Beta Decay Neutrino Hypothesis Statement

Not to be confused with neutron or neutralino.

For other uses, see Neutrino (disambiguation).

The first use of a hydrogen bubble chamber to detect neutrinos, on 13 November 1970, at Argonne National Laboratory. A neutrino hits a proton in a hydrogen atom. The collision occurs at the point where three tracks emanate on the right of the photograph.

CompositionElementary particle
GenerationFirst, second and third
InteractionsWeak interaction and gravitation
AntiparticleOpposite chirality from particle

e (Electron neutrino): Wolfgang Pauli (1930)

μ (Muon neutrino): Late 1940s

τ (Tau neutrino): Mid 1970s
e: Clyde Cowan, Frederick Reines (1956)

μ: Leon Lederman, Melvin Schwartz and Jack Steinberger (1962)

τ: DONUT collaboration (2000)
Types3 – electron neutrino, muon neutrino and tau neutrino
Mass≤ 0.120 eV/c2 (95% confidence level, sum of 3 flavors)[1]
Electric chargee
Weak isospinLH: +1/2, RH: 0
Weak hyperchargeLH: -1, RH: 0

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.[2][3] The mass of the neutrino is much smaller than that of the other known elementary particles.[1] Although only differences of squares of the three mass values are known as of 2016,[4]cosmological observations imply that the sum of the three masses must be less than one millionth that of the electron.[1][5] 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.[2][3]

Weak interactions create neutrinos in one of three leptonic flavors: electron neutrinos (
e), muon neutrinos (
μ), or tau neutrinos (
τ), in association with the corresponding charged lepton.[6] 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.[7][8]

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.[9][10]

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 (7010650000000000000♠6.5×1010) solar neutrinos per second pass through every square centimeter perpendicular to the direction of the Sun.[11][12]

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.[13][14]


Pauli's proposal[edit]

The neutrino[nb 1] 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.[15][nb 2]

James Chadwick discovered a much more massive nuclear particle in 1932 and also named it a neutron, leaving two kinds of particles with the same name. Pauli earlier (in 1930) had used the term "neutron" for both the neutral particle that conserved energy in beta decay, and a presumed neutral particle in the nucleus, and initially did not consider these two neutral particles as distinct from each other.[15] 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 neutron.[16]

In Fermi's theory of beta decay, Chadwick's large neutral particle could decay to a proton, electron, and the smaller neutral particle (flavored as an electron antineutrino):



Fermi'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. However, 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.[17]:24[18]

However, 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.[17]:25

Direct detection[edit]

In 1942, Wang Ganchang first proposed the use of beta capture to experimentally detect neutrinos.[19] 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,[20][21] a result that was rewarded almost forty years later with the 1995 Nobel Prize.[22]

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:

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.

Neutrino flavor[edit]

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),[23] 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 summer of 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.[24]

Solar neutrino problem[edit]

Main article: 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.[25]


Main article: Neutrino oscillation

A practical method for investigating neutrino oscillations was first suggested by Bruno Pontecorvo in 1957 using an analogy with kaonoscillations; 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.[26]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[edit]

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 1987Asupernova. These efforts marked the beginning of neutrino astronomy.[27] As of today SN 1987A represents the only verified detection of neutrinos from a supernova.

Properties and reactions[edit]

The neutrino has half-integer spin (½ħ) 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[edit]

Weak interactions create neutrinos in one of three leptonic flavors: electron neutrinos (
e), muon neutrinos (
μ), or tau neutrinos (
τ), in association with the corresponding electron, muon, and tau charged leptons, respectively.[6]

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,[4] 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.[1][5]

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 mass2 being lighter than mass3 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.[28]

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. Recent experimental efforts have established values for the elements of this matrix, and the precision is rapidly improving.[4]

The existence of a neutrino mass allows the existence of a tiny neutrino magnetic moment, in which case neutrinos could interact electromagnetically as well; however, no such interaction has been discovered.[29]

Flavor oscillations[edit]

Main article: Neutrino oscillation

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.[7][8]

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.[30]

Mikheyev–Smirnov–Wolfenstein effect[edit]

Main article: 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.[31]


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 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.[9][10]

Antineutrinos are produced in nuclearbeta 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.[32][33][34]

Majorana mass[edit]

See also: seesaw mechanism

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, however 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.[35] 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.[36]

Nuclear reactions[edit]

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.[25][37]

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[edit]

Very much like neutrons do in nuclear reactors, neutrinos can induce fission reactions within heavy nuclei.[38] 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.[37] Neutrino fission of deuterium nuclei has been observed in the Sudbury Neutrino Observatory, which uses a heavy water detector.

No self interaction[edit]

Observations of the cosmic microwave background suggest that neutrinos do not interact with themselves.[39]


Generation 1
Electron neutrino
Electron antineutrino
Generation 2
Muon neutrino
Muon antineutrino
Generation 3
Tau neutrino
Tau antineutrino

There are three known types (flavors) of neutrinos: electron neutrino
e, muon neutrino
μ and tau neutrino
τ, 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[nb 3] 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.[6] 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. However, actual proof that there are only three kinds of neutrinos remains an elusive goal of particle physics.


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[edit]

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.[4]

The KATRIN experiment in Germany will begin to acquire data in 2017 to determine the value of the mass of the electron neutrino, with other approaches to this problem in the planning stages.[1]

Tests of neutrino oscillation[edit]

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.[40][41]

Gravitational effects[edit]

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.[42]

Sterile neutrino searches[edit]

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.[43][44][45][46] 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,[47] 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.[48] A recent re-analysis of reference electron spectra data from the Institut Laue-Langevin[49] has also hinted at a fourth, sterile neutrino.[50]

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.[51]

Neutrinoless double-beta decay searches[edit]

There are also experiments searching for 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 now conventionally called a “neutrino” and corresponding “antineutrino”, with opposite signs of lepton number.

If this were discovered the two could no longer be mutual antiparticles, and each of the resulting six distinct neutrinos would have no distinct antiparticle partner.[52]Cosmic ray neutrino experiments detect neutrinos from space to study both the nature of neutrinos and the cosmic sources producing them.[53]


Main article: Measurements of neutrino 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; however, 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 6990480652946099999♠3 GeV neutrinos to be, at the 99% confidence level, in the range between 6999999976000000000♠0.999976 c and 7000100012600000000♠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 6988801088243500000♠50 MeV at 99% confidence.[54][55] 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%).[56]

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.[57][58]

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. However, 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.[59]

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.[60]


The Standard Model of particle physics assumed that neutrinos are massless. However, 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.[61] 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. This can be done in two ways. 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 no other Standard Model interactions (apart from the Yukawa interactions with the neutral component of the Higgsdoublet), 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 6982801088243500000♠50 eV per neutrino, there would be so much mass in the universe that it would collapse.[62] This limit can be circumvented by assuming that the neutrino is unstable; however, 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 6980480652946099999♠0.3 eV.[63]

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.[64][65]

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.[66] 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.[67] The best estimate of the difference in the squares of the masses of mass eigenstates 1 and 2 was published by KamLAND in 2005: |Δm2
21| = 6995790000000000000♠0.000079 eV2.[68] 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 |Δm2
32| = 0.0027 eV2

Clyde Cowan conducting the neutrino experiment c. 1956

The Neutrino Hypothesis

The remarkable story of the neutrino

The enigma of the missing energy of beta électrons
Around 1930, beta decay was considered to produce two particles: the recoiling nucleus and an electron. Like in alpha decay, it was supposed to be a ‘monokinetic’ reaction, with the electron carrying away all of the available energy. Beta decay, however, produced a wide spectrum of possible and smaller energies for the electron, as the above figure shows. Where did the missing energy go? When confronted with this dilemma, Niels Bohr went so far as to ask himself whether or not the law of conservation of energy was still valid.

The study of radioactive disintegrations had established that alpha rays were ‘monokinetic’ – in that they always took away the same percentage (100%) of the energy available in the decay. Beta rays, by comparison, could have any of a range of energy values. Whereas the alpha energy distribution is reduced to a single value, the energy distribution (or spectrum) of beta rays can take any value between zero and the total energy available.

In 1930, this evidence was problematic for physicists working in the field. What happened to the law of conservation of energy for beta decay? The seemingly missing energy even led Niels Bohr to propose doing away with that most fundamental conservation law. A mortal sin for a physicist.

In order to save the law of conservation of energy, the Swiss physicist Wolfgang Pauli postulated the existence of an electrically-neutral, low mass (at most 1/100 the mass of the proton) particle that would be emitted along with the beta particle. This hypothetical third body could then take away whatever energy was not given to the beta particle; solving that most vexing of issues. Pauli first proposed this hypothesis in a humorous letter to his colleagues Lise Meitner and Hans Geiger.

Resolving the issue by adding a new particle
It would be Wolfgang Pauli who resolved the issue of the missing energy by proposing the existence of a third particle capable of avoiding detection: the neutrino. Taking the example of bismuth 210 decay, the figure above shows the situation where all three bodies have equal momenta. The recoiling nucleus, some 400,000 times heavier than the electron, takes away a negligible amount of energy. The remaining energy is divided between the electron and the neutrino, shown here as a ghost particle. It would take almost a quarter of a century for the first experimental evidence of a neutrino to come to light.

Enrico Fermi, the great Italian physicist, was immediately convinced. Building on the discussions held at the Solvay Conference on October 1933 (devoted to James Chadwick’s discovery of the neutron), he proposed the theory of beta decay based on a hypothesis that an electron-neutrino pair is spontaneously produced by a nucleus in the same way that photons can spontaneously be emitted by excited atoms.

Francis Perrin concluded that for such a particle to exist it must either have zero mass or be lightweight even by comparison with the electron.

Fermi’s theory was the precursor of today theory of ‘weak interaction’. The Fermi’s theory of a point-like interaction of four particles (for instance, an initial neutron becoming a proton, an electron and an antineutrino), was accepted as a canon, an article of faith without proof during a quarter of century..

The neutrino remained a hypothetical particle until evidence for its existence was brought forward by Reines and Cowan in 1956.

In 1955, the American physicist Murray Gell Mann introduced the notion of a weak force active not only in radioactive processes, but in other processes whose effects involving several types of neutrinos could be seen in a host of subatomic phenomena.

Since its ‘invention’ by Pauli and the subsequent experimental evidence found in its favour, the neutrino and its antiparticle have played a vital role in the fundamentals of particle physics. Possessing no electrical charge, neutrinos are affected solely by the weak interaction, which allows for closer examination of that force without the ‘background noise’ provided by the other nuclear or atomic forces.

Besides the crucial role it plays in the physics of the infinitely small, the neutrino plays an important role in astrophysics. It could be for instance a key to understand the ‘hidden mass of the Universe’.

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