance of isotopes
seen in the universe. Neutrino fission of
deuterium nuclei has been observed in the
Sudbury Neutrino Observatory, which uses a
heavy water detector.
=== No self interaction ===
Observations of the cosmic microwave background
suggest that neutrinos do not interact with
themselves.
=== Types ===
There are three known types (flavors) of neutrinos:
electron neutrino νe, muon neutrino νμ
and tau neutrino ντ, named after their partner
leptons in the Standard Model (see table at
right). The current best measurement of the
number of neutrino types comes from observing
the decay of the Z boson. This particle can
decay into any light neutrino and its antineutrino,
and the more types of light neutrinos available,
the shorter the lifetime of the Z boson. Measurements
of the Z lifetime have shown that the number
of light neutrino flavors that couple to the
Z is 3. The correspondence between the six
quarks in the Standard Model and the six leptons,
among them the three neutrinos, suggests to
physicists' intuition that there should be
exactly three types of neutrino. Proof that
there are only three kinds of neutrinos remains
an elusive goal of particle physics.
== Research ==
There are several active research areas involving
the neutrino. Some are concerned with testing
predictions of neutrino behavior. Other research
is focused on measurement of unknown properties
of neutrinos, especially their masses and
CP violation, as they cannot be predicted
with existing theories.
=== Detectors near artificial neutrino sources
===
International scientific collaborations install
large neutrino detectors near nuclear reactors
or in neutrino beams from particle accelerators
to better constrain the neutrino masses and
the values for the magnitude and rates of
oscillations between neutrino flavors. These
experiments are thereby searching for the
existence of CP violation in the neutrino
sector; that is, whether or not the laws of
physics treat neutrinos and antineutrinos
differently.The KATRIN experiment in Germany
has begun to acquire data in June 2018 to
determine the value of the mass of the electron
neutrino, with other approaches to this problem
in the planning stages.
=== Tests of neutrino oscillation ===
On 19 July 2013, the results from the T2K
experiment presented at the European Physical
Society Conference on High Energy Physics
in Stockholm, Sweden, confirmed neutrino oscillation
theory.
=== Gravitational effects ===
Despite their tiny masses, neutrinos are so
numerous that their gravitational force can
influence other matter in the universe.
The three known neutrino flavors are the only
established elementary particle candidates
for dark matter, specifically hot dark matter,
although that possibility appears to be largely
ruled out by observations of the cosmic microwave
background. If heavier sterile neutrinos exist,
they might serve as warm dark matter, which
still seems plausible.
=== Sterile neutrino searches ===
Other efforts search for evidence of a sterile
neutrino – a fourth neutrino flavor that
does not interact with matter like the three
known neutrino flavors. The possibility of
sterile neutrinos is unaffected by the Z-boson
decay measurements described above: If their
mass is greater than half the Z-boson's mass,
they would not be a decay product. Therefore,
heavy sterile neutrinos would have a mass
of at least 45.6 GeV.
The existence of such particles is in fact
hinted by experimental data from the LSND
experiment. On the other hand, the currently
running MiniBooNE experiment suggested that
sterile neutrinos are not required to explain
the experimental data, although the latest
research into this area is on-going and anomalies
in the MiniBooNE data may allow for exotic
neutrino types, including sterile neutrinos.
A recent re-analysis of reference electron
spectra data from the Institut Laue-Langevin
has also hinted at a fourth, sterile neutrino.According
to an analysis published in 2010, data from
the Wilkinson Microwave Anisotropy Probe of
the cosmic background radiation is compatible
with either three or four types of neutrinos.
=== Neutrinoless double-beta decay searches
===
Another hypothesis concerns "neutrinoless
double-beta decay", which, if it exists, would
violate lepton number conservation and imply
a minuscule splitting (or difference) between
the physical masses of what are conventionally
called a “neutrino” and its corresponding
“antineutrino” having the opposite sign
in its lepton number. Searches for this mechanism
are underway but have not yet found strong
evidenced for it. If they were to, then what
are now called antineutrinos could not be
true antiparticles. The resulting six distinct
neutrinos would have no distinct antiparticle
partner. Cosmic ray neutrino experiments detect
neutrinos from space to study both the nature
of neutrinos and the cosmic sources producing
them.
=== Speed ===
Before neutrinos were found to oscillate,
they were generally assumed to be massless,
propagating at the speed of light. According
to the theory of special relativity, the question
of neutrino velocity is closely related to
their mass: if neutrinos are massless, they
must travel at the speed of light, and if
they have mass they cannot reach the speed
of light. Due to their tiny mass, the predicted
speed is extremely close to the speed of light
in all experiments, and current detectors
are not sensitive to the expected difference.
Also some Lorentz-violating variants of quantum
gravity might allow faster-than-light neutrinos.
A comprehensive framework for Lorentz violations
is the Standard-Model Extension (SME).
In the early 1980s, first measurements of
neutrino speed were done using pulsed pion
beams (produced by pulsed proton beams hitting
a target). The pions decayed producing neutrinos,
and the neutrino interactions observed within
a time window in a detector at a distance
were consistent with the speed of light. This
measurement was repeated in 2007 using the
MINOS detectors, which found the speed of
3 GeV neutrinos to be, at the 99% confidence
level, in the range between 0.999976 c and
1.000126 c. The central value of 1.000051c
is higher than the speed of light but is also
consistent with a velocity of exactly c or
even slightly less. This measurement set an
upper bound on the mass of the muon neutrino
of 50 MeV at 99% confidence. After the detectors
for the project were upgraded in 2012, MINOS
refined their initial result and found agreement
with the speed of light, with the difference
in the arrival time of neutrinos and light
of −0.0006% (±0.0012%).A similar observation
was made, on a much larger scale, with supernova
1987A (SN 1987A). 10 MeV antineutrinos from
the supernova were detected within a time
window that was consistent with the speed
of light for the neutrinos. So far, all measurements
of neutrino speed have been consistent with
the speed of light.In September 2011, the
OPERA collaboration released calculations
showing velocities of 17 GeV and 28 GeV neutrinos
exceeding the speed of light in their experiments
(see Faster-than-light neutrino anomaly).
In November 2011, OPERA repeated its experiment
with changes so that the speed could be determined
individually for each detected neutrino. The
results showed the same faster-than-light
speed. In February 2012, reports came out
that the results may have been caused by a
loose fiber optic cable attached to one of
the atomic clocks which measured the departure
and arrival times of the neutrinos. An independent
recreation of the experiment in the same laboratory
by ICARUS found no discernible difference
between the speed of a neutrino and the speed
of light.In June 2012, CERN announced that
new measurements conducted by all four Gran
Sasso experiments (OPERA, ICARUS, Borexino
and LVD) found agreement between the speed
of light and the speed of neutrinos, finally
refuting the initial OPERA claim.
=== Mass ===
The Standard Model of particle physics assumed
that neutrinos are massless. The experimentally
established phenomenon of neutrino oscillation,
which mixes neutrino flavour states with neutrino
mass states (analogously to CKM mixing), requires
neutrinos to have nonzero masses. Massive
neutrinos were originally conceived by Bruno
Pontecorvo in the 1950s. Enhancing the basic
framework to accommodate their mass is straightforward
by adding a right-handed Lagrangian.
Providing for neutrino mass can be done in
two ways, and some proposals use both:
If, like other fundamental Standard Model
particles, mass is generated by the Dirac
mechanism, then the framework would require
an SU(2) singlet. This particle would have
the Yukawa interactions with the neutral component
of the Higgs doublet, but otherwise would
have no interactions with Standard Model particles,
so is called a “sterile” neutrino.
Or, mass can be generated by the Majorana
mechanism, which would require the neutrino
and antineutrino to be the same particle.The
strongest upper limit on the masses of neutrinos
comes from cosmology: the Big Bang model predicts
that there is a fixed ratio between the number
of neutrinos and the number of photons in
the cosmic microwave background. If the total
energy of all three types of neutrinos exceeded
an average of 50 eV per neutrino, there would
be so much mass in the universe that it would
collapse. This limit can be circumvented by
assuming that the neutrino is unstable, but
there are limits within the Standard Model
that make this difficult. A much more stringent
constraint comes from a careful analysis of
cosmological data, such as the cosmic microwave
background radiation, galaxy surveys, and
the Lyman-alpha forest. These indicate that
the summed masses of the three neutrinos must
be less than 0.3 eV.The Nobel prize in Physics
2015 was awarded to both Takaaki Kajita and
Arthur B. McDonald for their experimental
discovery of neutrino oscillations, which
demonstrates that neutrinos have mass.In 1998,
research results at the Super-Kamiokande neutrino
detector determined that neutrinos can oscillate
from one flavor to another, which requires
that they must have a nonzero mass. While
this shows that neutrinos have mass, the absolute
neutrino mass scale is still not known. This
is because neutrino oscillations are sensitive
only to the difference in the squares of the
masses. The best estimate of the difference
in the squares of the masses of mass eigenstates
1 and 2 was published by KamLAND 
in 2005: |Δm221| = 0.000079 eV2. In 2006,
the MINOS experiment measured oscillations
from an intense muon neutrino beam, determining
the difference in the squares of the masses
between neutrino mass eigenstates 2 and 3.
The initial results indicate |Δm232| = 0.0027
eV2, consistent with previous results from
Super-Kamiokande. Since |Δm232| is the difference
of two squared masses, at least one of them
has to have a value which is at least the
square root of this value. Thus, there exists
at least one neutrino mass eigenstate with
a mass of at least 0.05 eV.In 2009, lensing
data of a galaxy cluster were analyzed to
predict a neutrino mass of about 1.5 eV. This
surprisingly high value requires that the
three neutrino masses be nearly equal, with
neutrino oscillations on the order of milli
electron-Volts. In 2016 this was updated to
a mass of 1.85 eV. It predicts 3 sterile neutrinos
of the same mass, stems with the Planck dark
matter fraction and the non-observation of
neutrinoless double beta decay. The masses
lie below the Mainz-Troitsk upper bound of
2.2 eV for the electron antineutrino. The
latter is being tested since June 2018 in
the KATRIN experiment, that searches for a
mass between 0.2 eV and 2 eV.A number of efforts
are under way to directly determine the absolute
neutrino mass scale in laboratory experiments.
The methods applied involve nuclear beta decay
(KATRIN and MARE).
On 31 May 2010, OPERA researchers observed
the first tau neutrino candidate event in
a muon neutrino beam, the first time this
transformation in neutrinos had been observed,
providing further evidence that they have
mass.In July 2010, the 3-D MegaZ DR7 galaxy
survey reported that they had measured a limit
of the combined mass of the three neutrino
varieties to be less than 0.28 eV. A tighter
upper bound yet for this sum of masses, 0.23
eV, was reported in March 2013 by the Planck
collaboration, whereas a February 2014 result
estimates the sum as 0.320 ± 0.081 eV based
on discrepancies between the cosmological
consequences implied by Planck's detailed
measurements of the Cosmic Microwave Background
and predictions arising from observing other
phenomena, combined with the assumption that
neutrinos are responsible for the observed
weaker gravitational lensing than would be
expected from massless neutrinos.If the neutrino
is a Majorana particle, the mass may be calculated
by finding the half-life of neutrinoless double-beta
decay of certain nuclei. The current lowest
upper limit on the Majorana mass of the neutrino
has been set by KamLAND-Zen: 0.060–0.161
eV.
=== Size ===
Standard Model neutrinos are fundamental point-like
particles, without any width or volume. Since
the neutrino is an elementary particle it
does not have a size in the same sense as
everyday objects. An effective size can be
defined using their electroweak cross section
(apparent size in electroweak interaction).
The characteristic areas for the electroweak
interaction are measured in units called nanobarns
(nb) which are 10−33 cm² or 10−37 m²,
roughly the area of a disc a little more than
0.3 attometer in diameter, or about 1 billionth
of the size of a uranium nucleus. The electron
neutrino cross section is 3.2 nanobarns the
muon neutrino cross section is 1.7 nanobarns,
and the tau neutrino 1.0 nanobarn. These scattering
cross sections depend on no other properties
than the masses of the corresponding charged
leptons. This size is relevant only to the
probability of scattering. Properties associated
with conventional "size" are absent: neutrinos
cannot be condensed to form a separate uniform
substance and they have no minimal distance
between them.
=== Chirality ===
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 chiralities included in
the Standard Model of particle interactions.
It is possible that their counterparts (right-handed
neutrinos and left-handed antineutrinos) simply
do not exist. If they do, their properties
are substantially different from observable
neutrinos and antineutrinos. It is theorized
that they are either very heavy (on the order
of GUT scale—see Seesaw mechanism), do not
participate in weak interaction (so-called
sterile neutrinos), or both.
The existence of nonzero neutrino masses somewhat
complicates the situation. Neutrinos are produced
in weak interactions as chirality eigenstates.
Chirality of a massive particle is not a constant
of motion; helicity is, but the chirality
operator does not share eigenstates with the
helicity operator. Free neutrinos propagate
as mixtures of left- and right-handed helicity
states, with mixing amplitudes on the order
of mν/E. This does not significantly affect
the experiments, because neutrinos involved
are nearly always ultrarelativistic, and thus
mixing amplitudes are vanishingly small. Effectively,
they travel so quickly and time passes so
slowly in their rest-frames that they do not
have enough time to change over any observable
path. For example, most solar neutrinos have
energies on the order of 0.100 MeV–1 MeV,
so the fraction of neutrinos with "wrong"
helicity among them cannot exceed 10−10.
=== GSI anomaly ===
An unexpected series of experimental results
for the rate of decay of heavy highly charged
radioactive ions circulating in a storage
ring has provoked theoretical activity in
an effort to find a convincing explanation.
The rates of weak decay of two radioactive
species with half lives of about 40 s and
200 s are found to have a significant oscillatory
modulation, with a period of about 7 s.
The observed phenomenon is known as the GSI
anomaly, as the storage ring is a facility
at the GSI Helmholtz Centre for Heavy Ion
Research in Darmstadt Germany. As the decay
process produces an electron neutrino, some
of the proposed explanations for the observed
oscillation rate invoke neutrino properties.
Initial ideas related to flavour oscillation
were met with skepticism. A more recent proposal
involves mass differences between neutrino
mass eigenstates.
== Sources ==
=== 
Artificial ===
==== 
Reactor neutrinos ====
Nuclear reactors are the major source of human-generated
neutrinos. The majority of energy in a nuclear
reactor is generated by fission (the four
main fissile isotopes in nuclear reactors
are 235U, 238U, 239Pu and 241Pu), the resultant
neutron-rich daughter nuclides rapidly undergo
additional beta decays, each converting one
neutron to a proton and an electron and releasing
an electron antineutrino (n → p + e− +
νe). Including these subsequent decays, the
average nuclear fission releases about 200
MeV of energy, of which roughly 95.5% is retained
in the core as heat, and roughly 4.5% (or
about 9 MeV) is radiated away as antineutrinos.
For a typical nuclear reactor with a thermal
power of 4000 MW, the total power production
from fissioning atoms is actually 4185 MW,
of which 185 MW is radiated away as antineutrino
radiation and never appears in the engineering.
This is to say, 185 MW of fission energy is
lost from this reactor and does not appear
as heat available to run turbines, since antineutrinos
penetrate all building materials practically
without interaction.
The antineutrino energy spectrum depends on
the degree to which the fuel is burned (plutonium-239
fission antineutrinos on average have slightly
more energy than those from uranium-235 fission),
but in general, the detectable antineutrinos
from fission have a peak energy between about
3.5 and 4 MeV, with a maximum energy of about
10 MeV. There is no established experimental
method to measure the flux of low-energy antineutrinos.
Only antineutrinos with an energy above threshold
of 1.8 MeV can trigger inverse beta decay
and thus be unambiguously identified (see
§ Detection below). An estimated 3% of all
antineutrinos from a nuclear reactor carry
an energy above this threshold. Thus, an average
nuclear power plant may generate over 1020
antineutrinos per second above this threshold,
but also a much larger number (97%/3% ≈ 30
times this number) below the energy threshold,
which cannot be seen with present detector
technology. The ND280 detector has been proposed
as a viable safeguard unit.
==== Accelerator neutrinos ====
Some particle accelerators have been used
to make neutrino beams. The technique is to
collide protons with a fixed target, producing
charged pions or kaons. These unstable particles
are then magnetically focused into a long
tunnel where they decay while in flight. Because
of the relativistic boost of the decaying
particle, the neutrinos are produced as a
beam rather than isotropically. Efforts to
construct an accelerator facility where neutrinos
are produced through muon decays are ongoing.
Such a setup is generally known as a "neutrino
factory".
==== Nuclear weapons ====
Nuclear weapons also produce very large quantities
of neutrinos. Fred Reines and Clyde Cowan
considered the detection of neutrinos from
a bomb prior to their search for reactor neutrinos;
a fission reactor was recommended as a better
alternative by Los Alamos physics division
leader J.M.B. Kellogg. Fission weapons produce
antineutrinos (from the fission process),
and fusion weapons produce both neutrinos
(from the fusion process) and antineutrinos
(from the initiating fission explosion).
=== Geologic ===
Neutrinos are produced together with the natural
background radiation. In particular, the decay
chains of 238U and 232Th isotopes, as well
as40K, include beta decays which emit antineutrinos.
These so-called geoneutrinos can provide valuable
information on the Earth's interior. A first
indication for geoneutrinos was found by the
KamLAND experiment in 2005, updated results
have been presented by KamLAND and Borexino.
The main background in the geoneutrino measurements
are the antineutrinos coming from reactors.
=== Atmospheric ===
Atmospheric neutrinos result from the interaction
of cosmic rays with atomic nuclei in the Earth's
atmosphere, creating showers of particles,
many of which are unstable and produce neutrinos
when they decay. A collaboration of particle
physicists from Tata Institute of Fundamental
Research (India), Osaka City University (Japan)
and Durham University (UK) recorded the first
cosmic ray neutrino interaction in an underground
laboratory in Kolar Gold Fields in India in
1965.
=== Solar ===
Solar neutrinos originate from the nuclear
fusion powering the Sun and other stars.
The details of the operation of the Sun are
explained by the Standard Solar Model. In
short: when four protons fuse to become one
helium nucleus, two of them have to convert
into neutrons, and each such conversion releases
one electron neutrino.
The Sun sends enormous numbers of neutrinos
in all directions. Each second, about 65 billion
(6.5×1010) solar neutrinos pass through every
square centimeter on the part of the Earth
orthogonal to the direction of the Sun. Since
neutrinos are insignificantly absorbed by
the mass of the Earth, the surface area on
the side of the Earth opposite the Sun receives
about the same number of neutrinos as the
side facing the Sun.
=== Supernovae ===
In 1966, Colgate and White
calculated that neutrinos carry away most
of the gravitational energy released by the
collapse of massive stars, events now categorized
as Type Ib and Ic and Type II supernovae.
When such stars collapse, matter densities
at the core become so high (1017 kg/m3) that
the degeneracy of electrons is not enough
to prevent protons and electrons from combining
to form a neutron and an electron neutrino.
A second and more important neutrino source
is the thermal energy (100 billion kelvins)
of the newly formed neutron core, which is
dissipated via the formation of neutrino–antineutrino
pairs of all flavors.Colgate and White's theory
of supernova neutrino production was confirmed
in 1987, when neutrinos from Supernova 1987A
were detected. The water-based detectors Kamiokande
II and IMB detected 11 and 8 antineutrinos
(lepton number = −1) of thermal origin,
respectively, while the scintillator-based
Baksan detector found 5 neutrinos (lepton
number = +1) of either thermal or electron-capture
origin, in a burst less than 13 seconds long.
The neutrino signal from the supernova arrived
at earth several hours before the arrival
of the first electromagnetic radiation, as
expected from the evident fact that the latter
emerges along with the shock wave. The exceptionally
feeble interaction with normal matter allowed
the neutrinos to pass through the churning
mass of the exploding star, while the electromagnetic
photons were slowed.
Because neutrinos interact so little with
matter, it is thought that a supernova's neutrino
emissions carry information about the innermost
regions of the explosion. Much of the visible
light comes from the decay of radioactive
elements produced by the supernova shock wave,
and even light from the explosion itself is
scattered by dense and turbulent gases, and
thus delayed. The neutrino burst is expected
to reach Earth before any electromagnetic
waves, including visible light, gamma rays,
or radio waves. The exact time delay of the
electromagnetic waves' arrivals depends on
the velocity of the shock wave and on the
thickness of the outer layer of the star.
For a Type II supernova, astronomers expect
the neutrino flood to be released seconds
after the stellar core collapse, while the
first electromagnetic signal may emerge hours
later, after the explosion shock wave has
had time to reach the surface of the star.
The Supernova Early Warning System project
uses a network of neutrino detectors to monitor
the sky for candidate supernova events; the
neutrino signal will provide a useful advance
warning of a star exploding in the Milky Way.
Although neutrinos pass through the outer
gases of a supernova without scattering, they
provide information about the deeper supernova
core with evidence that here, even neutrinos
scatter to a significant extent. In a supernova
core the densities are those of a neutron
star (which is expected to be formed in this
type of supernova), becoming large enough
to influence the duration of the neutrino
signal by delaying some neutrinos. The 13
second-long neutrino signal from SN 1987A
lasted far longer than it would take for unimpeded
neutrinos to cross through the neutrino-generating
core of a supernova, expected to be only 3200
kilometers in diameter for SN 1987A.
The number of neutrinos counted was also consistent
with a total neutrino energy of 2.2×1046
joules, which was estimated to be nearly all
of the total energy of the supernova.For an
average supernova, approximately 10+57 (an
octodecillion) neutrinos are released, but
the actual number detected at a terrestrial
detector
N
{\displaystyle N}
will be far smaller, at the level of
N
∼
10
4
(
M
25
k
t
o
n
)
(
d
10
k
p
c
)
−
2
{\displaystyle N\sim 10^{4}\left({\frac {M}{25\mathrm
{kton} }}\right)\left({\frac {d}{10\mathrm
{kpc} }}\right)^{-2}}
,
where
M
{\displaystyle M}
is the mass of the detector (with e.g. Super
Kamiokande having a mass of 50 kton) and
d
{\displaystyle d}
is the distance to the supernova. Hence in
practice it will only be possible to detect
neutrino bursts from supernovae within or
nearby the Milky Way (our own galaxy). In
addition to the detection of neutrinos from
individual supernovae, it should also be possible
to detect the diffuse supernova neutrino background,
which originates from all supernovae in the
Universe.
=== Supernova remnants ===
The energy of supernova neutrinos ranges from
a few to several tens of MeV. The sites where
cosmic rays are accelerated are expected to
produce neutrinos that are at least one million
times more energetic, produced from turbulent
gaseous environments left over by supernova
explosions: the supernova remnants. The origin
of the cosmic rays was attributed to supernovas
by Walter Baade and Fritz Zwicky; this hypothesis
was refined by Vitaly L. Ginzburg and Sergei
I. Syrovatsky who attributed the origin to
supernova remnants, and supported their claim
by the crucial remark, that the cosmic ray
losses of the Milky Way is compensated, if
the efficiency of acceleration in supernova
remnants is about 10 percent. Ginzburg and
Syrovatskii's hypothesis is supported by the
specific mechanism of "shock wave acceleration"
happening in supernova remnants, which is
consistent with the original theoretical picture
drawn by Enrico Fermi, and is receiving support
from observational data. The very-high-energy
neutrinos are still to be seen, but this branch
of neutrino astronomy is just in its infancy.
The main existing or forthcoming experiments
that aim at observing very-high-energy neutrinos
from our galaxy are Baikal, AMANDA, IceCube,
ANTARES, NEMO and Nestor. Related information
is provided by very-high-energy gamma ray
observatories, such as VERITAS, HESS and MAGIC.
Indeed, the collisions of cosmic rays are
supposed to produce charged pions, whose decay
give the neutrinos, and also neutral pions,
whose decay give gamma rays: the environment
of a supernova remnant is transparent to both
types of radiation.
Still-higher-energy neutrinos, resulting from
the interactions of extragalactic cosmic rays,
could be observed with the Pierre Auger Observatory
or with the dedicated experiment named ANITA.
=== Big Bang ===
It is thought that, just like the cosmic microwave
background radiation left over from the Big
Bang, there is a background of low-energy
neutrinos in our Universe. In the 1980s it
was proposed that these may be the explanation
for the dark matter thought to exist in the
universe. Neutrinos have one important advantage
over most other dark matter candidates: it
is known that they exist. This idea also has
serious problems.
From particle experiments, it is known that
neutrinos are very light. This means that
they easily move at speeds close to the speed
of light. For this reason, dark matter made
from neutrinos is termed "hot dark matter".
The problem is that being fast moving, the
neutrinos would tend to have spread out evenly
in the universe before cosmological expansion
made them cold enough to congregate in clumps.
This would cause the part of dark matter made
of neutrinos to be smeared out and unable
to cause the large galactic structures that
we see.
These same galaxies and groups of galaxies
appear to be surrounded by dark matter that
is not fast enough to escape from those galaxies.
Presumably this matter provided the gravitational
nucleus for formation. This implies that neutrinos
cannot make up a significant part of the total
amount of dark matter.
From cosmological arguments, relic background
neutrinos are estimated to have density of
56 of each type per cubic centimeter and temperature
1.9 K (1.7×10−4 eV) if they are massless,
much colder if their mass exceeds 0.001 eV.
Although their density is quite high, they
have not yet been observed in the laboratory,
as their energy is below thresholds of most
detection methods, and due to extremely low
neutrino interaction cross-sections at sub-eV
energies. In contrast, boron-8 solar neutrinos—which
are emitted with a higher energy—have been
detected definitively despite having a space
density that is lower than that of relic neutrinos
by some 6 orders of magnitude.
== Detection ==
Neutrinos cannot be detected directly, because
they do not ionize the materials they are
passing through (they do not carry electric
charge and other proposed effects, like the
MSW effect, do not produce traceable radiation).
A unique reaction to identify antineutrinos,
sometimes referred to as inverse beta decay,
as applied by Reines and Cowan (see below),
requires a very large detector to detect a
significant number of neutrinos. All detection
methods require the neutrinos to carry a minimum
threshold energy. So far, there is no detection
method for low-energy neutrinos, in the sense
that potential neutrino interactions (for
example by the MSW effect) cannot be uniquely
distinguished from other causes. Neutrino
detectors are often built underground to isolate
the detector from cosmic rays and other background
radiation.
Antineutrinos were first detected in the 1950s
near a nuclear reactor. Reines and Cowan used
two targets containing a solution of cadmium
chloride in water. Two scintillation detectors
were placed next to the cadmium targets. Antineutrinos
with an energy above the threshold of 1.8
MeV caused charged current interactions with
the protons in the water, producing positrons
and neutrons. This is very much like β+ decay,
where energy is used to convert a proton into
a neutron, a positron (e+) and an electron
neutrino (νe) is emitted:
From known β+ decay:
Energy + p → n + e+ + νeIn the Cowan and
Reines experiment, instead of an outgoing
neutrino, you have an incoming antineutrino
(νe) from a nuclear reactor:
Energy (>1.8 MeV) + p + νe → n + e+The
resulting positron annihilation with electrons
in the detector material created photons with
an energy of about 0.5 MeV. Pairs of photons
in coincidence could be detected by the two
scintillation detectors above and below the
target. The neutrons were captured by cadmium
nuclei resulting in gamma rays of about 8
MeV that were detected a few microseconds
after the photons from a positron annihilation
event.
Since then, various detection methods have
been used. Super Kamiokande is a large volume
of water surrounded by photomultiplier tubes
that watch for the Cherenkov radiation emitted
when an incoming neutrino creates an electron
or muon in the water. The Sudbury Neutrino
Observatory is similar, but uses heavy water
as the detecting medium, which uses the same
effects, but also allows the additional reaction
any-flavor neutrino photo-dissociation of
deuterium, resulting in a free neutron which
is then detected from gamma radiation after
chlorine-capture. Other detectors have consisted
of large volumes of chlorine or gallium which
are periodically checked for excesses of argon
or germanium, respectively, which are created
by electron-neutrinos interacting with the
original substance. MINOS used a solid plastic
scintillator coupled to photomultiplier tubes,
while Borexino uses a liquid pseudocumene
scintillator also watched by photomultiplier
tubes and the NOνA detector uses liquid scintillator
watched by avalanche photodiodes. The IceCube
Neutrino Observatory uses 1 km3 of the Antarctic
ice sheet near the south pole with photomultiplier
tubes distributed throughout the volume.
The University of Liverpool ND280 detector
employs the novel use of gadolinium encased
light detectors in a temperature controlled
magnetic field capturing double light pulse
events. The T2K experiment developed the technology
and practical experiments were successful
in both Japan and at Wylfa power station.
== Scientific interest ==
Neutrinos' low mass and neutral charge mean
they interact exceedingly weakly with other
particles and fields. This feature of weak
interaction interests scientists because it
means neutrinos can be used to probe environments
that other radiation (such as light or radio
waves) cannot penetrate.
Using neutrinos as a probe was first proposed
in the mid-20th century as a way to detect
conditions at the core of the Sun. The solar
core cannot be imaged directly because electromagnetic
radiation (such as light) is diffused by the
great amount and density of matter surrounding
the core. On the other hand, neutrinos pass
through the Sun with few interactions. Whereas
photons emitted from the solar core may require
40,000 years to diffuse to the outer layers
of the Sun, neutrinos generated in stellar
fusion reactions at the core cross this distance
practically unimpeded at nearly the speed
of light.Neutrinos are also useful for probing
astrophysical sources beyond the Solar System
because they are the only known particles
that are not significantly attenuated by their
travel through the interstellar medium. Optical
photons can be obscured or diffused by dust,
gas, and background radiation. High-energy
cosmic rays, in the form of swift protons
and atomic nuclei, are unable to travel more
than about 100 megaparsecs due to the Greisen–Zatsepin–Kuzmin
limit (GZK cutoff). Neutrinos, in contrast,
can travel even greater distances barely attenuated.
The galactic core of the Milky Way is fully
obscured by dense gas and numerous bright
objects. Neutrinos produced in the galactic
core might be measurable by Earth-based neutrino
telescopes.Another important use of the neutrino
is in the observation of supernovae, the explosions
that end the lives of highly massive stars.
The core collapse phase of a supernova is
an extremely dense and energetic event. It
is so dense that no known particles are able
to escape the advancing core front except
for neutrinos. Consequently, supernovae are
known to release approximately 99% of their
radiant energy in a short (10-second) burst
of neutrinos. These neutrinos are a very useful
probe for core collapse studies.
The rest mass of the neutrino is an important
test of cosmological and astrophysical theories
(see Dark matter). The neutrino's significance
in probing cosmological phenomena is as great
as any other method, and is thus a major focus
of study in astrophysical communities.The
study of neutrinos is important in particle
physics because neutrinos typically have the
lowest mass, and hence are examples of the
lowest-energy particles theorized in extensions
of the Standard Model of particle physics.
In November 2012, American scientists used
a particle accelerator to send a coherent
neutrino message through 780 feet of rock.
This marks the first use of neutrinos for
communication, and future research may permit
binary neutrino messages to be sent immense
distances through even the densest materials,
such as the Earth's core.In July 2018, the
IceCube Neutrino Observatory announced that
they have traced an extremely-high-energy
neutrino that hit their Antarctica-based research
station in September 2017 back to its point
of origin in the blazar TXS 0506 +056 located
3.7 billion light-years away in the direction
of the constellation Orion. This is the first
time that a neutrino detector has been used
to locate an object in space and that a source
of cosmic rays has been identified.
== See also ==
List of neutrino experiments
Neutrino oscillation
Neutrino astronomy
Multi-messenger astronomy – Coordinated
observation and interpretation of disparate
"messenger" signals, created by different
astrophysical processes
Sterile neutrino
== Notes
