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119-400: The Standard Model of particle physics contains three generations or " flavors " of neutrinos, ν e {\displaystyle \nu _{\mathrm {e} }} , ν μ {\displaystyle \nu _{\mu }} , and ν τ {\displaystyle \nu _{\tau }} , each labeled with a subscript showing

238-498: A G a μ ν , {\displaystyle {\mathcal {L}}_{\text{QCD}}={\overline {\psi }}i\gamma ^{\mu }D_{\mu }\psi -{\frac {1}{4}}G_{\mu \nu }^{a}G_{a}^{\mu \nu },} where ψ {\displaystyle \psi } is a three component column vector of Dirac spinors , each element of which refers to a quark field with a specific color charge (i.e. red, blue, and green) and summation over flavor (i.e. up, down, strange, etc.)

357-614: A μ ν W μ ν a − 1 4 B μ ν B μ ν , {\displaystyle {\mathcal {L}}_{\text{EW}}={\overline {Q}}_{Lj}i\gamma ^{\mu }D_{\mu }Q_{Lj}+{\overline {u}}_{Rj}i\gamma ^{\mu }D_{\mu }u_{Rj}+{\overline {d}}_{Rj}i\gamma ^{\mu }D_{\mu }d_{Rj}+{\overline {\ell }}_{Lj}i\gamma ^{\mu }D_{\mu }\ell _{Lj}+{\overline {e}}_{Rj}i\gamma ^{\mu }D_{\mu }e_{Rj}-{\tfrac {1}{4}}W_{a}^{\mu \nu }W_{\mu \nu }^{a}-{\tfrac {1}{4}}B^{\mu \nu }B_{\mu \nu },} where

476-560: A complete theory of fundamental interactions . For example, it does not fully explain why there is more matter than anti-matter , incorporate the full theory of gravitation as described by general relativity , or account for the universe's accelerating expansion as possibly described by dark energy . The model does not contain any viable dark matter particle that possesses all of the required properties deduced from observational cosmology . It also does not incorporate neutrino oscillations and their non-zero masses. The development of

595-400: 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

714-408: A consequence. For example, an electron neutrino produced in a beta decay reaction may interact in a distant detector as a muon or tau neutrino. The three mass values are not yet known as of 2024, but laboratory experiments and cosmological observations have determined the differences of their squares, an upper limit on their sum (<  2.14 × 10  kg ), and an upper limit on the mass of

833-628: 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 are Majorana or Dirac particles. It is possible to test this property experimentally. For example, if neutrinos are indeed Majorana particles, then lepton-number violating processes such as neutrinoless double-beta decay would be allowed, while they would not if neutrinos are Dirac particles. Several experiments have been and are being conducted to search for this process, e.g. GERDA , EXO , SNO+ , and CUORE . The cosmic neutrino background

952-504: 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 and Friedel Sellschop . The experiment was performed in a specially prepared chamber at a depth of 3 km in the East Rand ("ERPM") gold mine near Boksburg , South Africa. A plaque in

1071-438: A graphical representation of the perturbation theory approximation, invoke "force mediating particles", and when applied to analyze high-energy scattering experiments are in reasonable agreement with the data. However, perturbation theory (and with it the concept of a "force-mediating particle") fails in other situations. These include low-energy quantum chromodynamics, bound states , and solitons . The interactions between all

1190-605: A laboratory, but is predicted to happen within stars and supernovae. The process affects the abundance of isotopes seen in the universe . Neutrino-induced disintegration of deuterium nuclei has been observed in the Sudbury Neutrino Observatory, which uses a heavy water detector. 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

1309-1043: A member of the group SU(3), and ϕ a ( x ) {\displaystyle \phi ^{a}(x)} is an arbitrary function of spacetime. The electroweak sector is a Yang–Mills gauge theory with the symmetry group U(1) × SU(2) L , L EW = Q ¯ L j i γ μ D μ Q L j + u ¯ R j i γ μ D μ u R j + d ¯ R j i γ μ D μ d R j + ℓ ¯ L j i γ μ D μ ℓ L j + e ¯ R j i γ μ D μ e R j − 1 4 W

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1428-473: A new major field of research that still continues. Eventual confirmation of the phenomenon of neutrino oscillation led to two Nobel prizes, one to R. Davis , who conceived and led the Homestake experiment and Masatoshi Koshiba of Kamiokande, whose work confirmed it, and one to Takaaki Kajita of Super-Kamiokande and A.B. McDonald of Sudbury Neutrino Observatory for their joint experiment, which confirmed

1547-546: A new particle with a mass of about 125  GeV/ c (about 133 proton masses, on the order of 10  kg ), which is "consistent with the Higgs boson". On 13 March 2013, it was confirmed to be the searched-for Higgs boson. Technically, quantum field theory provides the mathematical framework for the Standard Model, in which a Lagrangian controls the dynamics and kinematics of the theory. Each kind of particle

1666-465: A non-zero Vacuum expectation value , which generates masses for the Electroweak gauge fields (the Higgs' mechanism), and λ > 0 {\displaystyle \lambda >0} , so that the potential is bounded from below. The quartic term describes self-interactions of the scalar field φ {\displaystyle \varphi } . The minimum of the potential

1785-566: 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 Mikheyev–Smirnov–Wolfenstein effect . Only a small fraction of the neutrino's energy is transferred to the material. Onia 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

1904-418: A proton, electron, and the smaller neutral particle (now called 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. By 1934, there was experimental evidence against Bohr's idea that energy conservation is invalid for beta decay: At

2023-456: A variety of experiments (see neutrino mixing for a description). The CP-violating phase δ C P {\displaystyle \delta _{\mathrm {CP} }} has not been measured directly, but estimates can be obtained by fits using the other measurements. As of November 2022, the current best-fit values from Nu-FIT.org, from direct and indirect measurements, using normal ordering, are: As of November 2022,

2142-605: 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. There are other possibilities in which neutrinos could oscillate even if they were massless: If Lorentz symmetry were not an exact symmetry, neutrinos could experience Lorentz-violating oscillations . Neutrinos traveling through matter, in general, undergo

2261-472: 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. 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

2380-545: Is associated with the correspondingly named charged lepton . Although neutrinos were long believed to be massless, it is now known that there are three discrete neutrino masses with different tiny values (the smallest of which could even be zero ), 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 (a quantum superposition ). Similar to some other neutral particles , neutrinos oscillate between different flavors in flight as

2499-468: Is conventionally called a " positron ". The Standard Model includes 12 elementary particles of spin 1 ⁄ 2 , known as fermions . Fermions respect the Pauli exclusion principle , meaning that two identical fermions cannot simultaneously occupy the same quantum state in the same atom. Each fermion has a corresponding antiparticle , which are particles that have corresponding properties with

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2618-493: Is conventionally called the "normal hierarchy", while in the "inverted hierarchy", the opposite would hold. Several major experimental efforts are underway to help establish which is correct. A neutrino created in a specific flavor eigenstate is in an associated specific quantum superposition of all three mass eigenstates. 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

2737-431: Is degenerate with an infinite number of equivalent ground state solutions, which occurs when φ † φ = μ 2 2 λ {\displaystyle \varphi ^{\dagger }\varphi ={\tfrac {\mu ^{2}}{2\lambda }}} . It is possible to perform a gauge transformation on φ {\displaystyle \varphi } such that

2856-412: Is described in terms of a dynamical field that pervades space-time . The construction of the Standard Model proceeds following the modern method of constructing most field theories: by first postulating a set of symmetries of the system, and then by writing down the most general renormalizable Lagrangian from its particle (field) content that observes these symmetries. The global Poincaré symmetry

2975-503: Is identical to the matrix for neutrinos under CPT symmetry . Due to the difficulties of detecting neutrinos , it is much more difficult to determine the individual coefficients than in the equivalent matrix for the quarks (the CKM matrix ). In the Standard Model, the PMNS matrix is unitary . This implies that the sum of the squares of the values in each row and in each column, which represent

3094-477: Is implied. The gauge covariant derivative of QCD is defined by D μ ≡ ∂ μ − i g s 1 2 λ a G μ a {\displaystyle D_{\mu }\equiv \partial _{\mu }-ig_{s}{\frac {1}{2}}\lambda ^{a}G_{\mu }^{a}} , where The QCD Lagrangian is invariant under local SU(3) gauge transformations; i.e., transformations of

3213-463: 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:

3332-405: Is mediated by mesons, such as the pion . The color charges inside the nucleon cancel out, meaning most of the gluon and quark fields cancel out outside of the nucleon. However, some residue is "leaked", which appears as the exchange of virtual mesons, that causes the attractive force between nucleons. The (fundamental) strong interaction is described by quantum chromodynamics, which is a component of

3451-533: Is no experimental evidence for a non-zero magnetic moment in neutrinos. Weak interactions create neutrinos in one of three leptonic flavors : electron neutrinos ( ν e ), muon neutrinos ( ν μ ), or tau neutrinos ( ν τ ), associated with the corresponding charged leptons, the electron ( e ), muon ( μ ), and tau ( τ ), respectively. Although neutrinos were long believed to be massless, it

3570-456: 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, experiments have shown that these masses are tiny compared to any other particle. From cosmological measurements, it has been calculated that the sum of the three neutrino masses must be less than one-millionth that of

3689-404: Is postulated for all relativistic quantum field theories. It consists of the familiar translational symmetry , rotational symmetry and the inertial reference frame invariance central to the theory of special relativity . The local SU(3)×SU(2)×U(1) gauge symmetry is an internal symmetry that essentially defines the Standard Model. Roughly, the three factors of the gauge symmetry give rise to

Pontecorvo–Maki–Nakagawa–Sakata matrix - Misplaced Pages Continue

3808-436: Is the theory describing three of the four known fundamental forces ( electromagnetic , weak and strong interactions – excluding gravity ) in the universe and classifying all known elementary particles . It was developed in stages throughout the latter half of the 20th century, through the work of many scientists worldwide, with the current formulation being finalized in the mid-1970s upon experimental confirmation of

3927-561: Is the Higgs doublet and φ ~ = i τ 2 φ ∗ {\displaystyle {\tilde {\varphi }}=i\tau _{2}\varphi ^{*}} is its charge conjugate state. The Yukawa terms are invariant under the SU ⁡ ( 2 ) L × U ⁡ ( 1 ) Y {\displaystyle \operatorname {SU} (2)_{\text{L}}\times \operatorname {U} (1)_{\text{Y}}} gauge symmetry of

4046-467: Is the electroweak gauge covariant derivative defined above and V ( φ ) {\displaystyle V(\varphi )} is the potential of the Higgs field. The square of the covariant derivative leads to three and four point interactions between the electroweak gauge fields W μ a {\displaystyle W_{\mu }^{a}} and B μ {\displaystyle B_{\mu }} and

4165-469: Is the only long-range force in the Standard Model. It is mediated by photons and couples to electric charge. Electromagnetism is responsible for a wide range of phenomena including atomic electron shell structure , chemical bonds , electric circuits and electronics . Electromagnetic interactions in the Standard Model are described by quantum electrodynamics. The weak interaction is responsible for various forms of particle decay , such as beta decay . It

4284-424: Is weak and short-range, due to the fact that the weak mediating particles, W and Z bosons, have mass. W bosons have electric charge and mediate interactions that change the particle type (referred to as flavour) and charge. Interactions mediated by W bosons are charged current interactions . Z bosons are neutral and mediate neutral current interactions, which do not change particle flavour. Thus Z bosons are similar to

4403-475: The 1995 Nobel Prize . In this experiment, now known as the Cowan–Reines neutrino experiment , antineutrinos created in a nuclear reactor by beta decay reacted with protons to produce neutrons and positrons: 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

4522-564: The GIM mechanism , predicting the charm quark . In 1973 Gross and Wilczek and Politzer independently discovered that non-Abelian gauge theories, like the color theory of the strong force, have asymptotic freedom . In 1976, Martin Perl discovered the tau lepton at the SLAC . In 1977, a team led by Leon Lederman at Fermilab discovered the bottom quark. The Higgs mechanism is believed to give rise to

4641-455: 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

4760-520: 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 available types of light neutrinos, the shorter the lifetime of the Z ;boson. Measurements of the Z lifetime have shown that three light neutrino flavors couple to

4879-471: The atomic nucleus , ultimately constituted of up and down quarks. On the other hand, second- and third-generation charged particles decay with very short half-lives and can only be observed in high-energy environments. Neutrinos of all generations also do not decay, and pervade the universe, but rarely interact with baryonic matter. There are six quarks: up , down , charm , strange , top , and bottom . Quarks carry color charge , and hence interact via

Pontecorvo–Maki–Nakagawa–Sakata matrix - Misplaced Pages Continue

4998-523: The cosmic neutrino background (CNB). R. Davis and M. Koshiba were jointly awarded the 2002 Nobel Prize in Physics. Both conducted pioneering work on solar neutrino detection, and Koshiba's work also resulted in the first real-time observation of neutrinos from the SN 1987A supernova in the nearby Large Magellanic Cloud . These efforts marked the beginning of neutrino astronomy . SN 1987A represents

5117-628: The electron , electron neutrino , muon , muon neutrino , tau , and tau neutrino . The leptons do not carry color charge, and do not respond to strong interaction. The main leptons carry an electric charge of -1 e , while the three neutrinos carry a neutral electric charge. Thus, the neutrinos' motion are only influenced by weak interaction and gravity , making them difficult to observe. The Standard Model includes 4 kinds of gauge bosons of spin 1, with bosons being quantum particles containing an integer spin. The gauge bosons are defined as force carriers , as they are responsible for mediating

5236-566: The fundamental interactions . The Standard Model explains the four fundamental forces as arising from the interactions, with fermions exchanging virtual force carrier particles, thus mediating the forces. At a macroscopic scale, this manifests as a force . As a result, they do not follow the Pauli exclusion principle that constrains fermions; bosons do not have a theoretical limit on their spatial density . The types of gauge bosons are described below. The Feynman diagram calculations, which are

5355-499: The masses of all the elementary particles in the Standard Model. This includes the masses of the W and Z bosons , and the masses of the fermions , i.e. the quarks and leptons . After the neutral weak currents caused by Z boson exchange were discovered at CERN in 1973, the electroweak theory became widely accepted and Glashow, Salam, and Weinberg shared the 1979 Nobel Prize in Physics for discovering it. The W and Z bosons were discovered experimentally in 1983; and

5474-651: The mn term giving the coupling of the generations m and n , and h.c. means Hermitian conjugate of preceding terms. The fields Q L {\displaystyle Q_{\text{L}}} and ℓ L {\displaystyle \ell _{\text{L}}} are left-handed quark and lepton doublets. Likewise, u R , d R {\displaystyle u_{\text{R}},d_{\text{R}}} and e R {\displaystyle e_{\text{R}}} are right-handed up-type quark, down-type quark, and lepton singlets. Finally φ {\displaystyle \varphi }

5593-529: The muon neutrino (already hypothesised with the name neutretto ), which earned them the 1988 Nobel Prize in Physics . When the third type of lepton, the tau , was discovered in 1975 at the Stanford Linear Accelerator Center , it 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

5712-405: 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 and had a mass similar to the electron. James Chadwick discovered a much more massive neutral nuclear particle in 1932 and named it a neutron also, leaving two kinds of particles with the same name. The word "neutrino" entered

5831-585: The strong interaction . The color confinement phenomenon results in quarks being strongly bound together such that they form color-neutral composite particles called hadrons ; quarks cannot individually exist and must always bind with other quarks. Hadrons can contain either a quark-antiquark pair ( mesons ) or three quarks ( baryons ). The lightest baryons are the nucleons : the proton and neutron . Quarks also carry electric charge and weak isospin , and thus interact with other fermions through electromagnetism and weak interaction . The six leptons consist of

5950-454: The 2015 Nobel Prize for Physics for their landmark finding, theoretical and experimental, that neutrinos can change flavors. 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. Around 1 second after the Big Bang , neutrinos decoupled, giving rise to a background level of neutrinos known as

6069-2194: The 3  σ ranges (99.7% confidence) for the magnitudes of the elements of the matrix were: | U | = [   | U e 1 |   | U e 2 |   | U e 3 |   | U μ 1 |   | U μ 2 |   | U μ 3 |   | U τ 1 |   | U τ 2 |   | U τ 3 |   ] = [   0.803 ∼ 0.845     0.514 ∼ 0.578     0.142 ∼ 0.155     0.233 ∼ 0.505     0.460 ∼ 0.693     0.630 ∼ 0.779     0.262 ∼ 0.525     0.473 ∼ 0.702     0.610 ∼ 0.762   ] {\displaystyle |U|={\begin{bmatrix}~|U_{\mathrm {e} 1}|~&|U_{\mathrm {e} 2}|~&|U_{\mathrm {e} 3}|\\~|U_{\mu 1}|~&|U_{\mu 2}|~&|U_{\mu 3}|\\~|U_{\tau 1}|~&|U_{\tau 2}|~&|U_{\tau 3}|~\end{bmatrix}}=\left[{\begin{array}{rrr}~0.803\sim 0.845~~&0.514\sim 0.578~~&0.142\sim 0.155~\\~0.233\sim 0.505~~&0.460\sim 0.693~~&0.630\sim 0.779~\\~0.262\sim 0.525~~&0.473\sim 0.702~~&0.610\sim 0.762~\end{array}}\right]} Gonzalez-Garcia, M.C.; Maltoni, Michele; Salvado, Jordi; Schwetz, Thomas (21 December 2012). "Global fit to three neutrino mixing: Critical look at present precision". Journal of High Energy Physics . 2012 (12): 123. arXiv : 1209.3023 . Bibcode : 2012JHEP...12..123G . CiteSeerX   10.1.1.762.7366 . doi : 10.1007/JHEP12(2012)123 . S2CID   118566415 . Standard Model The Standard Model of particle physics

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6188-548: The Higgs boson is massive, it must interact with itself. Because the Higgs boson is a very massive particle and also decays almost immediately when created, only a very high-energy particle accelerator can observe and record it. Experiments to confirm and determine the nature of the Higgs boson using the Large Hadron Collider (LHC) at CERN began in early 2010 and were performed at Fermilab 's Tevatron until its closure in late 2011. Mathematical consistency of

6307-1333: The Higgs' mass could not be predicted beforehand and had to be determined experimentally. The Yukawa interaction terms are: L Yukawa = ( Y u ) m n ( Q ¯ L ) m φ ~ ( u R ) n + ( Y d ) m n ( Q ¯ L ) m φ ( d R ) n + ( Y e ) m n ( ℓ ¯ L ) m φ ( e R ) n + h . c . {\displaystyle {\mathcal {L}}_{\text{Yukawa}}=(Y_{\text{u}})_{mn}({\bar {Q}}_{\text{L}})_{m}{\tilde {\varphi }}(u_{\text{R}})_{n}+(Y_{\text{d}})_{mn}({\bar {Q}}_{\text{L}})_{m}\varphi (d_{\text{R}})_{n}+(Y_{\text{e}})_{mn}({\bar {\ell }}_{\text{L}})_{m}{\varphi }(e_{\text{R}})_{n}+\mathrm {h.c.} } where Y u {\displaystyle Y_{\text{u}}} , Y d {\displaystyle Y_{\text{d}}} , and Y e {\displaystyle Y_{\text{e}}} are 3 × 3 matrices of Yukawa couplings, with

6426-568: The PMNS matrix can be fully described by four free parameters. The PMNS matrix is most commonly parameterized by three mixing angles ( θ 12 {\displaystyle \theta _{12}} , θ 23 {\displaystyle \theta _{23}} , and θ 13 {\displaystyle \theta _{13}} ) and a single phase angle called δ C P {\displaystyle \delta _{\mathrm {CP} }} related to charge-parity violations (i.e. differences in

6545-510: The Standard Model and generate masses for all fermions after spontaneous symmetry breaking. The Standard Model describes three of the four fundamental interactions in nature; only gravity remains unexplained. In the Standard Model, such an interaction is described as an exchange of bosons between the objects affected, such as a photon for the electromagnetic force and a gluon for the strong interaction. Those particles are called force carriers or messenger particles . Despite being perhaps

6664-479: The Standard Model requires that any mechanism capable of generating the masses of elementary particles must become visible at energies above 1.4  TeV ; therefore, the LHC (designed to collide two 7 TeV proton beams) was built to answer the question of whether the Higgs boson actually exists. On 4 July 2012, two of the experiments at the LHC ( ATLAS and CMS ) both reported independently that they had found

6783-510: The Standard Model was driven by theoretical and experimental particle physicists alike. The Standard Model is a paradigm of a quantum field theory for theorists, exhibiting a wide range of phenomena, including spontaneous symmetry breaking , anomalies , and non-perturbative behavior. It is used as a basis for building more exotic models that incorporate hypothetical particles , extra dimensions , and elaborate symmetries (such as supersymmetry ) to explain experimental results at variance with

6902-500: The Standard Model, such as the existence of dark matter and neutrino oscillations. In 1928, Paul Dirac introduced the Dirac equation which implied the existence of antimatter . In 1954, Yang Chen-Ning and Robert Mills extended the concept of gauge theory for abelian groups , e.g. quantum electrodynamics , to nonabelian groups to provide an explanation for strong interactions . In 1957, Chien-Shiung Wu demonstrated parity

7021-465: The Standard Model. Antineutrino A neutrino ( / nj uː ˈ t r iː n oʊ / new- TREE -noh ; denoted by the Greek letter ν ) is an elementary particle that interacts via the weak interaction and gravity . 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 rest mass of

7140-473: The Z. 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. There are several active research areas involving the neutrino with aspirations of finding: International scientific collaborations install large neutrino detectors near nuclear reactors or in neutrino beams from particle accelerators to better constrain

7259-465: The addition of fermion mass terms into the electroweak Lagrangian is forbidden, since terms of the form m ψ ¯ ψ {\displaystyle m{\overline {\psi }}\psi } do not respect U(1) × SU(2) L gauge invariance. Neither is it possible to add explicit mass terms for the U(1) and SU(2) gauge fields. The Higgs mechanism is responsible for the generation of

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7378-411: The amplitude of mass eigenstate i = 1 , 2 , 3 {\displaystyle \,i=1,2,3\;} in terms of flavor   α = {\displaystyle ~\alpha =\;} " e ", " μ ", " τ "; parameterizes the unitary transformation between the two bases: The vector on the left represents a generic neutrino expressed in the flavor-eigenstate basis, and on

7497-529: The beta decay leading to the discovery of the electron neutrino. The first detection of tau neutrino interactions was announced in 2000 by the DONUT collaboration at Fermilab ; its existence had already been inferred by both theoretical consistency and experimental data from the Large Electron–Positron Collider . In the 1960s, the now-famous Homestake experiment made the first measurement of

7616-471: 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. The first evidence of the reality of neutrinos came in 1938 via simultaneous cloud-chamber measurements of

7735-482: The case of Majorana neutrinos, two extra complex phases are needed, as the phase of Majorana fields cannot be freely redefined due to the condition ν = ν c   {\displaystyle \nu =\nu ^{c}~} . An infinite number of possible parameterizations exist; one other common example being the Wolfenstein parameterization . The mixing angles have been measured by

7854-544: The charged lepton that it partners with in the charged-current weak interaction . These three eigenstates of the weak interaction form a complete, orthonormal basis for the Standard Model neutrino. Similarly, one can construct an eigenbasis out of three neutrino states of definite mass, ν 1 {\displaystyle \nu _{1}} , ν 2 {\displaystyle \nu _{2}} , and ν 3 {\displaystyle \nu _{3}} , which diagonalize

7973-409: 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 would have the property that the neutrino and antineutrino could be distinguished only by chirality; what experiments observe as

8092-466: The context of preventing the proliferation of nuclear weapons . Because antineutrinos and neutrinos are neutral particles, it is possible that they are the same particle. Rather than conventional Dirac fermions , neutral particles can be another type of spin  ⁠ 1  / 2 ⁠ particle called Majorana particles , named after the Italian physicist Ettore Majorana who first proposed

8211-417: The electron and the recoil of the nucleus. In 1942, Wang Ganchang first proposed the use of beta capture to experimentally detect neutrinos. In the 20 July 1956 issue of Science , Clyde Cowan , Frederick Reines , Francis B. "Kiko" Harrison, Herald W. Kruse, and Austin D. McGuire published confirmation that they had detected the neutrino, a result that was rewarded almost forty years later with

8330-728: The electron neutrino. Neutrinos are fermions with spin of ⁠ 1  / 2 ⁠ . For each neutrino, there also exists a corresponding antiparticle , called an antineutrino , which also has spin of ⁠ 1  / 2 ⁠ and no electric charge. Antineutrinos are distinguished from neutrinos by having opposite-signed lepton number and weak isospin , and right-handed instead of left-handed chirality. To conserve total lepton number (in nuclear beta decay), electron neutrinos only appear together with positrons (anti-electrons) or electron-antineutrinos, whereas electron antineutrinos only appear with electrons or electron neutrinos. Neutrinos are created by various radioactive decays ;

8449-405: 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

8568-451: The electron. More formally, neutrino flavor eigenstates (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. The neutrino mass hierarchy consists of two possible configurations. In analogy with the mass hierarchy of the charged leptons, the configuration with mass 2 being lighter than mass 3

8687-626: The exception of opposite charges . Fermions are classified based on how they interact, which is determined by the charges they carry, into two groups: quarks and leptons . Within each group, pairs of particles that exhibit similar physical behaviors are then grouped into generations (see the table). Each member of a generation has a greater mass than the corresponding particle of generations prior. Thus, there are three generations of quarks and leptons. As first-generation particles do not decay, they comprise all of ordinary ( baryonic ) matter. Specifically, all atoms consist of electrons orbiting around

8806-597: The existence of quarks . Since then, proof of the top quark (1995), the tau neutrino (2000), and the Higgs boson (2012) have added further credence to the Standard Model. In addition, the Standard Model has predicted various properties of weak neutral currents and the W and Z bosons with great accuracy. Although the Standard Model is believed to be theoretically self-consistent and has demonstrated some success in providing experimental predictions , it leaves some physical phenomena unexplained and so falls short of being

8925-600: The existence of all three neutrino flavors and found no deficit. A practical method for investigating neutrino oscillations was first suggested by Bruno Pontecorvo in 1957 using an analogy with kaon oscillations; over the subsequent 10 years, he developed the mathematical formalism and the modern formulation of vacuum oscillations. In 1985 Stanislav Mikheyev and Alexei Smirnov (expanding on 1978 work by Lincoln Wolfenstein ) noted that flavor oscillations can be modified when neutrinos propagate through matter. This so-called Mikheyev–Smirnov–Wolfenstein effect (MSW effect)

9044-424: The experimental neutrino oscillation data to an extended PMNS matrix with a fourth, light "sterile" neutrino and four mass eigenvalues, although the current experimental data tends to disfavor that possibility. In general, there are nine degrees of freedom in any unitary three by three matrix. However, in the case of the PMNS matrix, five of those real parameters can be absorbed as phases of the lepton fields and thus

9163-486: 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

9282-451: 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 × 10 ) solar neutrinos , per second per square centimeter. Neutrinos can be used for tomography of the interior of the Earth. The neutrino

9401-486: The form ψ → ψ ′ = U ψ {\displaystyle \psi \rightarrow \psi '=U\psi } , where U = e − i g s λ a ϕ a ( x ) {\displaystyle U=e^{-ig_{s}\lambda ^{a}\phi ^{a}(x)}} is 3 × 3 {\displaystyle 3\times 3} unitary matrix with determinant 1, making it

9520-862: The gauge boson masses, and the fermion masses result from Yukawa-type interactions with the Higgs field. In the Standard Model, the Higgs field is an SU ⁡ ( 2 ) L {\displaystyle \operatorname {SU} (2)_{\text{L}}} doublet of complex scalar fields with four degrees of freedom: φ = ( φ + φ 0 ) = 1 2 ( φ 1 + i φ 2 φ 3 + i φ 4 ) , {\displaystyle \varphi ={\begin{pmatrix}\varphi ^{+}\\\varphi ^{0}\end{pmatrix}}={\frac {1}{\sqrt {2}}}{\begin{pmatrix}\varphi _{1}+i\varphi _{2}\\\varphi _{3}+i\varphi _{4}\end{pmatrix}},} where

9639-428: The ground state is transformed to a basis where φ 1 = φ 2 = φ 4 = 0 {\displaystyle \varphi _{1}=\varphi _{2}=\varphi _{4}=0} and φ 3 = μ λ ≡ v {\displaystyle \varphi _{3}={\tfrac {\mu }{\sqrt {\lambda }}}\equiv v} . This breaks

9758-593: 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. Very much like neutrons do in nuclear reactors , neutrinos can induce fission reactions within heavy nuclei . So far, this reaction has not been measured in

9877-513: 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. Antineutrinos are produced in nuclear beta decay together with a beta particle (in beta decay a neutron decays into a proton, electron, and antineutrino). All antineutrinos observed thus far had right-handed helicity (i.e., only one of

9996-614: The interactions between quarks and gluons, which is a Yang–Mills gauge theory with SU(3) symmetry, generated by T a = λ a / 2 {\displaystyle T^{a}=\lambda ^{a}/2} . Since leptons do not interact with gluons, they are not affected by this sector. The Dirac Lagrangian of the quarks coupled to the gluon fields is given by L QCD = ψ ¯ i γ μ D μ ψ − 1 4 G μ ν

10115-642: The left-handed doublet and right-handed singlet lepton fields. The electroweak gauge covariant derivative is defined as D μ ≡ ∂ μ − i g ′ 1 2 Y W B μ − i g 1 2 τ → L W → μ {\displaystyle D_{\mu }\equiv \partial _{\mu }-ig'{\tfrac {1}{2}}Y_{\text{W}}B_{\mu }-ig{\tfrac {1}{2}}{\vec {\tau }}_{\text{L}}{\vec {W}}_{\mu }} , where Notice that

10234-505: The main building commemorates the discovery. The experiments also implemented a primitive neutrino astronomy and looked at issues of neutrino physics and weak interactions. The antineutrino discovered by Clyde Cowan and Frederick Reines was 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

10353-408: The massive spin-zero particle, was proposed as the Higgs boson , and is a key building block in the Standard Model. It has no intrinsic spin , and for that reason is classified as a boson with spin-0. The Higgs boson plays a unique role in the Standard Model, by explaining why the other elementary particles, except the photon and gluon , are massive. In particular, the Higgs boson explains why

10472-415: The most familiar fundamental interaction, gravity is not described by the Standard Model, due to contradictions that arise when combining general relativity, the modern theory of gravity, and quantum mechanics. However, gravity is so weak at microscopic scales, that it is essentially unmeasurable. The graviton is postulated to be the mediating particle, but has not yet been proved to exist. Electromagnetism

10591-514: The neutrino is much smaller than that of the other known elementary particles (excluding massless particles ). 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 the electromagnetic interaction or the strong interaction . Thus, neutrinos typically pass through normal matter unimpeded and undetected. Weak interactions create neutrinos in one of three leptonic flavors : Each flavor

10710-513: The neutrino masses and the values for the magnitude and rates of oscillations between neutrino flavors. These experiments are thereby searching for the existence of CP violation in the neutrino sector; that is, whether or not the laws of physics treat neutrinos and antineutrinos differently. The KATRIN experiment in Germany began to acquire data in June 2018 to determine the value of the mass of

10829-497: The neutrino's free-particle Hamiltonian . Observations of neutrino oscillation established experimentally that for neutrinos, as for quarks , these two eigenbases are different – they are 'rotated' relative to each other. Consequently, each flavor eigenstate can be written as a combination of mass eigenstates, called a " superposition ", and vice versa. The PMNS matrix, with components U α i {\displaystyle U_{\alpha \,i}} corresponding to

10948-404: The neutrinos by having opposite signs of lepton number and opposite chirality (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

11067-578: The only verified detection of neutrinos from a supernova. However, many stars have gone supernova in the universe, leaving a theorized diffuse supernova neutrino background . Neutrinos have half-integer spin ( ⁠ 1  / 2 ⁠ ħ ); therefore they are fermions . Neutrinos are leptons. They have only been observed to interact through the weak 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

11186-427: The particles described by the Standard Model are summarized by the diagrams on the right of this section. The Higgs particle is a massive scalar elementary particle theorized by Peter Higgs ( and others ) in 1964, when he showed that Goldstone's 1962 theorem (generic continuous symmetry, which is spontaneously broken) provides a third polarisation of a massive vector field. Hence, Goldstone's original scalar doublet,

11305-431: The photon has no mass, while the W and Z bosons are very heavy. Elementary-particle masses and the differences between electromagnetism (mediated by the photon) and the weak force (mediated by the W and Z bosons) are critical to many aspects of the structure of microscopic (and hence macroscopic) matter. In electroweak theory , the Higgs boson generates the masses of the leptons (electron, muon, and tau) and quarks. As

11424-423: The photon, aside from them being massive and interacting with the neutrino. The weak interaction is also the only interaction to violate parity and CP . Parity violation is maximal for charged current interactions, since the W boson interacts exclusively with left-handed fermions and right-handed antifermions. In the Standard Model, the weak force is understood in terms of the electroweak theory, which states that

11543-552: The probabilities of different possible events given the same starting point, add up to 100%. In the simplest case, the Standard Model posits three generations of neutrinos with Dirac mass that oscillate between three neutrino mass eigenvalues, an assumption that is made when best fit values for its parameters are calculated. In other models the PMNS matrix is not necessarily unitary, and additional parameters are necessary to describe all possible neutrino mixing parameters in other models of neutrino oscillation and mass generation, such as

11662-409: The probability for an interaction. In general the interaction probability increases with the number of neutrons and protons within a nucleus. It is very hard to uniquely identify neutrino interactions among the natural background of radioactivity. For this reason, in early experiments a special reaction channel was chosen to facilitate the identification: the interaction of an antineutrino with one of

11781-688: The pure flavor states produced has been found to depend profoundly on the flavor. The relationship between flavor and mass eigenstates is encoded in the PMNS 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. A non-zero mass allows neutrinos to possibly have a tiny magnetic moment ; if so, neutrinos would interact electromagnetically, although no such interaction has ever been observed. Neutrinos oscillate between different flavors in flight. For example, an electron neutrino produced in

11900-627: The rates of oscillation between two states with opposite starting points which makes the order in time in which events take place necessary to predict their oscillation rates), in which case the matrix can be written as: where s i j {\displaystyle s_{ij}} and c i j {\displaystyle c_{ij}} are used to denote sin ⁡ θ i j {\displaystyle \sin \theta _{ij}} and cos ⁡ θ i j {\displaystyle \cos \theta _{ij}} respectively. In

12019-450: The ratio of their masses was found to be as the Standard Model predicted. The theory of the strong interaction (i.e. quantum chromodynamics , QCD), to which many contributed, acquired its modern form in 1973–74 when asymptotic freedom was proposed (a development which made QCD the main focus of theoretical research) and experiments confirmed that the hadrons were composed of fractionally charged quarks. The term "Standard Model"

12138-428: The reactor experiment KamLAND and the accelerator experiments such as MINOS . The KamLAND experiment has indeed identified oscillations as the neutrino flavor conversion mechanism involved in the solar electron neutrinos. Similarly MINOS confirms the oscillation of atmospheric neutrinos and gives a better determination of the mass squared splitting. Takaaki Kajita of Japan, and Arthur B. McDonald of Canada, received

12257-591: The right is the PMNS matrix multiplied by a vector representing that same neutrino in the mass-eigenstate basis. A neutrino of a given flavor α {\displaystyle \alpha } is thus a "mixed" state of neutrinos with distinct mass: If one could measure directly that neutrino's mass, it would be found to have mass m i {\displaystyle m_{i}} with probability | U α i | 2 {\displaystyle \left|U_{\alpha \,i}\right|^{2}} . The PMNS matrix for antineutrinos

12376-649: The scalar field φ {\displaystyle \varphi } . The scalar potential is given by V ( φ ) = − μ 2 φ † φ + λ ( φ † φ ) 2 , {\displaystyle V(\varphi )=-\mu ^{2}\varphi ^{\dagger }\varphi +\lambda \left(\varphi ^{\dagger }\varphi \right)^{2},} where μ 2 > 0 {\displaystyle \mu ^{2}>0} , so that φ {\displaystyle \varphi } acquires

12495-689: The scale of electroweak physics. This is the only dimensional parameter of the Standard Model and has a measured value of ~ 246 GeV/ c . After symmetry breaking, the masses of the W {\displaystyle {\text{W}}} and Z {\displaystyle {\text{Z}}} are given by m W = 1 2 g v {\displaystyle m_{\text{W}}={\frac {1}{2}}gv} and m Z = 1 2 g 2 + g ′ 2 v {\displaystyle m_{\text{Z}}={\frac {1}{2}}{\sqrt {g^{2}+g'^{2}}}v} , which can be viewed as predictions of

12614-947: The scientific vocabulary through Enrico Fermi , who used it during a conference in Paris in July ;1932 and at the Solvay Conference in October ;1933, where Pauli also employed it. The name (the Italian equivalent of "little neutral one") was jokingly coined by Edoardo Amaldi during a conversation with Fermi at the Institute of Physics of via Panisperna in Rome, in order to distinguish this light neutral particle from Chadwick's heavy neutron. In Fermi's theory of beta decay , Chadwick's large neutral particle could decay to

12733-413: The see-saw model, and in general, in the case of neutrinos that have Majorana mass rather than Dirac mass . There are also additional mass parameters and mixing angles in a simple extension of the PMNS matrix in which there are more than three flavors of neutrinos, regardless of the character of neutrino mass. As of July 2014, scientists studying neutrino oscillation are actively considering fits of

12852-430: The strong force becomes weaker, as the energy scale increases. The strong force overpowers the electrostatic repulsion of protons and quarks in nuclei and hadrons respectively, at their respective scales. While quarks are bound in hadrons by the fundamental strong interaction, which is mediated by gluons, nucleons are bound by an emergent phenomenon termed the residual strong force or nuclear force . This interaction

12971-522: The subscript j {\displaystyle j} sums over the three generations of fermions; Q L , u R {\displaystyle Q_{L},u_{R}} , and d R {\displaystyle d_{R}} are the left-handed doublet, right-handed singlet up type, and right handed singlet down type quark fields; and ℓ L {\displaystyle \ell _{L}} and e R {\displaystyle e_{R}} are

13090-782: The superscripts + and 0 indicate the electric charge Q {\displaystyle Q} of the components. The weak hypercharge Y W {\displaystyle Y_{\text{W}}} of both components is 1. Before symmetry breaking, the Higgs Lagrangian is L H = ( D μ φ ) † ( D μ φ ) − V ( φ ) , {\displaystyle {\mathcal {L}}_{\text{H}}=\left(D_{\mu }\varphi \right)^{\dagger }\left(D^{\mu }\varphi \right)-V(\varphi ),} where D μ {\displaystyle D_{\mu }}

13209-451: The symmetry of the ground state. The expectation value of φ {\displaystyle \varphi } now becomes ⟨ φ ⟩ = 1 2 ( 0 v ) , {\displaystyle \langle \varphi \rangle ={\frac {1}{\sqrt {2}}}{\begin{pmatrix}0\\v\end{pmatrix}},} where v {\displaystyle v} has units of mass and sets

13328-473: The theory. The photon remains massless. The mass of the Higgs Boson is m H = 2 μ 2 = 2 λ v {\displaystyle m_{\text{H}}={\sqrt {2\mu ^{2}}}={\sqrt {2\lambda }}v} . Since μ {\displaystyle \mu } and λ {\displaystyle \lambda } are free parameters,

13447-434: The three fundamental interactions. The fields fall into different representations of the various symmetry groups of the Standard Model (see table). Upon writing the most general Lagrangian, one finds that the dynamics depends on 19 parameters, whose numerical values are established by experiment. The parameters are summarized in the table (made visible by clicking "show") above. The quantum chromodynamics (QCD) sector defines

13566-449: The two possible spin states has ever been seen), while neutrinos were all left-handed. 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

13685-546: The weak and electromagnetic interactions become united into a single electroweak interaction at high energies. The strong nuclear force is responsible for hadronic and nuclear binding . It is mediated by gluons, which couple to color charge. Since gluons themselves have color charge, the strong force exhibits confinement and asymptotic freedom . Confinement means that only color-neutral particles can exist in isolation, therefore quarks can only exist in hadrons and never in isolation, at low energies. Asymptotic freedom means that

13804-708: Was introduced by Abraham Pais and Sam Treiman in 1975, with reference to the electroweak theory with four quarks. Steven Weinberg , has since claimed priority, explaining that he chose the term Standard Model out of a sense of modesty and used it in 1973 during a talk in Aix-en-Provence in France. The Standard Model includes members of several classes of elementary particles, which in turn can be distinguished by other characteristics, such as color charge . All particles can be summarized as follows: Notes : [†] An anti-electron ( e )

13923-508: Was not conserved in the weak interaction . In 1961, Sheldon Glashow combined the electromagnetic and weak interactions . In 1964, Murray Gell-Mann and George Zweig introduced quarks and that same year Oscar W. Greenberg implicitly introduced color charge of quarks. In 1967 Steven Weinberg and Abdus Salam incorporated the Higgs mechanism into Glashow's electroweak interaction , giving it its modern form. In 1970, Sheldon Glashow, John Iliopoulos, and Luciano Maiani introduced

14042-423: 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

14161-404: 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

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