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{{Short description|Theory of forces and subatomic particles}}
{{About|a non-mathematical general overview of the Standard Model of particle physics|a mathematical description|Mathematical formulation of the Standard Model|other uses|Standard model (disambiguation)}}
{{Use dmy dates|date=September 2020}}
{{Standard model of particle physics}}

The '''Standard Model''' of [[particle physics]] is the [[Scientific theory|theory]] describing three of the four known [[fundamental force]]s ([[electromagnetism|electromagnetic]], [[weak interaction|weak]] and [[strong interaction]]s – excluding [[gravity]]) in the [[universe]] and classifying all known [[elementary particle]]s. It was developed in stages throughout the latter half of the 20th century, through the work of many scientists worldwide,<ref>
{{cite book |author=R. Oerter |url=https://archive.org/details/theoryofalmostev0000oert |title=The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics |publisher=[[Penguin Group]] |year=2006 |isbn=978-0-13-236678-6 |edition=Kindle |page=[https://archive.org/details/theoryofalmostev0000oert/page/2 2] |access-date=28 March 2022 |url-access=registration}} {{Dead link |date=March 2022}}</ref> with the current formulation being finalized in the mid-1970s upon [[experimental confirmation]] of the existence of [[quark]]s. 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 current]]s and the [[W and Z bosons]] with great accuracy.

Although the Standard Model is believed to be theoretically self-consistent{{notetag|There are mathematical issues regarding quantum field theories still under debate (see e.g. [[Landau pole]]), but the predictions extracted from the Standard Model by current methods applicable to current experiments are all self-consistent.<ref>{{cite book|chapter=25 |author=R. Mann |title=An Introduction to Particle Physics and the Standard Model |publisher=[[CRC Press]] |year=2010 |isbn=978-1-4200-8298-2 |url=https://www.taylorfrancis.com/chapters/oa-mono/10.1201/9781420083002-25/beyond-standard-model-robert-mann?context=ubx&refId=4a659654-5432-4620-9f88-b125da855acd}}</ref>}} and has demonstrated some success in providing [[experimental prediction]]s, it leaves some [[physics beyond the standard model|physical phenomena unexplained]] and so falls short of being a [[theory of everything|complete theory of fundamental interactions]].<ref name="NYT-20230911">{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |date=11 September 2023 |title=Don't Expect a 'Theory of Everything' to Explain It All |url=https://www.nytimes.com/2023/09/11/science/space/astronomy-universe-simulations.html |url-access=limited |url-status=live |archiveurl=https://archive.today/20230911043212/https://www.nytimes.com/2023/09/11/science/space/astronomy-universe-simulations.html |archivedate=11 September 2023 |accessdate=11 September 2023 |work=[[The New York Times]]}}</ref> For example, it does not fully explain [[baryon asymmetry|why there is more matter than anti-matter]], incorporate the full [[theory of gravitation]]<ref>{{Cite book|isbn=978-1-59803-350-2 |oclc=288435552 |last1=Carroll |first1=Sean M. |url=https://www.worldcat.org/oclc/288435552 |title=Dark Matter, Dark Energy: The Dark Side of the Universe |last2=Rhoades |first2=Zachary H. |last3=Leven |first3=Jon |publisher=[[The Teaching Company]] |year=2007 |series=Guidebook Part 2 |location=Chantilly, VA |pages=59 |quote=...Standard Model of Particle Physics: The modern theory of elementary particles and their interactions ... It does not, strictly speaking, include gravity, although it's often convenient to include gravitons among the known particles of nature... |access-date=28 March 2022}}</ref> as described by [[general relativity]], or account for the [[accelerating expansion of the universe|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 [[physical cosmology|cosmology]]. It also does not incorporate [[neutrino oscillation]]s and their non-zero masses.

The development of the Standard Model was driven by [[theoretical physics|theoretical]] and [[experimental physics|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]], [[anomaly (physics)|anomalies]], and non-perturbative behavior. It is used as a basis for building more exotic models that incorporate [[hypothetical particle]]s, [[extra dimensions]], and elaborate symmetries (such as [[supersymmetry]]) to explain experimental results at variance with the Standard Model, such as the existence of dark matter and neutrino oscillations.

== Historical background ==
{{See also|History of quantum field theory|History of subatomic physics|Julian Schwinger|John Clive Ward}}
In 1928, [[Paul Dirac]] introduced the [[Dirac equation]], which implied the existence of [[antimatter]].

In 1954, [[Yang Chen-Ning]] and [[Robert Mills (physicist)|Robert Mills]] extended the concept of [[gauge theory]] for [[abelian group]]s, e.g. [[quantum electrodynamics]], to [[nonabelian group]]s to provide an explanation for [[strong interaction]]s.<ref name="YM">{{cite journal |author-link1=Chen-Ning Yang |first1=C. N. |last1=Yang |author-link2=Robert Mills (physicist) |first2=R. |last2=Mills |title=Conservation of Isotopic Spin and Isotopic Gauge Invariance |journal=[[Physical Review]] |volume=96 |issue=1 |pages=191–195 |year=1954 |doi=10.1103/PhysRev.96.191|bibcode = 1954PhRv...96..191Y |doi-access=free }}</ref> In 1957, [[Chien-Shiung Wu]] demonstrated [[parity (physics)|parity]] was not conserved in the [[weak interaction]].<ref>{{cite web|last=Cho|first=Adrian|title=Postage stamp to honor female physicist who many say should have won the Nobel Prize|date=5 February 2021|url=https://www.science.org/content/article/postage-stamp-honor-female-physicist-who-many-say-should-have-won-nobel-prize}}</ref> 

In 1961, [[Sheldon Glashow]] combined the [[electromagnetism|electromagnetic]] and [[weak interaction]]s.<ref>
{{cite journal
 |author=S.L. Glashow
 |year=1961
 |title=Partial-symmetries of weak interactions
 |journal=[[Nuclear Physics (journal)|Nuclear Physics]]
 |volume=22 |issue=4 |pages=579–588
 |bibcode=1961NucPh..22..579G
 |doi=10.1016/0029-5582(61)90469-2
}}</ref> In 1964, [[Murray Gell-Mann]] and [[George Zweig]] introduced quarks and that same year [[Oscar W. Greenberg]] implicitly introduced color charge of quarks.<ref>{{Citation |last=Greenberg |first=Oscar Wallace |title=Color Charge Degree of Freedom in Particle Physics |date=2009 |work=Compendium of Quantum Physics |pages=109–111 |editor-last=Greenberger |editor-first=Daniel |url=https://link.springer.com/chapter/10.1007/978-3-540-70626-7_32 |access-date=2024-09-17 |place=Berlin, Heidelberg |publisher=Springer |language=en |doi=10.1007/978-3-540-70626-7_32 |isbn=978-3-540-70626-7 |editor2-last=Hentschel |editor2-first=Klaus |editor3-last=Weinert |editor3-first=Friedel|url-access=subscription }}</ref> In 1967 [[Steven Weinberg]]<ref>
{{cite journal
 |author=S. Weinberg
 |year=1967
 |title=A Model of Leptons
 |journal=[[Physical Review Letters]]
 |volume=19 |issue=21 |pages=1264–1266
 |bibcode=1967PhRvL..19.1264W
 |doi=10.1103/PhysRevLett.19.1264
|doi-access=free
 }}</ref> and [[Abdus Salam]]<ref>
{{cite conference
 |author=A. Salam
 |editor=N. Svartholm
 |year=1968
 |book-title=Elementary Particle Physics: Relativistic Groups and Analyticity
 |pages=367
 |conference=Eighth Nobel Symposium
 |publisher=Almquvist and Wiksell
 |location=Stockholm
}}</ref> incorporated the [[Higgs mechanism]]<ref name="Englert1964">
{{cite journal
 |author1=F. Englert |author2=R. Brout |year=1964
 |title=Broken Symmetry and the Mass of Gauge Vector Mesons
 |journal=[[Physical Review Letters]]
 |volume=13 |issue=9 |pages=321–323
 |bibcode=1964PhRvL..13..321E
 |doi=10.1103/PhysRevLett.13.321
|doi-access=free}}</ref><ref name="Peter W. Higgs 1964 508–509">
{{cite journal |author=P.W. Higgs |year=1964 |title=Broken Symmetries and the Masses of Gauge Bosons |journal=[[Physical Review Letters]] |volume=13 |issue=16 |pages=508–509 |bibcode=1964PhRvL..13..508H |doi=10.1103/PhysRevLett.13.508 |doi-access=free}}</ref><ref name="G.S. Guralnik, C.R. Hagen, T.W.B. Kibble 1964 585–587">
{{cite journal
 |author1=G.S. Guralnik |author2=C.R. Hagen |author3=T.W.B. Kibble |year=1964
 |title=Global Conservation Laws and Massless Particles
 |journal=[[Physical Review Letters]]
 |volume=13 |issue=20 |pages=585–587
 |bibcode=1964PhRvL..13..585G
 |doi=10.1103/PhysRevLett.13.585
|doi-access=free}}</ref> into Glashow's [[electroweak interaction]], giving it its modern form.

In 1970, Sheldon Glashow, John Iliopoulos, and Luciano Maiani introduced the [[GIM mechanism]], predicting the [[charm quark]].<ref name=":2">{{Cite journal |last=Weinberg |first=S. |date=2004-05-01 |title=The making of the Standard Model |url=https://link.springer.com/article/10.1140/epjc/s2004-01761-1 |journal=European Physical Journal C |language=en |volume=34 |issue=1 |pages=5–13 |doi=10.1140/epjc/s2004-01761-1 |arxiv=hep-ph/0401010 |bibcode=2004EPJC...34....5W |issn=1434-6052}}</ref> 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]].<ref name=":2" />  In 1976, Martin Perl discovered the [[tau lepton]] at the [[SLAC National Accelerator Laboratory|SLAC]].<ref>{{Cite web |title=The Nobel Prize in Physics 1995 |url=https://www.nobelprize.org/prizes/physics/1995/perl/facts/#:~:text=In%20a%20series%20of%20experiments,alongside%20two%20previously%20known%20families. |access-date=2024-09-17 |website=NobelPrize.org |language=en-US}}</ref><ref>{{Cite web |last=magazine |first=STANFORD |date=2015-01-01 |title=In Memoriam |url=https://stanfordmag.org/contents/in-memoriam |access-date=2024-09-17 |website=stanfordmag.org |language=en}}</ref> In 1977, a team led by Leon Lederman at Fermilab discovered the bottom quark.<ref>{{Cite web |title=Inquiring Minds {{!}} Discoveries at Fermilab - The Bottom Quark |url=https://www.fnal.gov/pub/inquiring/physics/discoveries/bottom_quark.html |access-date=2024-09-17 |website=www.fnal.gov}}</ref>

The Higgs mechanism is believed to give rise to the [[mass]]es of all the [[elementary particle]]s in the Standard Model. This includes the masses of the [[W and Z bosons]], and the masses of the [[fermion]]s, i.e. the [[quark]]s and [[lepton]]s.

After the [[Neutral current|neutral weak currents]] caused by [[Subatomic particle|Z boson]] exchange [[Gargamelle|were discovered]] at [[CERN]] in 1973,<ref>
{{cite journal
 |author=F.J. Hasert |display-authors=etal 
 |year=1973
 |title=Search for elastic muon-neutrino electron scattering
 |journal=[[Physics Letters B]]
 |volume=46 |issue=1 |page=121
 |bibcode=1973PhLB...46..121H
 |doi=10.1016/0370-2693(73)90494-2
}}</ref><ref>
{{cite journal
 |author=F.J. Hasert |display-authors=etal 
 |year=1973
 |title=Observation of neutrino-like interactions without muon or electron in the Gargamelle neutrino experiment
 |journal=[[Physics Letters B]]
 |volume=46 |issue=1 |page=138
 |bibcode=1973PhLB...46..138H
 |doi=10.1016/0370-2693(73)90499-1
}}</ref><ref>
{{cite journal
 |author=F.J. Hasert
 |year=1974
 |title=Observation of neutrino-like interactions without muon or electron in the Gargamelle neutrino experiment
 |journal=[[Nuclear Physics B]]
 |volume=73 |issue=1 |page=1
 |bibcode=1974NuPhB..73....1H
 |doi=10.1016/0550-3213(74)90038-8
|display-authors=etal}}</ref><ref>{{cite web
 |author=D. Haidt
 |date=4 October 2004
 |title=The discovery of the weak neutral currents
 |url=http://cerncourier.com/cws/article/cern/29168
 |work=[[CERN Courier]]
 |access-date=8 May 2008
 |archive-date=20 May 2011
 |archive-url=https://web.archive.org/web/20110520115858/http://cerncourier.com/cws/article/cern/29168
 |url-status=dead
 }}</ref> the electroweak theory became widely accepted and Glashow, Salam, and Weinberg shared the 1979 [[Nobel Prize in Physics]] for discovering it. The W<sup>±</sup> and Z<sup>0</sup> [[boson]]s were discovered experimentally in 1983; and the ratio of their masses was found to be as the Standard Model predicted.<ref>{{cite journal|last1=Gaillard|first1=Mary K.|author-link1=Mary K. Gaillard|last2=Grannis|first2= Paul D. |last3=Sciulli|first3=Frank J.|title=The Standard Model of Particle Physics|date=January 1999|journal=Reviews of Modern Physics|doi=10.1103/RevModPhys.71.S96|volume=71|issue=2 |pages=S96–S111|arxiv=hep-ph/9812285|bibcode=1999RvMPS..71...96G|s2cid=119012610}}</ref>

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<ref>
{{cite journal
 |author1=D.J. Gross |author2=F. Wilczek |year=1973
 |title=Ultraviolet behavior of non-abelian gauge theories
 |journal=[[Physical Review Letters]]
 |volume=30 |issue= 26|pages= 1343–1346
 |bibcode=1973PhRvL..30.1343G
 |doi=10.1103/PhysRevLett.30.1343
|doi-access=free}}</ref><ref>
{{cite journal
 |author=H.D. Politzer
 |year=1973
 |title=Reliable perturbative results for strong interactions
 |journal=[[Physical Review Letters]]
 |volume=30 |issue=26 |pages=1346–1349
 |bibcode=1973PhRvL..30.1346P
 |doi=10.1103/PhysRevLett.30.1346
|url=https://authors.library.caltech.edu/6668/1/POLprl73.pdf |archive-url=https://web.archive.org/web/20180719010018/https://authors.library.caltech.edu/6668/1/POLprl73.pdf |archive-date=2018-07-19 |url-status=live
 |doi-access=free
 }}</ref> (a development that made QCD the main focus of theoretical research)<ref>[[Dean Rickles]] (2014). ''A Brief History of String Theory: From Dual Models to M-Theory''. Springer, p. 11 n. 22.</ref> and experiments confirmed that the [[hadron]]s were composed of fractionally charged quarks.<ref>
{{cite journal
 |last1=Aubert |first1=J.
 |year=1974
 |title=Experimental Observation of a Heavy Particle J
 |journal=[[Physical Review Letters]]
 |volume=33 |issue=23 |pages=1404–1406
 |bibcode = 1974PhRvL..33.1404A
 |doi=10.1103/PhysRevLett.33.1404
|display-authors=etal|doi-access=free
 }}</ref><ref>
{{cite journal
 |last1=Augustin |first1=J.
 |year=1974
 |title=Discovery of a Narrow Resonance in e<sup>+</sup>e<sup>−</sup> Annihilation
 |journal=[[Physical Review Letters]]
 |volume=33 |issue=23 |pages=1406–1408
 |bibcode = 1974PhRvL..33.1406A
 |doi=10.1103/PhysRevLett.33.1406
 |display-authors=etal|doi-access=free
 }}</ref>

The term "Standard Model" was introduced by [[Abraham Pais]] and [[Sam Treiman]] in 1975,<ref>
{{cite journal |last1=Pais |first1=A. |last2=Treiman |first2=S. B. |year=1975 |title=How Many Charm Quantum Numbers are There? |journal=[[Physical Review Letters]] |volume=35 |issue=23 |pages=1556–1559 |doi=10.1103/PhysRevLett.35.1556 |bibcode=1975PhRvL..35.1556P |doi-access=}}</ref> with reference to the electroweak theory with four quarks.<ref>{{Cite book |last=Cao |first=Tian Yu |url=http://dx.doi.org/10.1017/9781108566926 |title=Conceptual Developments of 20th Century Field Theories |date=1 October 2019 |publisher=Cambridge University Press |isbn=978-1-108-56692-6 |publication-date=1998 |page=320|doi=10.1017/9781108566926 |bibcode=2019code.book.....C |s2cid=243686857 }}</ref> [[Steven Weinberg]] has since claimed priority, explaining that he chose the term Standard [[Model]] out of a sense of modesty<ref>A [[model]] is a representation of reality, whereas a [[theory]] is an explanation of reality; this Wikipedia article and some of the literature refers to the Standard Model as a theory.</ref><ref>{{Cite web |last=Weinberg |first=Steven |title=This World and the Universe |url=https://www.youtube.com/watch?v=Gnk0rnBQrR0&t=1080s |access-date=29 March 2022 |website=[[YouTube]] |date=20 April 2010 |publisher=Talks at Google}}</ref><ref>{{Cite web |year=2015 |title=World Science Festival |url=https://www.youtube.com/watch?v=g-y3DPJRVhE&t=435s |access-date=29 March 2022 |website=[[YouTube]]}}</ref>{{Better source needed|reason=The current source is insufficiently reliable ([[WP:NOTRS]]).|date=March 2022}} and used it in 1973 during a talk in Aix-en-Provence in France.<ref>{{cite web| url = https://www.aps.org/publications/apsnews/201902/weinberg.cfm| title = Q&A with Standard Bearer Steven Weinberg}}</ref>

== Particle content ==
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:
{{Elementary particles|SM=yes}}

=== Fermions ===
<!--
[[File:Standard Model.svg|upright=1.5|right|thumb|The pattern of [[weak isospin]], T<sub>3</sub>, [[weak hypercharge]], Y<sub>W</sub>, and [[color charge]] of all known elementary particles, rotated by the [[Weinberg angle|weak mixing angle]] to show electric charge, Q, roughly along the vertical. The neutral [[Higgs field]] (gray square) breaks the [[electroweak symmetry]] and interacts with other particles to give them mass.]]
-->

The Standard Model includes 12 [[elementary particle]]s of [[Spin (physics)|spin]] {{1/2}}, known as [[fermion]]s.<ref name=":0">{{Cite web |title=The Standard Model |url=https://www-project.slac.stanford.edu/e158/StandardModel.html |url-status=live |archive-url=https://web.archive.org/web/20060620190613/http://www-project.slac.stanford.edu/e158/StandardModel.html |archive-date=June 20, 2006 |access-date=January 18, 2024 |website=[[SLAC National Accelerator Laboratory]]}}</ref> Fermions respect the [[Pauli exclusion principle]], meaning that two [[Indistinguishable particles|identical fermions]] cannot simultaneously occupy the same quantum state in the same atom.<ref>{{Cite journal |last=Eisert |first=Jens |date=January 22, 2013 |title=Pauli Principle, Reloaded |url=https://physics.aps.org/articles/v6/8 |journal=Physics |language=en |volume=6 |issue=4 |pages=8 |doi=10.1103/PhysRevLett.110.040404|pmid=25166142 |arxiv=1210.5531 }}</ref> Each fermion has a corresponding [[antiparticle]], which are particles that have corresponding properties with the exception of [[Additive inverse|opposite]] [[Charge (physics)|charges]].<ref>{{Cite web |date=January 24, 2002 |title=What is antimatter? |url=https://www.scientificamerican.com/article/what-is-antimatter-2002-01-24/ |url-status=live |archive-url=https://web.archive.org/web/20140331153524/http://www.scientificamerican.com/article/what-is-antimatter-2002-01-24 |archive-date=March 31, 2014 |access-date=January 19, 2024 |website=[[Scientific American]]}}</ref> Fermions are classified based on how they interact, which is determined by the charges they carry, into two groups: [[Quark|quarks]] and [[Lepton|leptons]]. Within each group, pairs of particles that exhibit similar physical behaviors are then grouped into [[Generation (particle physics)|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.<ref name=":1">{{cite web |title=Standard Model - ATLAS Physics Cheat Sheet |url=https://cds.cern.ch/record/2759492/files/Standard%20Model%20-%20ATLAS%20Physics%20Cheat%20Sheet.pdf |access-date=2024-01-19 |website=[[ATLAS experiment|ATLAS]] |publisher=[[CERN]]}}</ref>  As first-generation particles do not decay, they comprise all of ordinary ([[baryon]]ic) matter. Specifically, all atoms consist of electrons orbiting around 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-life|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 quark|up]], [[down quark|down]], [[charm quark|charm]], [[strange quark|strange]], [[top quark|top]], and [[bottom quark|bottom]].<ref name=":0" /><ref name=":1" /> Quarks carry [[color charge]], and hence interact via the [[strong interaction]]. The [[color confinement]] phenomenon results in quarks being strongly bound together such that they form color-neutral composite particles called [[hadron]]s; quarks cannot individually exist and must always bind with other quarks. Hadrons can contain either a quark-antiquark pair ([[meson]]s) or three quarks ([[baryon]]s).<ref>{{cite web |title=Color Charge and Confinement |url=https://fafnir.phyast.pitt.edu/particles/color.html |url-status=live |archive-url=https://web.archive.org/web/20020322100232/http://fafnir.phyast.pitt.edu/particles/color.html |archive-date=March 22, 2002 |access-date=January 8, 2024 |website=[[University of Pittsburgh]]}}</ref> The lightest baryons are the [[Nucleon|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 the [[electron]], [[electron neutrino]], [[muon]], [[muon neutrino]], [[tau (particle)|tau]], and [[tau neutrino]]. The leptons do not carry color charge, and do not respond to strong interaction. The charged leptons carry an [[electric charge]] of −1&nbsp;''[[Elementary charge|e]]'', while the three [[neutrino]]s carry zero electric charge. Thus, the neutrinos' motions are influenced by only the [[weak interaction]] and [[gravity]], making them difficult to observe.

=== Gauge bosons ===
[[File:Standard Model – All Feynman diagram vertices.svg|upright=1.5|thumb|right|class=skin-invert-image|Interactions in the Standard Model. All Feynman diagrams in the model are built from combinations of these vertices. ''q'' is any quark, ''g'' is a gluon, 

''X'' is any charged particle, γ is a photon, ''f'' is any fermion, ''m'' is any particle with mass (with the possible exception of the neutrinos), ''m''<sub>B</sub> is any boson with mass. 

In diagrams with multiple particle labels separated by '/', one particle label is chosen. In diagrams with particle labels separated by '<nowiki>|</nowiki>', the labels must be chosen in the same order. For example, in the four boson electroweak case the valid diagrams are WWWW, WWZZ, WWγγ, WWZγ. The conjugate of each listed vertex (reversing the direction of arrows) is also allowed.<ref>{{cite thesis |type=PhD |last=Lindon |first=Jack |date=2020 |title=Particle Collider Probes of Dark Energy, Dark Matter and Generic Beyond Standard Model Signatures in Events With an Energetic Jet and Large Missing Transverse Momentum Using the ATLAS Detector at the LHC |publisher=CERN |url=https://cds.cern.ch/record/2746537/ }}</ref>]]

The Standard Model includes 4 kinds of [[gauge boson]]s of [[Spin (physics)|spin]] 1,<ref name=":0" /> with bosons being quantum particles containing an integer spin. The gauge bosons are defined as [[force carrier]]s, as they are responsible for mediating the [[fundamental interaction]]s. The Standard Model explains the four fundamental forces as arising from the interactions, with fermions [[Static forces and virtual-particle exchange|exchanging]] [[Virtual particle|virtual]] force carrier particles, thus mediating the forces. At a macroscopic scale, this manifests as a [[force]].<ref>{{cite journal |last1=Jaeger |first1=Gregg |year=2021 |title=Exchange Forces in Particle Physics |journal=Foundations of Physics |volume=51 |issue=1 |page=13 |bibcode=2021FoPh...51...13J |doi=10.1007/s10701-021-00425-0 |s2cid=231811425}}</ref> As a result, they do not follow the Pauli exclusion principle that constrains fermions; bosons do not have a theoretical limit on their [[volume number density|spatial density]]. The types of gauge bosons are described below.
* [[Electromagnetism]]: [[Photon]]s mediate the electromagnetic force, responsible for interactions between electrically charged particles. The photon is massless and is described by the theory of [[quantum electrodynamics]] (QED).
* [[Strong interaction|Strong Interactions]]: [[Gluon]]s mediate the strong interactions, which binds quarks to each other by influencing the [[color charge]], with the interactions being described in the theory of [[quantum chromodynamics]] (QCD). They have no mass, and there are eight distinct gluons, with each being denoted through a color-anticolor charge combination (e.g. red–antigreen).{{NoteTag|Although nine color–anticolor combinations mathematically exist, gluons form color octet particles. As one color-symmetric combination is linear and forms a color singlet particles, there are eight possible gluons.<ref>{{Cite book |last1=Cahn |first1=Robert N. |title=The Experimental Foundations of Particle Physics |last2=Goldbaher |first2=Gerson |publisher=[[Cambridge University Press]] |year=2010 |isbn=978-0521521475 |edition=2nd |publication-date=August 31, 2009 |pages=306 |chapter=Quarks, gluons, and jets |chapter-url=http://hitoshi.berkeley.edu/129A/Cahn-Goldhaber/chapter10.pdf |chapter-format=[[PDF]] |archive-url=https://web.archive.org/web/20120714015451/http://hitoshi.berkeley.edu/129A/Cahn-Goldhaber/chapter10.pdf |archive-date=July 14, 2012 |url-status=live}}</ref>}} As gluons have an effective color charge, they can also interact amongst themselves.
* [[Weak interaction|Weak Interactions]]: The [[W and Z bosons|{{SubatomicParticle|W boson+}}, {{SubatomicParticle|W boson-}}, and {{SubatomicParticle|Z boson}}]] gauge bosons mediate the weak interactions between all fermions, being responsible for [[Radioactive decay|radioactivity]]. They contain mass, with the {{SubatomicParticle|Z boson}} having more mass than the {{SubatomicParticle|W boson+-}}. The weak interactions involving the {{SubatomicParticle|W boson+-}} act only on [[Chirality (physics)|''left-handed'' particles and ''right-handed'' antiparticles]] respectively. The {{SubatomicParticle|W boson+-}} carries an electric charge of +1 and −1 and couples to the electromagnetic interaction. The electrically neutral {{SubatomicParticle|Z boson}} boson interacts with both left-handed particles and right-handed antiparticles. These three gauge bosons along with the photons are grouped together, as collectively mediating the [[electroweak]] interaction.
* [[Gravity]]: It is currently unexplained in the Standard Model, as the hypothetical mediating particle [[graviton]] has been proposed, but not observed.<ref>{{Cite web |last=Hooper |first=Dan |date=2022-05-19 |title=What is the Standard Model of particle physics, and why are scientists looking beyond it? |url=https://www.astronomy.com/science/what-is-the-standard-model-of-particle-physics-and-why-are-scientists-looking-beyond-it/ |access-date=2024-01-20 |website=[[Astronomy Magazine]] |language=en-US}}</ref> This is due to the incompatibility of quantum mechanics and [[General relativity|Einstein's theory of general relativity]], regarded as being the best explanation for gravity. In general relativity, gravity is explained as being the geometric curving of spacetime.<ref>{{Cite news |last=Butterworth |first=Jon |date=2014-06-01 |title=Gravity versus the Standard Model |url=https://www.theguardian.com/science/life-and-physics/2014/jun/01/gravity-versus-the-standard-model |access-date=2024-01-20 |work=[[The Guardian]] |language=en-GB |issn=0261-3077}}</ref>
The [[Feynman diagram]] calculations, which are a graphical representation of the [[perturbation theory (quantum mechanics)|perturbation theory]] approximation, invoke "force mediating particles", and when applied to analyze [[particle accelerator|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 state]]s, and [[soliton]]s. The interactions between all the particles described by the Standard Model are summarized by the diagrams on the right of this section.

=== Higgs boson ===
{{Main|Higgs boson}}

The Higgs particle is a massive [[Scalar field theory|scalar]] elementary particle theorized by [[Peter Higgs]] ([[1964 PRL symmetry breaking papers|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, the massive spin-zero particle, was [[1964 PRL symmetry breaking papers|proposed as the Higgs boson]], and is a key building block in the Standard Model.<ref>
{{cite journal
 |author=G.S. Guralnik
 |year=2009
 |title=The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles
 |journal=[[International Journal of Modern Physics A]]
 |volume=24 |issue=14 |pages=2601–2627
 |arxiv=0907.3466
 |bibcode=2009IJMPA..24.2601G
 |doi=10.1142/S0217751X09045431
 |s2cid=16298371
}}</ref> It has no intrinsic [[Spin (physics)|spin]], and for that reason is classified as a [[boson]] with spin-0.<ref name=":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 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 interaction|electroweak theory]], the Higgs boson generates the masses of the leptons (electron, muon, and tau) and quarks.  As 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 the Standard Model requires that any mechanism capable of generating the masses of elementary particles must become visible{{clarify|reason=Isn't "apparent" or "manifest" needed here instead of "visible"?|date=July 2013}} at energies above {{val|1.4|ul=TeV}};<ref>
{{cite journal
 |author1=B.W. Lee |author2=C. Quigg |author3=H.B. Thacker |year=1977
 |title=Weak interactions at very high energies: The role of the Higgs-boson mass
 |journal=[[Physical Review D]]
 |volume=16 |issue=5 |pages=1519–1531
 |bibcode=1977PhRvD..16.1519L
 |doi=10.1103/PhysRevD.16.1519
}}</ref> therefore, the LHC (designed to collide two {{val|7|u=TeV}} proton beams) was built to answer the question of whether the Higgs boson actually exists.<ref>
{{cite news
 |date=11 November 2009
 |title=Huge $10 billion collider resumes hunt for 'God particle'
 |url=http://www.cnn.com/2009/TECH/11/11/lhc.large.hadron.collider.beam/index.html
 |publisher=CNN
 |access-date=2010-05-04
}}</ref>

On 4 July 2012, two of the experiments at the LHC ([[ATLAS experiment|ATLAS]] and [[Compact Muon Solenoid|CMS]]) both reported independently that they had found a new particle with a mass of about {{val|125|ul=GeV/c2}} (about 133 proton masses, on the order of {{val|e=-25|u=kg}}), which is "consistent with the Higgs boson".<ref>
{{cite web
 |date=4 July 2012
 |title=Observation of a New Particle with a Mass of 125&nbsp;GeV
 |url=http://cms.web.cern.ch/news/observation-new-particle-mass-125-gev
 |publisher=CERN
 |access-date=2012-07-05
}}</ref><ref name="NYT-20120704">
{{cite news
 |author=D. Overbye
 |date=4 July 2012
 |title=A New Particle Could Be Physics' Holy Grail
 |url=https://www.nytimes.com/2012/07/05/science/cern-physicists-may-have-discovered-higgs-boson-particle.html
 |newspaper=The New York Times
 |access-date=2012-07-04
}}</ref> On 13 March 2013, it was confirmed to be the searched-for Higgs boson.<ref name="CERN_20130314">
{{cite web
 |url=https://home.cern/news/press-release/cern/new-results-indicate-particle-discovered-cern-higgs-boson
 |title=New results indicate that particle discovered at CERN is a Higgs boson
 |date=14 March 2013
 |publisher=CERN
 |access-date=2020-06-14
}}</ref><ref name="CERN_EPS2017">
{{cite web
 |url=https://press.cern/update/2017/07/lhc-experiments-delve-deeper-precision
 |title=LHC experiments delve deeper into precision
 |date=11 July 2017
 |publisher=CERN
 |access-date=2017-07-23
 |archive-date=14 July 2017
 |archive-url=https://web.archive.org/web/20170714090456/http://press.cern/update/2017/07/lhc-experiments-delve-deeper-precision
 |url-status=dead
}}</ref>

== Theoretical aspects ==
{{Main|Mathematical formulation of the Standard Model}}

=== Construction of the Standard Model Lagrangian ===
{| class="wikitable collapsible collapsed"
!colspan="6"|Parameters of the Standard Model
|-
! #
! Symbol
! Description
! Renormalization<br /> scheme (point)
! Value
|-
|1
|''m''<sub>e</sub>
|Electron mass
|
|0.511 MeV
|-
|2
|''m''<sub>μ</sub>
|Muon mass
|
|105.7 MeV
|-
|3
|''m''<sub>τ</sub>
|Tau mass
|
|1.78 GeV
|-
|4
|''m''<sub>u</sub>
|Up quark mass
|''μ''<sub>{{overline|MS}}</sub> = 2 GeV
|1.9 MeV
|-
|5
|''m''<sub>d</sub>
|Down quark mass
|''μ''<sub>{{overline|MS}}</sub> = 2 GeV
|4.4 MeV
|-
|6
|''m''<sub>s</sub>
|Strange quark mass
|''μ''<sub>{{overline|MS}}</sub> = 2 GeV
|87 MeV
|-
|7
|''m''<sub>c</sub>
|Charm quark mass
|''μ''<sub>{{overline|MS}}</sub> = ''m''<sub>c</sub>
|1.32 GeV
|-
|8
|''m''<sub>b</sub>
|Bottom quark mass
|''μ''<sub>{{overline|MS}}</sub> = ''m''<sub>b</sub>
|4.24 GeV
|-
|9
|''m''<sub>t</sub>
|Top quark mass
| On shell scheme
|173.5 GeV
|-
|10
|''θ''<sub>12</sub>
|CKM 12-mixing angle
|
|13.1°
|-
|11
|''θ''<sub>23</sub>
|CKM 23-mixing angle
|
|2.4°
|-
|12
|''θ''<sub>13</sub>
|CKM 13-mixing angle
|
|0.2°
|-
|13
|''δ''
|CKM CP violation Phase
|
|0.995
|-
|14
|''g''<sub>1</sub> or ''g''{{'}}
|U(1) gauge coupling
|''μ''<sub>{{overline|MS}}</sub> = ''m''<sub>Z</sub>
|0.357
|-
|15
|''g''<sub>2</sub> or ''g''
|SU(2) gauge coupling
|''μ''<sub>{{overline|MS}}</sub> = ''m''<sub>Z</sub>
|0.652
|-
|16
|''g''<sub>3</sub> or ''g''<sub>s</sub>
|SU(3) gauge coupling
|''μ''<sub>{{overline|MS}}</sub> = ''m''<sub>Z</sub>
|1.221
|-
|17
|''θ''<sub>QCD</sub>
|QCD vacuum angle
|
|~0
|-
|18
|''v''
|Higgs vacuum expectation value
|
|246 GeV
|-
|19
|''m''<sub>H</sub>
|Higgs mass
|
|{{val|125.09|0.24|u=GeV}}
|}

Technically, [[quantum field theory]] provides the mathematical framework for the Standard Model, in which a [[Lagrangian (field theory)|Lagrangian]] controls the dynamics and kinematics of the theory. Each kind of particle is described in terms of a dynamical [[field (physics)|field]] that pervades [[space-time]].<ref>{{cite journal | author=Gregg Jaeger | year=2021 | title=The Elementary Particles of Quantum Fields | journal=[[Entropy]] | volume=23 | issue=11 | pages=1416 | doi=10.3390/e23111416 | pmid=34828114 | pmc=8623095 | bibcode=2021Entrp..23.1416J | doi-access=free }}</ref>
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 [[renormalization|renormalizable]] Lagrangian from its particle (field) content that observes these symmetries.

The [[Global symmetry|global]] [[Poincaré group|Poincaré symmetry]] 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 symmetry|local]] SU(3) × SU(2) × U(1) [[gauge symmetry]] is an [[Internal symmetries|internal symmetry]] that essentially defines the Standard Model. Roughly, the three factors of the gauge symmetry give rise to the three fundamental interactions. The fields fall into different [[Representation of a Lie group|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.

==== Quantum chromodynamics sector ====
{{Main|Quantum chromodynamics}}
The quantum chromodynamics (QCD) sector defines the interactions between quarks and gluons, which is a [[Yang–Mills theory|Yang–Mills gauge theory]] with SU(3) symmetry, generated by <math>T^a = \lambda^a/2</math>. 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
<math display="block">\mathcal{L}_\text{QCD} = \overline{\psi} i\gamma^\mu D_{\mu} \psi - \frac{1}{4} G^a_{\mu\nu} G^{\mu\nu}_a,</math>
where <math>\psi</math> is a three component column vector of [[Dirac spinor]]s, each element of which refers to a quark field with a specific [[color charge]] (i.e. red, blue, and green) and summation over [[Flavour (particle physics)|flavor]] (i.e. up, down, strange, etc.) is implied. 

The gauge covariant derivative of QCD is defined by <math>D_{\mu} \equiv \partial_\mu - i g_\text{s}\frac{1}{2}\lambda^a G_\mu^a</math>, where
* {{math|''γ''{{isup|''μ''}}}} are the [[Dirac matrices]],
* {{math|''G''{{su|lh=0.9|b=''μ''|p=''a''}}}} is the 8-component (<math>a = 1, 2, \dots, 8</math>) SU(3) gauge field,
* {{math|''λ''{{su|lh=0.9|p=''a''}}}} are the 3 × 3 [[Gell-Mann matrices]], generators of the SU(3) color group,
* {{math|''G''{{su|lh=0.9|b=''μν''|p=''a''}}}} represents the [[gluon field strength tensor]], and
* {{math|''g''<sub>s</sub>}} is the strong coupling constant.

The QCD Lagrangian is invariant under local SU(3) gauge transformations; i.e., transformations of the form <math>\psi \rightarrow \psi' = U\psi</math>, where <math>U = e^{-i g_\text{s}\lambda^a \phi^{a}(x)}</math> is 3 × 3 unitary matrix with determinant 1, making it a member of the group SU(3), and <math>\phi^{a}(x)</math> is an arbitrary function of spacetime.

==== Electroweak sector ====
{{Main|Electroweak interaction}}
The electroweak sector is a [[Yang–Mills theory|Yang–Mills gauge theory]] with the symmetry group {{nowrap|U(1) × SU(2)<sub>L</sub>}},
<math display="block">\mathcal{L}_\text{EW} = \overline{Q}_{\text{L}j} i\gamma^\mu D_{\mu} Q_{\text{L}j} + \overline{u}_{\text{R}j} i\gamma^\mu D_{\mu} u_{\text{R}j} + \overline{d}_{\text{R}j} i\gamma^\mu D_{\mu} d_{\text{R}j} + \overline{\ell}_{\text{L}j} i\gamma^\mu D_{\mu} \ell_{\text{L}j} + \overline{e}_{\text{R}j} i\gamma^\mu D_{\mu} e_{\text{R}j} - \tfrac{1}{4} W_a^{\mu\nu} W_{\mu\nu}^a - \tfrac{1}{4} B^{\mu\nu} B_{\mu\nu}, </math>
where the subscript <math>j</math> sums over the three generations of fermions; <math>Q_\text{L}, u_\text{R}</math>, and <math>d_\text{R}</math> are the left-handed doublet, right-handed singlet up type, and right handed singlet down type quark fields; and <math>\ell_\text{L}</math> and <math>e_\text{R}</math> are the left-handed doublet and right-handed singlet lepton fields. 

The electroweak [[gauge covariant derivative]] is defined as <math>D_\mu \equiv \partial_\mu - ig' \tfrac12 Y_\text{W} B_\mu - ig \tfrac{1}{2} \vec\tau_\text{L} \vec W_\mu</math>, where 
* {{mvar|B<sub>μ</sub>}} is the U(1) gauge field,
* {{math|''Y''<sub>W</sub>}} is the [[weak hypercharge]] – the generator of the U(1) group,
* {{math|{{vec|''W''}}<sub>''μ''</sub>}} is the 3-component SU(2) gauge field,
* {{math|{{overset|lh=0.5|→|''τ''}}<sub>L</sub>}} are the [[Pauli matrices]] – infinitesimal generators of the SU(2) group – with subscript L to indicate that they only act on ''left''-chiral fermions,
* {{mvar|g'}} and {{mvar|g}} are the U(1) and SU(2) coupling constants respectively,
* <math>W^{a\mu\nu}</math> (<math>a = 1, 2, 3</math>) and <math>B^{\mu\nu}</math> are the [[field strength tensor]]s for the weak isospin and weak hypercharge fields.

Notice that the addition of fermion mass terms into the electroweak Lagrangian is forbidden, since terms of the form <math>m\overline\psi\psi</math> do not respect {{nowrap|U(1) × SU(2)<sub>L</sub>}} 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 the gauge boson masses, and the fermion masses result from Yukawa-type interactions with the Higgs field.

==== Higgs sector ====
{{Main|Higgs mechanism}}
In the Standard Model, the [[Higgs field]] is an SU(2){{sub|L}} doublet of complex [[Scalar (physics)|scalar]] fields with four degrees of freedom:
<math display="block"> 
\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},
</math>
where the superscripts + and 0 indicate the electric charge <math>Q</math> of the components. The weak hypercharge <math>Y_\text{W}</math> of both components is 1. Before symmetry breaking, the Higgs Lagrangian is
<math display="block"> \mathcal{L}_\text{H} = \left(D_{\mu}\varphi\right)^{\dagger} \left(D^{\mu}\varphi \right) - V(\varphi),</math>
where <math>D_{\mu}</math> is the electroweak gauge covariant derivative defined above and <math>V(\varphi)</math> 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 <math>W^{a}_{\mu}</math> and <math>B_{\mu}</math> and the scalar field <math>\varphi</math>. The scalar potential is given by
<math display="block"> V(\varphi) = -\mu^2\varphi^{\dagger}\varphi + \lambda \left( \varphi^{\dagger}\varphi \right)^2, </math>
where <math>\mu^2>0</math>, so that <math>\varphi</math> acquires a non-zero [[Vacuum expectation value]], which generates masses for the Electroweak gauge fields (the Higgs mechanism), and <math>\lambda>0</math>, so that the potential is bounded from below. The quartic term describes self-interactions of the scalar field <math>\varphi</math>.

The minimum of the potential is degenerate with an infinite number of equivalent [[ground state]] solutions, which occurs when <math>\varphi^{\dagger}\varphi = \tfrac{\mu^2}{2\lambda}</math>. It is possible to perform a [[Unitary gauge|gauge transformation]] on <math>\varphi</math> such that the ground state is transformed to a basis where <math>\varphi_1 = \varphi_2 = \varphi_4 = 0</math> and <math>\varphi_3 = \tfrac{\mu}{\sqrt{\lambda}} \equiv v </math>. This breaks the symmetry of the ground state. The expectation value of <math>\varphi</math> now becomes 
<math display="block"> \langle \varphi \rangle = \frac{1}{\sqrt{2}} \begin{pmatrix} 0 \\ v \end{pmatrix},</math>
where <math>v</math> has units of mass and sets the scale of electroweak physics. This is the only dimensional parameter of the Standard Model and has a measured value of ~{{val|246|u=GeV/c2}}. 

After symmetry breaking, the masses of the W and Z are given by <math>m_\text{W}=\frac{1}{2}gv</math> and <math> m_\text{Z}=\frac{1}{2}\sqrt{g^2+g'^2}v</math>, which can be viewed as predictions of the theory. The photon remains massless. The mass of the [[Higgs boson]] is <math>m_\text{H}=\sqrt{2\mu^2}=\sqrt{2\lambda}v</math>. Since <math>\mu</math> and <math>\lambda</math> are free parameters, the Higgs's mass could not be predicted beforehand and had to be determined experimentally.

==== Yukawa sector ====
The [[Yukawa interaction]] terms are:
<math display="block">\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.} </math>
where <math>Y_\text{u}</math>, <math>Y_\text{d}</math>, and <math>Y_\text{e}</math> are {{math|3 × 3}} matrices of Yukawa couplings, with the {{mvar|mn}} term giving the coupling of the generations {{mvar|m}} and {{mvar|n}}, and h.c. means Hermitian conjugate of preceding terms. The fields <math>Q_\text{L}</math> and <math>\ell_\text{L}</math> are left-handed quark and lepton doublets. Likewise, <math>u_\text{R}, d_\text{R}</math> and <math>e_\text{R}</math> are right-handed up-type quark, down-type quark, and lepton singlets. Finally <math>\varphi</math> is the Higgs doublet and <math>\tilde{\varphi} = i\tau_2\varphi^{*}</math> is its charge conjugate state.

The Yukawa terms are invariant under the SU(2){{sub|L}} × U(1){{sub|Y}} gauge symmetry of the Standard Model and generate masses for all fermions after spontaneous symmetry breaking.

== Fundamental interactions ==
{{Main|Fundamental interaction}}
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 [[boson]]s between the objects affected, such as a [[photon]] for the electromagnetic force and a [[gluon]] for the strong interaction. Those particles are called [[force carrier]]s or messenger [[particles]].<ref>{{Cite web|url=https://home.cern/science/physics/standard-model|title=The Standard Model|website=CERN|date=15 December 2023 }}</ref>

{| style="margin: 1em auto 1em auto;" class="wikitable floatcenter"
|+ The four fundamental interactions of nature<ref>{{cite web|url=http://www.pha.jhu.edu/~dfehling/particle.gif |title=Standard Model of Particles and Interactions |author=<!--Staff writer(s); no by-line.--> |website=jhu.edu |publisher=[[Johns Hopkins University]] |access-date=18 August 2016 |url-status=dead |archive-url=https://web.archive.org/web/20160304133522/https://www.pha.jhu.edu/~dfehling/particle.gif |archive-date=4 March 2016 }}</ref>
! style="" rowspan="2" | Property/Interaction
! style="background-color:#8080BF" rowspan="2" |Gravitation
! style="background-color:#BFA080" colspan="2" |Electroweak
! style="background-color:#80BF80" colspan="2" |Strong
|-
! style="background-color:#BFBF80" |Weak
! style="background-color:#BF8080" |Electromagnetic
! style="background-color:#AAD4AA" |<small>Fundamental</small>
! style="background-color:#D5EAD5" |<small>Residual</small>
|-
|Mediating particles
| align="center" {{Not yet}} observed<br /><small>([[Graviton]] hypothesised)</small>
| align="center" |[[W and Z bosons|W<sup>+</sup>, W<sup>−</sup> and Z<sup>0</sup>]]
| align="center" |[[Photon|γ]] (photon)
| align="center" |Gluons
| align="center" |[[Pion|π]], [[Rho meson|ρ]] and [[Omega meson|ω]] [[meson]]s
|-
|Affected particles
| align="center" |All particles
| align="center" |W<sup>+</sup>, W<sup>−</sup>: Left-handed [[fermions]]; Z<sup>0</sup>: All fermions 
| align="center" |Electrically charged
| align="center" |Quarks, [[gluon]]s
| align="center" |[[Hadron]]s
|-
|Acts on
| align="center" | [[Stress–energy tensor]]
| align="center" |[[Flavour (particle physics)|Flavor]]
| align="center" |Electric charge
| align="center" |[[Color charge]]
| align="center" |
|-
|Bound states formed
| align="center" |Planets, stars, galaxies, galaxy groups
| align="center" {{n/a}}
| align="center" |Atoms, molecules
| align="center" |Hadrons
| align="center" |Atomic nuclei
|-
|Strength at the scale of quarks<br /> (relative to electromagnetism)
| align="center" |{{val||e=-41}} <small>(predicted)</small>
| align="center" |{{val||e=-4}}
| align="center" |1
| align="center" |60
| align="center" {{No|Not applicable <br />to quarks}}
|-
|Strength at the scale of <br />protons/neutrons <br /> (relative to electromagnetism)
| align="center" |{{val||e=-36}} <small>(predicted)</small>
| align="center" |{{val||e=-7}}
| align="center" |1
| align="center" {{No|Not applicable <br />to hadrons}}
| align="center" |20
|}

{{Unreferenced section|date=June 2021}}

=== Gravity ===
{{See also|Quantum gravity|Gravity}}

[[File:Fundamental Interactions.png|thumb|Fundamental Interactions of the Standard Model including the hypothetical graviton]]

Despite being perhaps 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.<ref>{{Cite journal |last=Ashtekar |first=Abhay |date=2005-09-29 |title=Gravity and the quantum |url=https://iopscience.iop.org/article/10.1088/1367-2630/7/1/198 |journal=New Journal of Physics |volume=7 |pages=198–198 |doi=10.1088/1367-2630/7/1/198 |issn=1367-2630|arxiv=gr-qc/0410054 }}</ref><ref>{{Cite journal |last=Kuchař |first=Karel V. |date=2011-07-31 |title=TIME AND INTERPRETATIONS OF QUANTUM GRAVITY |url=https://www.worldscientific.com/doi/abs/10.1142/S0218271811019347 |journal=International Journal of Modern Physics D |language=en |volume=20 |issue=supp01 |pages=3–86 |doi=10.1142/S0218271811019347 |issn=0218-2718|url-access=subscription }}</ref> 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.<ref>{{Cite journal |last=Carney |first=Daniel |date=2024 |title=Graviton detection and the quantization of gravity |url=https://journals.aps.org/prd/abstract/10.1103/PhysRevD.109.044009 |journal=Physical Review D |volume=109 |issue=4 |doi=10.1103/PhysRevD.109.044009|arxiv=2308.12988 }}</ref>

=== Electromagnetism ===
{{See also|Electromagnetism|Quantum electrodynamics}}
Electromagnetism is the only long-range force in the Standard Model. It is mediated by photons and couples to electric charge.<ref>{{Cite web |date=2023-12-04 |title=The Standard Model |url=https://home.cern/science/physics/standard-model |access-date=2023-12-17 |website=CERN |language=en}}</ref> Electromagnetism is responsible for a wide range of phenomena including [[Electron shell|atomic electron shell structure]], [[chemical bonds]], [[electric circuit]]s and [[electronics]]. Electromagnetic interactions in the Standard Model are described by quantum electrodynamics.

=== Weak nuclear force ===
{{See also|Weak interaction|Electroweak interaction}}
The weak interaction is responsible for various forms of [[particle decay]], such as [[beta decay]]. It 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 flavor) and charge. Interactions mediated by W bosons are [[charged current interaction]]s. Z bosons are neutral and mediate neutral current interactions, which do not change particle flavor. Thus Z bosons are similar to the photon, aside from them being massive and interacting with the neutrino. The weak interaction is also the only interaction to violate [[Parity violation|parity]] and [[CP violation|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 the weak and electromagnetic interactions become united into a single ''electroweak'' interaction at high energies.

=== Strong nuclear force ===
{{See also|Strong interaction|Nuclear force|Quantum chromodynamics}}
The strong nuclear force is responsible for hadronic and [[Nuclear binding energy|nuclear binding]]. It is mediated by gluons, which couple to color charge. Since gluons themselves have color charge, the strong force exhibits [[Color confinement|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 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 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 the Standard Model.

== Tests and predictions ==
The Standard Model predicted the existence of the [[W and Z bosons]], [[gluon]], [[top quark]] and [[charm quark]], and predicted many of their properties before these particles were observed. The predictions were experimentally confirmed with good precision.<ref>
{{cite journal |last1=Woithe |first1=Julia |last2=Wiener |first2=Gerfried |last3=Van der Veken |first3=Frederik |title=Let's have a coffee with the Standard Model of particle physics! |journal=Phys. Educ. |volume=52 |issue= 3|pages=034001 |doi=10.1088/1361-6552/aa5b25 |year=2017 |bibcode=2017PhyEd..52c4001W |doi-access=free |url=http://cds.cern.ch/record/2807969/files/Woithe_2017_Phys._Educ._52_034001.pdf }}</ref>

The Standard Model also predicted the existence of the [[Higgs boson]], which was found in 2012 at the [[Large Hadron Collider]], the final fundamental particle predicted by the Standard Model to be experimentally confirmed.<ref>
{{cite arXiv|eprint=1407.2122|last1=Altarelli|first1=Guido|title=The Higgs and the Excessive Success of the Standard Model|class=hep-ph|year=2014}}</ref>

== Challenges ==
{{See also|Physics beyond the Standard Model}}
{{unsolved|physics|
* What gives rise to the Standard Model of particle physics?
* Why do particle masses and [[coupling constant]]s have the values that we measure?
* Why are there three [[Generation (particle physics)|generations]] of particles?
* Why is there more matter than [[antimatter]] in the universe?
* Where does [[dark matter]] fit into the model? Does it even consist of one or more new particles?
}}

Self-consistency of the Standard Model (currently formulated as a non-[[abelian group|abelian]] gauge theory quantized through path-integrals) has not been mathematically proved.  While regularized versions useful for approximate computations (for example [[lattice gauge theory]]) exist, it is not known whether they converge (in the sense of S-matrix elements) in the limit that the regulator is removed.  A key question related to the consistency is the [[Yang–Mills existence and mass gap]] problem.

Experiments indicate that [[neutrinos]] have [[mass]], which the classic Standard Model did not allow.<ref>
{{cite web
 |date=31 May 2010
 |title=Particle chameleon caught in the act of changing
 |url = http://press.cern/press-releases/2010/05/particle-chameleon-caught-act-changing
 |publisher=[[CERN]]
 |access-date=2016-11-12
}}</ref> To accommodate this finding, the classic Standard Model can be modified to include neutrino mass, although it is not obvious exactly how this should be done.

If one insists on using only Standard Model particles, this can be achieved by adding a non-renormalizable interaction of leptons with the Higgs boson.<ref>
{{cite journal
 |author=S. Weinberg
 |year=1979
 |title=Baryon and Lepton Nonconserving Processes
 |journal=[[Physical Review Letters]]
 |volume=43 |issue=21 |pages=1566–1570
 |bibcode=1979PhRvL..43.1566W
 |doi=10.1103/PhysRevLett.43.1566
}}</ref> On a fundamental level, such an interaction emerges in the [[seesaw mechanism]] where heavy right-handed neutrinos are added to the theory.
This is natural in the [[left-right symmetry|left-right symmetric]] extension of the Standard Model<ref name="Minkowski1977">
{{cite journal
 |author=P. Minkowski
 |year=1977
 |title=μ → e γ at a Rate of One Out of 10<sup>9</sup> Muon Decays?
 |journal=[[Physics Letters B]]
 |volume=67 |issue=4 |pages=421–428
 |bibcode=1977PhLB...67..421M
 |doi=10.1016/0370-2693(77)90435-X
}}</ref><ref name="MohapatraSenjanovic1980">
{{cite journal
 |author1=R.N. Mohapatra |author2=G. Senjanovic |year=1980
 |title=Neutrino Mass and Spontaneous Parity Nonconservation
 |journal=[[Physical Review Letters]]
 |volume=44|issue=14|pages=912–915
 |bibcode = 1980PhRvL..44..912M
 |doi=10.1103/PhysRevLett.44.912
}}</ref> and in certain [[grand unified theory|grand unified theories]].<ref name="Gell-Mann1979">
{{cite book
 |author1=M. Gell-Mann, P. Ramond  |author2=R. Slansky
 |name-list-style=amp |year=1979
 |pages=315–321
 |title=Supergravity
 |editor1=F. van Nieuwenhuizen |editor2=D.Z. Freedman |publisher=[[North Holland]]
 |isbn=978-0-444-85438-4
}}</ref> As long as new physics appears below or around 10<sup>14</sup> [[electronvolt|GeV]], the neutrino masses can be of the right order of magnitude.

Theoretical and experimental research has attempted to extend the Standard Model into a [[unified field theory]] or a [[theory of everything]], a complete theory explaining all physical phenomena including constants. Inadequacies of the Standard Model that motivate such research include:
* The model does not explain [[gravitation]], although physical confirmation of a theoretical particle known as a [[graviton]] would account for it to a degree. Though it addresses strong and electroweak interactions, the Standard Model does not consistently explain the canonical theory of gravitation, [[general relativity]], in terms of [[quantum field theory]]. The reason for this is, among other things, that quantum field theories of gravity generally break down before reaching the [[Planck scale]]. As a consequence, we have no reliable theory for the very early universe.
* Some physicists consider it to be ''ad hoc'' and inelegant, requiring 19 numerical constants whose values are unrelated and arbitrary.<ref name="BlumhoferHutter1997">
{{cite journal
 |author1=A. Blumhofer |author2=M. Hutter |year = 1997
 |title = Family Structure from Periodic Solutions of an Improved Gap Equation
 |journal = Nuclear Physics
 |volume =  B484
 |issue=1 |pages = 80–96
 |doi = 10.1016/S0550-3213(96)00644-X
 |bibcode = 1997NuPhB.484...80B
 |arxiv = hep-ph/9605393
}}</ref> Although the Standard Model, as it now stands, can explain why neutrinos have masses, the specifics of neutrino mass are still unclear. It is believed that explaining neutrino mass will require an additional 7 or 8 constants, which are also arbitrary parameters.<ref>
{{cite arXiv|eprint=hep-ph/0606054|last1=Strumia|first1=Alessandro|title=Neutrino masses and mixings and...|year=2006}}</ref>
* The Higgs mechanism gives rise to the [[hierarchy problem]] if some new physics (coupled to the Higgs) is present at high energy scales. In these cases, in order for the weak scale to be much smaller than the [[Planck scale]], severe fine tuning of the parameters is required; there are, however, other scenarios that include [[Asymptotic safety in quantum gravity|quantum gravity]] in which such fine tuning can be avoided.<ref>
{{cite journal |title=Agravity |journal=Journal of High Energy Physics|volume=2014 |issue=6 |page = 080 |url = http://inspirehep.net/record/1286134 |arxiv = 1403.4226 |bibcode = 2014JHEP...06..080S |doi=10.1007/JHEP06(2014)080|pmid = 31258400|pmc = 6560704|last1 = Salvio|first1 = Alberto|last2 = Strumia|first2 = Alessandro|year = 2018}}</ref> There are also issues of [[quantum triviality]], which suggests that it may not be possible to create a consistent quantum field theory involving elementary scalar particles.<ref name="TrivPurs">
{{cite journal |author=D.J.E. Callaway |year=1988
|title=Triviality Pursuit: Can Elementary Scalar Particles Exist? |journal=[[Physics Reports]]
|volume=167 |issue=5 |pages=241–320 |doi=10.1016/0370-1573(88)90008-7
|bibcode = 1988PhR...167..241C |author-link=David J E Callaway
}}</ref>
* The model is inconsistent with the emerging [[Lambda-CDM model]] of cosmology. Contentions include the absence of an explanation in the Standard Model of particle physics for the observed amount of [[cold dark matter]] (CDM) and its contributions to [[dark energy]], which are many orders of magnitude too large. It is also difficult to accommodate the observed predominance of matter over antimatter ([[matter]]/[[antimatter]] [[Baryon asymmetry|asymmetry]]). The [[isotropic|isotropy]] and [[Homogeneity (physics)|homogeneity]] of the visible universe over large distances seems to require a mechanism like cosmic [[Inflation (cosmology)|inflation]], which would also constitute an extension of the Standard Model.

Currently, no proposed [[theory of everything]] has been widely accepted or verified.

== See also ==
{{cols|colwidth=27em}}
* [[Yang–Mills theory]]
* [[Fundamental interaction]]:
** [[Quantum electrodynamics]]
** [[Strong interaction]]: [[Color charge]], [[Quantum chromodynamics]], [[Quark model]]
** [[Weak interaction]]: [[Electroweak interaction]], [[Fermi's interaction]], [[Weak hypercharge]], [[Weak isospin]]
* [[Gauge theory]]: [[Introduction to gauge theory]]
* [[Generation (particle physics)|Generation]]
* [[Higgs mechanism]]: [[Higgs boson]], [[Alternatives to the Standard Higgs Model]]
* [[Lagrangian (field theory)|Lagrangian]]
* Open questions: [[CP violation]], [[Neutrino mass]]es, [[QCD matter]], [[Quantum triviality]]
* [[Quantum field theory]]
* Standard Model: [[Mathematical formulation of the Standard Model|Mathematical formulation of]], [[Physics beyond the Standard Model]]
* [[Electron electric dipole moment]]
{{colend}}

== Notes ==
{{NoteFoot}}

== References ==
{{reflist}}

== Further reading ==
* {{cite book
 | last=Oerter
 | first=Robert
 | year=2006
 | title=The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics
 | isbn=978-0-452-28786-0
 | publisher=Plume
}}
* {{cite book
 | last=Schumm
 | first=Bruce A.
 | year=2004
 | title=Deep Down Things: The Breathtaking Beauty of Particle Physics
 | publisher=Johns Hopkins University Press
 | isbn=978-0-8018-7971-5
 | url-access=registration
 | url=https://archive.org/details/deepdownthingsbr00schu
}}
* {{cite web
 |url = https://www.symmetrymagazine.org/standard-model/
 |title = The Standard Model of Particle Physics Interactive Graphic
}}

=== Introductory textbooks ===
* {{cite book
 | author=Robert Mann
 | year=2009
 | title=An Introduction to Particle Physics and the Standard Model
 | publisher=[[CRC Press]]
 | isbn=9780429141225
 | url=https://www.taylorfrancis.com/books/oa-mono/10.1201/9781420083002/introduction-particle-physics-standard-model-robert-mann
}}
* {{cite book
 | author1=W. Greiner
 | author2=B. Müller
 | year=2000
 | title=Gauge Theory of Weak Interactions
 | publisher=Springer
 | isbn=978-3-540-67672-0
}}
* {{cite book
 | author1=J.E. Dodd
 | author2=B.M. Gripaios
 | year=2020
 | title=The Ideas of Particle Physics: An Introduction for Scientists
 | publisher=Cambridge University Press
 | isbn=978-1-108-72740-2}}
* {{cite book
 | author=D.J. Griffiths
 | year=1987
 | title=Introduction to Elementary Particles
 | publisher=John Wiley & Sons
 | isbn=978-0-471-60386-3
}}
* {{cite book
 | author=W. N. Cottingham and D. A. Greenwood
 | year=2023
 | title=An Introduction to the Standard Model of Particle Physics
 | publisher=[[Cambridge University Press]]
 | isbn=9781009401685
 | url=https://www.cambridge.org/core/books/an-introduction-to-the-standard-model-of-particle-physics/61AAC3989C199E9ADE017D899F371B5F
}}

=== Advanced textbooks ===
* {{cite book
 | author1=T.P. Cheng
 | author2=L.F. Li
 | year=2006
 | title=Gauge theory of elementary particle physics
 | publisher=Oxford University Press
 | isbn=978-0-19-851961-4
}} Highlights the [[gauge theory]] aspects of the Standard Model.
* {{cite book
 | author1=J.F. Donoghue
 | author2=E. Golowich
 | author3=B.R. Holstein
 | year=1994
 | title=Dynamics of the Standard Model
 | publisher=Cambridge University Press
 | isbn=978-0-521-47652-2
}} Highlights dynamical and [[phenomenology (particle physics)|phenomenological]] aspects of the Standard Model.
* {{cite book
 | author=Ken J. Barnes
 | year=2010
 | title=Group Theory for the Standard Model of Particle Physics and Beyond
 | publisher=[[Taylor & Francis]]
 | isbn=9780429184550
 | url=https://www.taylorfrancis.com/books/oa-mono/10.1201/9781439895207/group-theory-standard-model-particle-physics-beyond-ken-barnes
}}
* {{cite book |url = https://books.google.com/books?id=QYlX6AL4CtwC |title=Elementary Particle Physics: Foundations of the Standard Model, Volume 2 |isbn=978-3-527-64890-0 |last1=Nagashima|first1=Yorikiyo|year=2013|publisher=Wiley}} 920 pages.
* {{cite book |url= https://books.google.com/books?id=HbdEAgAAQBAJ |title=Quantum Field Theory and the Standard Model |isbn=978-1-107-03473-0|last=Schwartz|first=Matthew D.|year=2014|publisher=Cambridge University}} 952 pages.
* {{cite book |url= https://www.taylorfrancis.com/books/oa-mono/10.1201/b22175/standard-model-beyond-paul-langacker |title=The Standard Model and Beyond |isbn=978-1-4200-7907-4|last=Langacker|first=Paul|year=2009|publisher=[[CRC Press]]}} 670 pages. Highlights [[finite group|group-theoretical]] aspects of the Standard Model.

=== Journal articles ===
* {{cite journal
 |author1=E.S. Abers
 |author2=B.W. Lee
 |year=1973
 |title=Gauge theories
 |journal=[[Physics Reports]]
 |volume=9 |issue=1
 |pages=1–141
 |doi=10.1016/0370-1573(73)90027-6
 |bibcode = 1973PhR.....9....1A
}}
* {{cite journal
 |author=M. Baak |display-authors=etal
 |year=2012
 |title=The Electroweak Fit of the Standard Model after the Discovery of a New Boson at the LHC
 |journal=[[The European Physical Journal C]]
 |volume=72 |issue=11 |pages=2205
 |arxiv=1209.2716
 |doi=10.1140/epjc/s10052-012-2205-9
 |bibcode = 2012EPJC...72.2205B
 |s2cid=15052448
}}
* {{cite journal
 |author=Y. Hayato |display-authors=etal
 |year=1999
 |title=Search for Proton Decay through ''p'' → ''νK''<sup>+</sup> in a Large Water Cherenkov Detector
 |journal=[[Physical Review Letters]]
 |volume=83 |issue=8 |pages=1529–1533
 |arxiv = hep-ex/9904020
 |bibcode=1999PhRvL..83.1529H
 |doi=10.1103/PhysRevLett.83.1529
 |s2cid = 118326409}}
* {{cite arXiv
 |author=S.F. Novaes
 |year=2000
 |title=Standard Model: An Introduction
 |eprint=hep-ph/0001283
}}
* {{cite arXiv
 |author=D.P. Roy
 |year=1999
 |title=Basic Constituents of Matter and their Interactions – A Progress Report
 |eprint=hep-ph/9912523
}}
* {{cite journal
 |author=F. Wilczek
 |year=2004
 |title=The Universe Is A Strange Place
 |doi=10.1016/j.nuclphysbps.2004.08.001
 |journal=Nuclear Physics B: Proceedings Supplements
 |volume=134
 |page=3
 |arxiv=astro-ph/0401347
 |bibcode = 2004NuPhS.134....3W
 |s2cid=28234516
}}

== External links ==
{{Commons}}
{{Wikiquote}}
* "[http://omegataupodcast.net/93-the-standard-model-of-particle-physics The Standard Model explained in Detail by CERN's John Ellis]" omega tau podcast.
* [http://home.web.cern.ch/about/physics/standard-model The Standard Model] on the CERN website explains how the basic building blocks of matter interact, governed by four fundamental forces.
* [https://av.tib.eu/series/56 Particle Physics: Standard Model], [[Leonard Susskind]] lectures (2010).

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