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Neutrino

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Neutrino
The first use of a hydrogenbubble chamberto detect neutrinos, on 13 November 1970, atArgonne National Laboratory.Here 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
StatisticsFermionic
FamilyLeptons,antileptons
GenerationFirst (
ν
e
), second (
ν
μ
), and third (
ν
τ
)
InteractionsWeak interactionandgravitation
Symbol
ν
e
,
ν
μ
,
ν
τ
,
ν
e
,
ν
μ
,
ν
τ
Particlespin:⁠±+ 1 /2ħ,chirality:Left,weak isospin:+ 1 /2,lepton nr.:+1,"flavor"in {e, μ, τ}
Antiparticlespin:⁠±+ 1 /2ħ,chirality:Right,weak isospin:− 1 /2,lepton nr.:−1,"flavor"in {e,μ,τ}
Theorized
Discovered
Types3 types:electron neutrino (
ν
e
)
,muon neutrino (
ν
μ
)
,andtau neutrino (
ν
τ
)
Mass< 0.120 eV(< 2.14 × 10−37kg), 95% confidence level, sum of 3"flavors"[1]
Electric charge0e
Spin 1 /2
Weak isospinLH: + 1 /2,RH: 0
Weak hyperchargeLH: −1,RH: 0
BL−1
X−3

Aneutrino(/njˈtrn/new-TREE-noh;denoted by the Greek letterν) is afermion(anelementary particlewithspin of 1 /2) that interacts only via theweak interactionandgravity.[2][3]The neutrino is so named because it iselectricallyneutral and because itsrest massis so small (-ino) that it was long thought to bezero.The restmassof the neutrino is much smaller than that of the other known elementary particles (excludingmassless particles).[1]The weak force has a very short range, the gravitational interaction is extremely weak due to the very small mass of the neutrino, and neutrinos do not participate in theelectromagnetic interactionor thestrong interaction.[4]Thus, neutrinos typically pass through normal matter unimpeded and undetected.[2][3]

Weak interactionscreate neutrinos in one of three leptonicflavors:

  1. electron neutrino,
    ν
    e
  2. muon neutrino,
    ν
    μ
  3. tau neutrino,
    ν
    τ

Each flavor is associated with the correspondingly named chargedlepton.[5]Although neutrinos were long believed to be massless, it is now known that there are three discrete neutrino masses with different tiny values (the smallest of which could even be zero[6]), but the three masses do not uniquely correspond to the three flavors: A neutrino created with a specific flavor is a specific mixture of all three mass states (aquantum superposition). Similar to someother neutral particles,neutrinos oscillatebetween different flavors in flight as a consequence. For example, an electron neutrino produced in abeta decayreaction may interact in a distant detector as a muon or tau neutrino.[7][8]The three mass values are not yet known as of 2024, but laboratory experiments andcosmologicalobservations have determined the differences of their squares,[9]an upper limit on their sum (<2.14×10−37kg),[1][10]and an upper limit on the mass of the electron neutrino.[11]

For each neutrino, there also exists a correspondingantiparticle,called anantineutrino,which also has spin of 1 /2and no electric charge. Antineutrinos are distinguished from neutrinos by having opposite-signedlepton numberandweak isospin,and right-handed instead of left-handed chirality. To conserve total lepton number (in nuclear beta decay), electron neutrinos only appear together withpositrons(anti-electrons) or electron-antineutrinos, whereas electron antineutrinos only appear with electrons or electron neutrinos.[12][13]

Neutrinos are created by variousradioactive decays;the following list is not exhaustive, but includes some of those processes:

The majority of neutrinos which are detected about the Earth are from nuclear reactions inside the Sun. At the surface of the Earth, the flux is about 65 billion (6.5×1010)solar neutrinos,per second per square centimeter.[14][15]Neutrinos can be used fortomographyof the interior of the Earth.[16][17]

History

[edit]

Pauli's proposal

[edit]

The neutrino[a] was postulated first byWolfgang Pauliin 1930 to explain how beta decay could conserveenergy,momentum,andangular momentum(spin). In contrast toNiels Bohr,who proposed a statistical version of the conservation laws to explain the observedcontinuous energy spectra in beta decay,Pauli hypothesized an undetected particle that he called a "neutron", using the same-onending employed for naming both theprotonand theelectron.He considered that the new particle was emitted from the nucleus together with the electron or beta particle in the process of beta decay and had a mass similar to the electron.[18][b]

James Chadwickdiscovered a much more massive neutral nuclear particle in 1932 and named it aneutronalso, leaving two kinds of particles with the same name. The word "neutrino" entered the scientific vocabulary throughEnrico 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 (theItalianequivalent of "little neutral one" ) was jokingly coined byEdoardo Amaldiduring 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.[19]

InFermi's theory of beta decay,Chadwick's large neutral particle could decay to a proton, electron, and the smaller neutral particle (now called anelectron antineutrino):


n0

p+
+
e
+
ν
e

Fermi's paper, written in 1934,[20]unified Pauli's neutrino withPaul Dirac'spositronandWerner Heisenberg's neutron–proton model and gave a solid theoretical basis for future experimental work.[20][21][22]: 24 

By 1934, there was experimental evidence against Bohr's idea that energy conservation is invalid for beta decay: At theSolvay conferenceof 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.[22]: 25 The first evidence of the reality of neutrinos came in 1938 via simultaneous cloud-chamber measurements of the electron and the recoil of the nucleus.[23]

Direct detection

[edit]
Fred Reines and Clyde Cowan conducting the neutrino experiment c. 1956

In 1942,Wang Ganchangfirst proposed the use ofbeta captureto experimentally detect neutrinos.[24] In the 20 July 1956 issue ofScience,Clyde Cowan,Frederick Reines,Francis B. "Kiko" Harrison, Herald W. Kruse, and Austin D. McGuire published confirmation that they had detected the neutrino,[25][26] a result that was rewarded almost forty years later with the1995 Nobel Prize.[27]

In this experiment, now known as theCowan–Reines neutrino experiment,antineutrinos created in a nuclear reactor by beta decay reacted with protons to produceneutronsand positrons:


ν
e
+
p+

n0
+
e+

The positron quickly finds an electron, and theyannihilateeach other. The two resultinggamma 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 by a group including Frederick Reines andFriedel Sellschop.[28][29]The experiment was performed in a specially prepared chamber at a depth of 3 km in theEast Rand ( "ERPM" ) gold minenearBoksburg,South Africa. 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.[30]

Neutrino flavor

[edit]

The antineutrino discovered byClyde CowanandFrederick Reineswas the antiparticle of the electron neutrino.

In 1962,Leon M. Lederman,Melvin Schwartz,andJack Steinbergershowed that more than one type of neutrino exists by first detecting interactions of themuonneutrino (already hypothesised with the nameneutretto),[31] which earned them the1988 Nobel Prize in Physics.

When the third type of lepton, thetau,was discovered in 1975 at theStanford Linear Accelerator Center,it was also expected to have an associated neutrino (the tau neutrino). The 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 theDONUT collaborationatFermilab;its existence had already been inferred by both theoretical consistency and experimental data from theLarge Electron–Positron Collider.[32]

Solar neutrino problem

[edit]

In the 1960s, the now-famousHomestake experimentmade 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 theStandard Solar Model.This discrepancy, which became known as thesolar 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 actually correct and that the discrepancy between them was due to neutrinos being more complex than was previously assumed. It was postulated that the three neutrinos had nonzero and slightly 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, one toR. Davis,who conceived and led the Homestake experiment andMasatoshi Koshibaof Kamiokande, whose work confirmed it, and one toTakaaki Kajitaof Super-Kamiokande andA.B. McDonaldofSNOfor their joint experiment, which confirmed the existence of all three neutrino flavors and found no deficit.[33]

Oscillation

[edit]

A practical method for investigating neutrino oscillations was first suggested byBruno Pontecorvoin 1957 using an analogy withkaonoscillations; over the subsequent 10 years, he developed the mathematical formalism and the modern formulation of vacuum oscillations. In 1985Stanislav MikheyevandAlexei Smirnov(expanding on 1978 work byLincoln Wolfenstein) noted that flavor oscillations can be modified when neutrinos propagate through matter. This so-calledMikheyev–Smirnov–Wolfenstein effect(MSW effect) is important to understand because many neutrinos emitted by fusion in the Sun pass through the dense matter in thesolar 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 (seeSuper-KamiokandeandSudbury 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 experimentKamLANDand the accelerator experiments such asMINOS.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.[34]Takaaki Kajitaof Japan, andArthur B. McDonaldof Canada, received the 2015 Nobel Prize for Physics for their landmark finding, theoretical and experimental, that neutrinos can change flavors.

Cosmic neutrinos

[edit]

As well as specific sources, a general background level of neutrinos is expected to pervade the universe, theorized to occur due to two main sources.

Cosmic neutrino background (Big Bang originated)

Around 1 second after theBig Bang,neutrinos decoupled, giving rise to a background level of neutrinos known as thecosmic neutrino background(CNB).

Diffuse supernova neutrino background (Supernova originated)

R. DavisandM. Koshibawere jointly awarded the 2002 Nobel Prize in Physics. Both conducted pioneering work onsolar neutrinodetection, and Koshiba's work also resulted in the first real-time observation of neutrinos from theSN 1987Asupernova in the nearbyLarge Magellanic Cloud.These efforts marked the beginning ofneutrino astronomy.[35]

SN 1987Arepresents the only verified detection of neutrinos from a supernova. However, many stars have gone supernova in the universe, leaving a theorizeddiffuse supernova neutrino background.

Properties and reactions

[edit]

Neutrinos have half-integerspin( 1 /2ħ); therefore they arefermions.Neutrinos are leptons. They have only been observed to interact through theweak force,although it is assumed that they also interact gravitationally. Since they have non-zero mass, theoretical considerations permit neutrinos to interact magnetically, but do not require them to. As yet there is no experimental evidence for a non-zeromagnetic momentin neutrinos.

Flavor, mass, and their mixing

[edit]

Weak interactions create neutrinos in one of three leptonicflavors:electron neutrinos (
ν
e
), muon neutrinos (
ν
μ
), ortau neutrinos(
ν
τ
), associated with the corresponding charged leptons, theelectron(
e
),muon(
μ
), andtau(
τ
), respectively.[36]

Although neutrinos were long believed to be massless, it is now known that there are three discrete neutrino masses; each neutrino flavor state is a linear combination of the three discrete mass eigenstates. Although only differences of squares of the three mass values are known as of 2016,[9]experiments have shown that these masses are tiny compared to any other particle. Fromcosmologicalmeasurements, it has been calculated that the sum of the three neutrino masses must be less than one-millionth that of the electron.[1][10]

More formally, neutrino flavoreigenstates(creation and annihilation combinations) are not the same as the neutrino mass eigenstates (simply labeled "1", "2", and "3" ). As of 2024, it is not known which of these three is the heaviest. Theneutrino mass hierarchyconsists of two possible configurations. 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.[37]

A neutrino created in a specific flavor eigenstate is in an associated specificquantum superpositionof all three mass eigenstates. The three masses differ so little that they cannot possibly be distinguished experimentally within any practical flight path. The proportion of each mass state in the pure flavor states produced has been found to depend profoundly on the flavor. The relationship between flavor and mass eigenstates is encoded in thePMNS matrix.Experiments have established moderate- to low-precision values for the elements of this matrix, with the single complex phase in the matrix being only poorly known, as of 2016.[9]

A non-zero mass allows neutrinos to possibly have a tinymagnetic moment;if so, neutrinos would interact electromagnetically, although no such interaction has ever been observed.[38]

Flavor oscillations

[edit]

Neutrinososcillatebetween 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 mechanicalwave packetsdevelop relativephase shiftsthat change how they combine to produce a varying superposition of three flavors. Each flavor component thereby oscillates 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 neutrinos could oscillate even if they were massless: IfLorentz symmetrywere not an exact symmetry, neutrinos could experienceLorentz-violating oscillations.[39]

Mikheyev–Smirnov–Wolfenstein effect

[edit]

Neutrinos traveling through matter, in general, undergo a process analogous tolight traveling through a transparent material.This process is not directly observable because it does not produceionizing radiation,but gives rise to theMikheyev–Smirnov–Wolfenstein effect.Only a small fraction of the neutrino's energy is transferred to the material.[40]

Antineutrinos

[edit]

For each neutrino, there also exists a correspondingantiparticle,called anantineutrino,which also has no electric charge and half-integer spin. They are distinguished from the neutrinos by having opposite signs oflepton numberand oppositechirality(and consequently opposite-sign weak isospin). As of 2016, no evidence has been found for any other difference.

So far, despite extensive and continuing searches for exceptions, in all observed leptonic processes there has never been any change in total lepton number; for example, if the total lepton number is zero in the initial state, then the final state has only matched lepton and anti-lepton pairs: electron neutrinos appear in the final state together with only positrons (anti-electrons) or electron antineutrinos, and electron antineutrinos with electrons or electron neutrinos.[12][13]

Antineutrinos are produced in nuclear beta decay together with abeta particle(in beta decay a neutron decays into a proton, electron, and antineutrino). All antineutrinos observed thus far had right-handedhelicity(i.e., only one of the two possible spin states has ever been seen), while neutrinos were all left-handed.[c]

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 (seeCowan–Reines neutrino experiment). Researchers around the world have begun to investigate the possibility of using antineutrinos for reactor monitoring in the context of preventing theproliferation of nuclear weapons.[41][42]

Majorana mass

[edit]

Because antineutrinos and neutrinos are neutral particles, it is possible that they are the same particle. Rather than conventionalDirac fermions,neutral particles can be another type of spin 1 /2particle calledMajorana particles,named after the Italian physicistEttore Majoranawho first proposed the concept. For the case of neutrinos this theory has gained popularity as it can be used, in combination with theseesaw mechanism,to explain why neutrino masses are so small compared to those of the other elementary particles, such as electrons or quarks. Majorana neutrinos would 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.

As of 2019,it is not known whether neutrinos areMajoranaorDiracparticles. It is possible to test this property experimentally. For example, if neutrinos are indeed Majorana particles, then lepton-number violating processes such asneutrinoless double-beta decaywould be allowed, while they would not if neutrinos areDiracparticles. Several experiments have been and are being conducted to search for this process, e.g.GERDA,[43]EXO,[44]SNO+,[45]andCUORE.[46] Thecosmic neutrino backgroundis also a probe of whether neutrinos areMajorana particles,since there should be a different number of cosmic neutrinos detected in either the Dirac or Majorana case.[47]

Nuclear reactions

[edit]

Neutrinos can interact with a nucleus, changing it to another nucleus. This process is used in radiochemicalneutrino 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.[33][48]

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, do not need to be considered for the detection experiment. Within a cubic meter 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 and other disintegration events

[edit]

Very much like neutrons do innuclear reactors,neutrinos can inducefission reactionswithin heavynuclei.[49]So far, this reaction has not been measured in a laboratory, but is predicted to happen within stars and supernovae. The process affects theabundance of isotopesseen in theuniverse.[48]Neutrino-induced disintegration ofdeuteriumnuclei has been observed in the Sudbury Neutrino Observatory, which uses aheavy waterdetector.[50]

Types

[edit]
Neutrinos in the Standard Model of elementary particles
Fermion Symbol
Generation 1
Electron neutrino
ν
e
Electron antineutrino
ν
e
Generation 2
Muon neutrino
ν
μ
Muon antineutrino
ν
μ
Generation 3
Tau neutrino
ν
τ
Tau antineutrino
ν
τ

There are three known types (flavors) of neutrinos: electron neutrino
ν
e
,muon neutrino
ν
μ
,and tau neutrino
ν
τ
,named after their partner leptons in theStandard Model(see table at right). The current best measurement of the number of neutrino types comes from observing the decay of theZ boson.This particle can decay into any light neutrino and its antineutrino, and the more available types of light neutrinos,[d] the shorter the lifetime of the Z boson. Measurements of the Z lifetime have shown that three light neutrino flavors couple to the Z.[36]The correspondence between the sixquarksin 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.

Research

[edit]

There are several active research areas involving the neutrino with aspirations of finding:

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 ofCP violationin the neutrino sector; that is, whether or not the laws of physics treat neutrinos and antineutrinos differently.[9]

TheKATRINexperiment in Germany began to acquire data in June 2018[51]to determine the value of the mass of the electron neutrino, with other approaches to this problem in the planning stages.[1]

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 candidates fordark matterthat are experimentally established elementary particles—specifically, they would behot dark matter.However, the currently known neutrino types seem to be essentially ruled out as a substantial proportion of dark matter, based on observations of thecosmic microwave background.It still seems plausible that heavier, sterile neutrinos might composewarm dark matter,if they exist.[52]

Sterile neutrino searches

[edit]

Other efforts search for evidence of asterile neutrino—a fourth neutrino flavor that would not interact with matter like the three known neutrino flavors.[53][54][55][56]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 could 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 theLSNDexperiment. On the other hand, the currently runningMiniBooNEexperiment suggested that sterile neutrinos are not required to explain the experimental data,[57]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.[58]A re-analysis of reference electron spectra data from theInstitut Laue-Langevin[59]in 2011 has also hinted at a fourth, light sterile neutrino.[60]Triggered by the 2011 findings, several experiments at very short distances from nuclear reactors have searched for sterile neutrinos since then. While most of them were able to rule out the existence of a light sterile neutrino, results are overall ambiguous.[61]

According to an analysis published in 2010, data from theWilkinson Microwave Anisotropy Probeof thecosmic background radiationis compatible with either three or four types of neutrinos.[62]

Neutrinoless double-beta decay searches

[edit]

Another hypothesis concerns "neutrinoless double-beta decay", which, if it exists, would violate lepton number conservation. Searches for this mechanism are underway but have not yet found evidence for it. If they were to, then what are now called antineutrinos could not be true antiparticles.

Cosmic ray neutrinos

[edit]

Cosmic rayneutrino experiments detect neutrinos from space to study both the nature of neutrinos and the cosmic sources producing them.[63]

Speed

[edit]

Before neutrinos were found to oscillate, they were generally assumed to be massless, propagating at thespeed of light(c). According to the theory ofspecial relativity,the question of neutrinovelocityis closely related to theirmass: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, there are someLorentz-violatingvariants ofquantum gravitywhich might allow faster-than-light neutrinos.[citation needed]A comprehensive framework for Lorentz violations is theStandard-Model Extension(SME).

The first measurements of neutrino speed were made in the early 1980s using pulsedpionbeams (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 theMINOSdetectors, which found the speed of3GeVneutrinos to be, at the 99% confidence level, in the range between0.999976cand1.000126c.The central value of1.000051cis higher than the speed of light but, with uncertainty taken into account, is also consistent with a velocity of exactlycor slightly less. This measurement set an upper bound on the mass of the muon neutrino at50 MeVwith 99%confidence.[64][65]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%).[66]

A similar observation was made, on a much larger scale, with supernova 1987A (SN 1987A). Antineutrinos with an energy of 10 MeV 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.[67][68]

Superluminal neutrino glitch

[edit]

In September 2011, theOPERA collaborationreleased calculations showing velocities of 17 GeV and 28 GeV neutrinos exceeding the speed of light in their experiments. 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 byICARUSfound no discernible difference between the speed of a neutrino and the speed of light.[69]

Mass

[edit]
Unsolved problem in physics:

Can we measure the neutrino masses? Do neutrinos followDiracorMajoranastatistics?

Timeline of neutrino mass measurements by different experiments[11]

The Standard Model of particle physics assumed that neutrinos are massless.[70]The experimentally established phenomenon of neutrino oscillation, which mixes neutrino flavor states with neutrino mass states (analogously toCKM mixing), requires neutrinos to have nonzero masses.[71]Massive neutrinos were originally conceived byBruno Pontecorvoin the 1950s. Enhancing the basic framework to accommodate their mass is straightforward by adding a right-handed Lagrangian.[72]

Providing for neutrino mass can be done in two ways, and some proposals use both:

  • If, like other fundamental Standard Model fermions, mass is generated by theDirac mechanism,then the framework would require an additional right-chiral component which is anSU(2) singlet.This component would have the conventionalYukawa interactionswith the neutral component of theHiggs doublet;but, otherwise, would have no interactions with Standard Model particles.
  • Or, else, mass can be generated by theMajorana mechanism,which would require the neutrino and antineutrino to be the same particle.

A hard upper limit on the masses of neutrinos comes fromcosmology:theBig Bangmodel predicts that there is a fixed ratio between the number of neutrinos and the number ofphotonsin thecosmic microwave background.If the total mass of all three types of neutrinos exceeded an average of50eV/c2per neutrino, there would be so much mass in the universe that it would collapse.[73]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 theLyman-alpha forest.Analysis of data from the WMAP microwave space telescope found that the sum of the masses of the three neutrino species must be less than0.3 eV/c2.[74]In 2018, thePlanck collaborationpublished a stronger bound of0.11 eV/c2,which was derived by combining their CMB total intensity, polarization and gravitational lensing observations with Baryon-Acoustic oscillation measurements from galaxy surveys and supernova measurements from Pantheon.[75]A 2021 reanalysis that adds redshift space distortion measurements from the SDSS-IV eBOSS survey gets an even tighter upper limit of0.09 eV/c2.[76]However, several ground-based telescopes with similarly sized error bars as Planck prefer higher values for the neutrino mass sum, indicating some tension in the data sets.[77]

The Nobel prize in Physics 2015 was awarded to Takaaki Kajita and Arthur B. McDonald for their experimental discovery of neutrino oscillations, which demonstrates that neutrinos have mass.[78][79]

In 1998, research results at theSuper-Kamiokandeneutrino detector determined that neutrinos can oscillate from one flavor to another, which requires that they must have a nonzero mass.[80]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.[81] As of 2020,[82]the best-fit value of the difference of the squares of the masses of mass eigenstates 1 and 2 is|Δm2
21
| =0.000074(eV/c2)2,
while for eigenstates 2 and 3 it is|Δm2
32
| =0.00251(eV/c2)2.
Since|Δm2
32
|
is the difference of two squared masses, at least one of them must have a value that is at least the square root of this value. Thus, there exists at least one neutrino mass eigenstate with a mass of at least0.05 eV/c2.[83]

A number of efforts are under way to directly determine the absolute neutrino mass scale in laboratory experiments, especially using nuclear beta decay. Upper limits on the effective electron neutrino masses come from beta decays of tritium. The Mainz Neutrino Mass Experiment set an upper limit ofm<2.2 eV/c2at 95% Confidence Level.[84]Since June 2018 theKATRINexperiment searches for a mass between0.2 eV/c2and2 eV/c2in tritium decays.[51]The February 2022 upper limit ismν < 0.8 eV/c2at 90% CL in combination with a previous campaign by KATRIN from 2019.[11][85]

On 31 May 2010,OPERAresearchers 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.[86]

If the neutrino is aMajorana particle,the mass may be calculated by finding thehalf-lifeofneutrinoless double-beta decayof certain nuclei. The current lowest upper limit on the Majorana mass of the neutrino has been set byKamLAND-Zen:0.060–0.161 eV/c2.[87]

Chirality

[edit]

Experimental results show that within the margin of error, all produced and observed neutrinos have left-handedhelicities(spins antiparallel tomomenta), and all antineutrinos have right-handed helicities.[88]In the massless limit, that 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 theydoexist, their properties are substantially different from observable neutrinos and antineutrinos. It is theorized that they are either very heavy (on the order ofGUT scale—seeSeesaw mechanism), do not participate in weak interaction (so-calledsterile 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 ofmν/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 of0.100 MeV~1.00 MeV;consequently, the fraction of neutrinos with "wrong" helicity among them cannot exceed 10−10.[89][90]

GSI anomaly

[edit]

An unexpected series of experimental results for the rate of decay of heavyhighly chargedradioactiveionscirculating in astorage ringhas provoked theoretical activity in an effort to find a convincing explanation. The observed phenomenon is known as theGSI anomaly,as the storage ring is a facility at theGSI Helmholtz Centre for Heavy Ion ResearchinDarmstadt,Germany.

The rates of weak decay of two radioactive species with half lives of about 40 seconds and 200 seconds were found to have a significant oscillatorymodulation,with a period of about 7 seconds.[91] As the decay process produces an electron neutrino, some of the suggested explanations for the observed oscillation rate propose new or altered neutrino properties. Ideas related to flavor oscillation met with skepticism.[92] A later proposal is based on differences between neutrino masseigenstates.[93]

Sources

[edit]

Artificial

[edit]

Reactor neutrinos

[edit]

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 are235
U
,238
U
,239
Pu
and241
Pu
), 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. Including these subsequent decays, the average nuclear fission releases about200 MeVof energy, of which roughly 95.5% remains in the core as heat, and roughly 4.5% (or about9 MeV)[94]is radiated away as antineutrinos. For a typical nuclear reactor with a thermal power of4000MW,[e]the total power production from fissioning atoms is actually4185 MW,of which185 MWis radiated away as antineutrino radiation and never appears in the engineering. This is to say,185 MWof fission energy islostfrom 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, thedetectableantineutrinos from fission have a peak energy between about 3.5 and4 MeV,with a maximum energy of about10 MeV.[95]There is no established experimental method to measure the flux of low-energy antineutrinos. Only antineutrinos with an energy above threshold of1.8 MeVcan triggerinverse beta decayand thus be unambiguously identified (see§ Detectionbelow).

An estimated 3% of all antineutrinos from a nuclear reactor carry an energy above that threshold. Thus, an average nuclear power plant may generate over1020antineutrinos per second above the threshold, but also a much larger number (97% / 3% ≈ 30 timesthis number) below the energy threshold; these lower-energy antineutrinos are invisible to present detector technology.

Accelerator neutrinos

[edit]

Someparticle acceleratorshave been used to make neutrino beams. The technique is to collideprotonswith a fixed target, producing chargedpionsorkaons.These unstable particles are then magnetically focused into a long tunnel where they decay while in flight. Because of therelativistic boostof the decaying particle, the neutrinos are produced as a beam rather than isotropically. Efforts to design an accelerator facility where neutrinos are produced through muon decays are ongoing.[96]Such a setup is generally known as a"neutrino factory".

Collider neutrinos

[edit]

Unlike other artificial sources, colliders produce both neutrinos and anti-neutrinos of all flavors at very high energies. The first direct observation of collider neutrinos was reported in 2023 by theFASER experimentat theLarge Hadron Collider.[97]

Nuclear weapons

[edit]

Nuclear weaponsalso produce very large quantities of neutrinos.Fred ReinesandClyde Cowanconsidered 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.[98]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

[edit]
AGM2015: A worldwide v̄eflux map combininggeoneutrinosfrom naturalUranium-238andThorium-232decay in the Earth’s crust and mantle as well as manmade reactor-v̄eemitted by power reactors worldwide.

Neutrinos are produced together with the naturalbackground radiation.In particular, the decay chains of238
U
and232
Th
isotopes, as well as40
K
,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,[99]andBorexino.[100]The main background in the geoneutrino measurements are the antineutrinos coming from reactors.

Solar neutrinos (proton–proton chain) in the Standard Solar Model

Atmospheric

[edit]

Atmospheric neutrinos result from the interaction of cosmic rays with atomic nuclei in theEarth's atmosphere,creating showers of particles, many of which are unstable and produce neutrinos when they decay. A collaboration of particle physicists fromTata Institute of Fundamental Research(India),Osaka City University(Japan) andDurham University(UK) recorded the first cosmic ray neutrino interaction in an underground laboratory inKolar Gold Fieldsin India in 1965.[101]

Solar

[edit]

Solar neutrinos originate from thenuclear fusionpowering theSunand other stars. The details of the operation of the Sun are explained by theStandard Solar Model.In short: when four protons fuse to become oneheliumnucleus, 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 65billion(6.5×1010) solar neutrinos pass through every square centimeter on the part of the Earth orthogonal to the direction of the Sun.[15]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

[edit]
SN 1987A

Colgate& White (1966)[102]calculated that neutrinos carry away most of the gravitational energy released during the collapse of massive stars,[102]events now categorized asType Ib and IcandType IIsupernovae. When such stars collapse, matterdensitiesat the core become so high (1017kg/m3) that thedegeneracyof electrons is not enough to prevent protons and electrons from combining to form a neutron and an electron neutrino.Mann(1997)[103]found a second and more profuse neutrino source is the thermal energy (100 billionkelvins) of the newly formed neutron core, which is dissipated via the formation of neutrino–antineutrino pairs of all flavors.[103]

Colgate and White's theory of supernova neutrino production was confirmed in 1987, when neutrinos from Supernova 1987A were detected. The water-based detectorsKamiokande IIandIMBdetected 11 and 8 antineutrinos (lepton number = −1) of thermal origin,[103]respectively, while the scintillator-basedBaksandetector 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 thevisiblelight 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. TheSuperNova Early Warning Systemproject 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 theMilky 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),[104]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 3,200 kilometers in diameter for SN 1987A.

The number of neutrinos counted was also consistent with a total neutrino energy of2.2×1046joules,which was estimated to be nearly all of the total energy of the supernova.[35]

For an average supernova, approximately 1057(anoctodecillion) neutrinos are released, but the actual number detected at a terrestrial detectorwill be far smaller, at the level of whereis the mass of the detector (with e.g.Super Kamiokandehaving a mass of 50 kton) andis the distance to the supernova.[105] Hence in practice it will only be possible to detect neutrino bursts from supernovae within or nearby theMilky Way(our own galaxy). In addition to the detection of neutrinos from individual supernovae, it should also be possible to detect thediffuse supernova neutrino background,which originates from all supernovae in the Universe.[106]

Supernova remnants

[edit]

The energy of supernova neutrinos ranges from a few to several tens of MeV. The sites wherecosmic raysare 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:Supernova remnants.The origin of the cosmic rays was attributed to supernovas byBaadeandZwicky;this hypothesis was refined byGinzburgandSyrovatskywho 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.Ginzburgand 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 byEnrico 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 areBaikal,AMANDA,IceCube,ANTARES,NEMOandNestor.Related information is provided byvery-high-energy gamma rayobservatories, such asVERITAS,HESSandMAGIC.Indeed, the collisions of cosmic rays are supposed to produce charged pions, whose decay give the neutrinos, neutral pions, and gamma rays the environment of a supernova remnant, which is transparent to both types of radiation.

Still-higher-energy neutrinos, resulting from the interactions of extragalactic cosmic rays, could be observed with thePierre Auger Observatoryor with the dedicated experiment namedANITA.

Big Bang

[edit]

It is thought that, just like the cosmic microwave background radiation leftover 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 thedark matterthought to exist in the universe. Neutrinos have one important advantage over most other dark matter candidates: They are known to 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 thespeed 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 theuniversebefore 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 largegalacticstructures that we see.

These same galaxies andgroups of galaxiesappear to be surrounded by dark matter that is not fast enough to escape from those galaxies. Presumably this matter provided the gravitational nucleus forformation.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 temperature1.9 K(1.7×10−4eV) if they are massless, much colder if their mass exceeds0.001 eV/c2.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-8solar 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 sixorders of magnitude.

Detection

[edit]

Neutrinos cannot be detected directly because they do not carry electric charge, which means they do not ionize the materials they pass through. Other ways neutrinos might affect their environment, such as theMSW effect,do not produce traceable radiation. A unique reaction to identify antineutrinos, sometimes referred to asinverse 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 ofcadmium chloridein water. Two scintillation detectors were placed next to the cadmium targets. Antineutrinos with an energy above the threshold of1.8 MeVcaused 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 (
ν
e
) is emitted:

From known
β+
decay:

Energy+
p

n
+
e+
+
ν
e

In the Cowan and Reines experiment, instead of an outgoing neutrino, you have an incoming antineutrino (
ν
e
) from a nuclear reactor:

Energy (>1.8 MeV)+
p
+
ν
e

n
+
e+

The resulting positron annihilation with electrons in the detector material created photons with an energy of about0.5 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 about8 MeVthat were detected a few microseconds after the photons from a positron annihilation event.

Since then, various detection methods have been used.Super Kamiokandeis a large volume of water surrounded byphotomultiplier tubesthat watch for theCherenkov radiationemitted when an incoming neutrino creates an electron or muon in the water. The Sudbury Neutrino Observatory is similar, but usedheavy wateras 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 ofchlorineorgalliumwhich are periodically checked for excesses ofargonorgermanium,respectively, which are created by electron-neutrinos interacting with the original substance. MINOS used a solid plasticscintillatorcoupled to photomultiplier tubes, while Borexino uses a liquidpseudocumenescintillator also watched by photomultiplier tubes and theNOνAdetector uses liquid scintillator watched byavalanche photodiodes.TheIceCube Neutrino Observatoryuses1 km3of theAntarctic ice sheetnear thesouth polewith photomultiplier tubes distributed throughout the volume.

Scientific interest

[edit]

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 require40000years 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.[107][108]

Neutrinos are also useful for probingastrophysicalsources beyond the Solar System because they are the only known particles that are not significantlyattenuatedby 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 100megaparsecsdue to theGreisen–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-basedneutrino telescopes.[22]

Another important use of the neutrino is in the observation ofsupernovae,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 theirradiant energyin a short (10-second) burst of neutrinos.[109]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. 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.[110]

The study of neutrinos is important inparticle physicsbecause neutrinos typically have the lowest rest mass among massive particles (i.e. the lowest non-zero rest mass, i.e. excluding the zero rest mass of photons and gluons), and hence are examples of the lowest-energy massive 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.[111]

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 blazarTXS 0506+056located 3.7 billionlight-yearsaway in the direction of the constellationOrion.This is the first time that aneutrino detectorhas been used to locate an object in space and that a source of cosmic rays has been identified.[112][113][114]

In November 2022, the IceCube Neutrino Observatory found evidence of high-energy neutrino emission from NGC 1068, also known asMessier 77,an active galaxy in the constellation Cetus and one of the most familiar and well-studied galaxies to date.[115]

In June 2023, astronomers reported using a new technique to detect, for the first time, the release of neutrinos from thegalactic planeof the Milky Waygalaxy.[116][117]

See also

[edit]

Notes

[edit]
  1. ^ More specifically, Pauli postulated what is now called theelectron neutrino.Two other types were discovered later: seeNeutrino flavorbelow.
  2. ^ Niels Bohrwas notably opposed to this interpretation of beta decay—he was ready to accept that energy, momentum, and angular momentum were not conserved quantities at the atomic level.
  3. ^Nevertheless, because neutrinos have mass, their helicity isframe-dependent, so particle physicists have fallen back on the frame-independent property ofchiralitythat is closely related to helicity, and for practical purposes the same as the helicity of the ultra-relativistic neutrinos that can be observed in detectors.
  4. ^ In this context, "light neutrino" means neutrinos with less than half the mass of the Z boson.
  5. ^ Like allthermal power plants,only about one third of the heat generated can be converted to electricity, so a4000 MWreactor would produce only1300 MWof electric power, with2700 MWbeingwaste heat.

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[edit]
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