Standard Model#Tests and predictions

{{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 extended the concept of gauge theory for abelian groups, e.g. quantum electrodynamics, to nonabelian groups to provide an explanation for strong interactions.{{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 }} In 1957, Chien-Shiung Wu demonstrated parity was not conserved in the weak interaction.{{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}}

In 1961, Sheldon Glashow combined the electromagnetic and weak interactions.

{{cite journal

|author=S.L. Glashow

|year=1961

|title=Partial-symmetries of weak interactions

|journal=Nuclear Physics

|volume=22 |issue=4 |pages=579–588

|bibcode=1961NucPh..22..579G

|doi=10.1016/0029-5582(61)90469-2

}} In 1964, Murray Gell-Mann and George Zweig introduced quarks and that same year Oscar W. Greenberg implicitly introduced color charge of quarks.{{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}} In 1967 Steven Weinberg

{{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

}} and Abdus Salam

{{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

}} incorporated the Higgs mechanism

{{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}}

{{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}}

{{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}} 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.{{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}} 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.{{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}}{{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}} In 1977, a team led by Leon Lederman at Fermilab discovered the bottom quark.{{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}}

The Higgs mechanism is believed to give rise to 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,

{{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

}}

{{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

}}

{{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}}{{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

}} the electroweak theory became widely accepted and Glashow, Salam, and Weinberg shared the 1979 Nobel Prize in Physics for discovering it. The W^± and Z⁰ bosons were discovered experimentally in 1983; and the ratio of their masses was found to be as the Standard Model predicted.{{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}}

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

{{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}}

{{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

}} (a development that made QCD the main focus of theoretical research)Dean Rickles (2014). A Brief History of String Theory: From Dual Models to M-Theory. Springer, p. 11 n. 22. and experiments confirmed that the hadrons were composed of fractionally charged quarks.

{{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

}}

{{cite journal

|last1=Augustin |first1=J.

|year=1974

|title=Discovery of a Narrow Resonance in e⁺e⁻ 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

}}

The term "Standard Model" was introduced by Abraham Pais and Sam Treiman in 1975,

{{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=}} with reference to the electroweak theory with four quarks.{{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 }} Steven Weinberg has since claimed priority, explaining that he chose the term Standard Model out of a sense of modestyA 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.{{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}}{{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}}{{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.{{cite web| url = https://www.aps.org/publications/apsnews/201902/weinberg.cfm| title = Q&A with Standard Bearer Steven Weinberg}}

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}}

The Standard Model includes 12 elementary particles of spin {{1/2}}, known as fermions.{{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}} Fermions respect the Pauli exclusion principle, meaning that two identical fermions cannot simultaneously occupy the same quantum state in the same atom.{{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 }} Each fermion has a corresponding antiparticle, which are particles that have corresponding properties with the exception of opposite charges.{{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}} 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.{{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 |publisher=CERN}} As first-generation particles do not decay, they comprise all of ordinary (baryonic) 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-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 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).{{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}} 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 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 charged leptons carry an electric charge of −1 e, while the three neutrinos carry zero electric charge. Thus, the neutrinos' motions are influenced by only the weak interaction and gravity, making them difficult to observe.

[[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_B 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 '|', 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.{{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/ }}]]

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 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.{{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}} 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.

• Electromagnetism: Photons 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 Interactions: Gluons 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.{{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}}}} As gluons have an effective color charge, they can also interact amongst themselves.
• Weak Interactions: The W and Z bosons gauge bosons mediate the weak interactions between all fermions, being responsible for 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 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.{{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}} This is due to the incompatibility of quantum mechanics and 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.{{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}}

The Feynman diagram calculations, which are 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 the particles described by the Standard Model are summarized by the diagrams on the right of this section.

{{Main|Higgs boson}}

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, the massive spin-zero particle, was proposed as the Higgs boson, and is a key building block in the Standard Model.

{{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

}} 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 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 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}};

{{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

}} 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.

{{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

}}

On 4 July 2012, two of the experiments at the LHC (ATLAS and 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".

{{cite web

|date=4 July 2012

|title=Observation of a New Particle with a Mass of 125 GeV

|url=http://cms.web.cern.ch/news/observation-new-particle-mass-125-gev

|publisher=CERN

|access-date=2012-07-05

}}

{{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

}} On 13 March 2013, it was confirmed to be the searched-for Higgs boson.

{{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

}}

{{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

}}

{{Main|Mathematical formulation of the Standard Model}}

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 is described in terms of a dynamical field that pervades space-time.{{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 }}

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 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 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.

{{Main|Quantum chromodynamics}}

The quantum chromodynamics (QCD) sector defines the interactions between quarks and gluons, which is a Yang–Mills gauge theory with SU(3) symmetry, generated by $T^a\; =\; \backslash lambda^a/2$. 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

$$\backslash mathcal\{L\}\_\backslash text\{QCD\}\; =\; \backslash overline\{\backslash psi\}\; i\backslash gamma^\backslash mu\; D\_\{\backslash mu\}\; \backslash psi\; -\; \backslash frac\{1\}\{4\}\; G^a\_\{\backslash mu\backslash nu\}\; G^\{\backslash mu\backslash nu\}\_a,$$

where $\backslash psi$ 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.) is implied.

The gauge covariant derivative of QCD is defined by $D\_\{\backslash mu\}\; \backslash equiv\; \backslash partial\_\backslash mu\; -\; i\; g\_\backslash text\{s\}\backslash frac\{1\}\{2\}\backslash lambda^a\; G\_\backslash mu^a$, where

• {{math|γ{{isup|μ}}}} are the Dirac matrices,
• {{math|G{{su|lh=0.9|b=μ|p=a}}}} is the 8-component ($a\; =\; 1,\; 2,\; \backslash dots,\; 8$) 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_s}} is the strong coupling constant.

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

{{Main|Electroweak interaction}}

The electroweak sector is a Yang–Mills gauge theory with the symmetry group {{nowrap|U(1) × SU(2)_L}},

$$\backslash mathcal\{L\}\_\backslash text\{EW\}\; =\; \backslash overline\{Q\}\_\{\backslash text\{L\}j\}\; i\backslash gamma^\backslash mu\; D\_\{\backslash mu\}\; Q\_\{\backslash text\{L\}j\}\; +\; \backslash overline\{u\}\_\{\backslash text\{R\}j\}\; i\backslash gamma^\backslash mu\; D\_\{\backslash mu\}\; u\_\{\backslash text\{R\}j\}\; +\; \backslash overline\{d\}\_\{\backslash text\{R\}j\}\; i\backslash gamma^\backslash mu\; D\_\{\backslash mu\}\; d\_\{\backslash text\{R\}j\}\; +\; \backslash overline\{\backslash ell\}\_\{\backslash text\{L\}j\}\; i\backslash gamma^\backslash mu\; D\_\{\backslash mu\}\; \backslash ell\_\{\backslash text\{L\}j\}\; +\; \backslash overline\{e\}\_\{\backslash text\{R\}j\}\; i\backslash gamma^\backslash mu\; D\_\{\backslash mu\}\; e\_\{\backslash text\{R\}j\}\; -\; \backslash tfrac\{1\}\{4\}\; W\_a^\{\backslash mu\backslash nu\}\; W\_\{\backslash mu\backslash nu\}^a\; -\; \backslash tfrac\{1\}\{4\}\; B^\{\backslash mu\backslash nu\}\; B\_\{\backslash mu\backslash nu\},$$

where the subscript $j$ sums over the three generations of fermions; $Q\_\backslash text\{L\},\; u\_\backslash text\{R\}$, and $d\_\backslash text\{R\}$ are the left-handed doublet, right-handed singlet up type, and right handed singlet down type quark fields; and $\backslash ell\_\backslash text\{L\}$ and $e\_\backslash text\{R\}$ are the left-handed doublet and right-handed singlet lepton fields.

The electroweak gauge covariant derivative is defined as $D\_\backslash mu\; \backslash equiv\; \backslash partial\_\backslash mu\; -\; ig\text{'}\; \backslash tfrac12\; Y\_\backslash text\{W\}\; B\_\backslash mu\; -\; ig\; \backslash tfrac\{1\}\{2\}\; \backslash vec\backslash tau\_\backslash text\{L\}\; \backslash vec\; W\_\backslash mu$, where

• {{mvar|B_μ}} is the U(1) gauge field,
• {{math|Y_W}} is the weak hypercharge – the generator of the U(1) group,
• {{math|{{vec|W}}_μ}} is the 3-component SU(2) gauge field,
• {{math|{{overset|lh=0.5|→|τ}}_L}} 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,
• $W^\{a\backslash mu\backslash nu\}$ ($a\; =\; 1,\; 2,\; 3$) and $B^\{\backslash mu\backslash nu\}$ are the field strength tensors 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 $m\backslash overline\backslash psi\backslash psi$ do not respect {{nowrap|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 the gauge boson masses, and the fermion masses result from Yukawa-type interactions with the Higgs field.

{{Main|Higgs mechanism}}

In the Standard Model, the Higgs field is an SU(2){{sub|L}} doublet of complex scalar fields with four degrees of freedom:

\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 the superscripts + and 0 indicate the electric charge $Q$ of the components. The weak hypercharge $Y\_\backslash text\{W\}$ of both components is 1. Before symmetry breaking, the Higgs Lagrangian is

$$\backslash mathcal\{L\}\_\backslash text\{H\}\; =\; \backslash left(D\_\{\backslash mu\}\backslash varphi\backslash right)^\{\backslash dagger\}\; \backslash left(D^\{\backslash mu\}\backslash varphi\; \backslash right)\; -\; V(\backslash varphi),$$

where $D\_\{\backslash mu\}$ is the electroweak gauge covariant derivative defined above and $V(\backslash varphi)$ 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 $W^\{a\}\_\{\backslash mu\}$ and $B\_\{\backslash mu\}$ and the scalar field $\backslash varphi$. The scalar potential is given by

$$V(\backslash varphi)\; =\; -\backslash mu^2\backslash varphi^\{\backslash dagger\}\backslash varphi\; +\; \backslash lambda\; \backslash left(\; \backslash varphi^\{\backslash dagger\}\backslash varphi\; \backslash right)^2,$$

where $\backslash mu^2>0$, so that $\backslash varphi$ acquires a non-zero Vacuum expectation value, which generates masses for the Electroweak gauge fields (the Higgs mechanism), and $\backslash lambda>0$, so that the potential is bounded from below. The quartic term describes self-interactions of the scalar field $\backslash varphi$.

The minimum of the potential is degenerate with an infinite number of equivalent ground state solutions, which occurs when $\backslash varphi^\{\backslash dagger\}\backslash varphi\; =\; \backslash tfrac\{\backslash mu^2\}\{2\backslash lambda\}$. It is possible to perform a gauge transformation on $\backslash varphi$ such that the ground state is transformed to a basis where $\backslash varphi\_1\; =\; \backslash varphi\_2\; =\; \backslash varphi\_4\; =\; 0$ and $\backslash varphi\_3\; =\; \backslash tfrac\{\backslash mu\}\{\backslash sqrt\{\backslash lambda\}\}\; \backslash equiv\; v$. This breaks the symmetry of the ground state. The expectation value of $\backslash varphi$ now becomes

$$\backslash langle\; \backslash varphi\; \backslash rangle\; =\; \backslash frac\{1\}\{\backslash sqrt\{2\}\}\; \backslash begin\{pmatrix\}\; 0\; \backslash \backslash \; v\; \backslash end\{pmatrix\},$$

where $v$ 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 $m\_\backslash text\{W\}=\backslash frac\{1\}\{2\}gv$ and $m\_\backslash text\{Z\}=\backslash frac\{1\}\{2\}\backslash sqrt\{g^2+g\text{'}^2\}v$, which can be viewed as predictions of the theory. The photon remains massless. The mass of the Higgs boson is $m\_\backslash text\{H\}=\backslash sqrt\{2\backslash mu^2\}=\backslash sqrt\{2\backslash lambda\}v$. Since $\backslash mu$ and $\backslash lambda$ are free parameters, the Higgs's mass could not be predicted beforehand and had to be determined experimentally.

The Yukawa interaction terms are:

$$\backslash mathcal\{L\}\_\backslash text\{Yukawa\}\; =\; (Y\_\backslash text\{u\})\_\{mn\}(\backslash bar\{Q\}\_\backslash text\{L\})\_m\; \backslash tilde\{\backslash varphi\}(u\_\backslash text\{R\})\_n\; +\; (Y\_\backslash text\{d\})\_\{mn\}(\backslash bar\{Q\}\_\backslash text\{L\})\_m\; \backslash varphi(d\_\backslash text\{R\})\_n\; +\; (Y\_\backslash text\{e\})\_\{mn\}(\backslash bar\{\backslash ell\}\_\backslash text\{L\})\_m\; \{\backslash varphi\}(e\_\backslash text\{R\})\_n\; +\; \backslash mathrm\{h.c.\}$$

where $Y\_\backslash text\{u\}$, $Y\_\backslash text\{d\}$, and $Y\_\backslash text\{e\}$ 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 $Q\_\backslash text\{L\}$ and $\backslash ell\_\backslash text\{L\}$ are left-handed quark and lepton doublets. Likewise, $u\_\backslash text\{R\},\; d\_\backslash text\{R\}$ and $e\_\backslash text\{R\}$ are right-handed up-type quark, down-type quark, and lepton singlets. Finally $\backslash varphi$ is the Higgs doublet and $\backslash tilde\{\backslash varphi\}\; =\; i\backslash tau\_2\backslash varphi^\{*\}$ 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.

{{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 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.{{Cite web|url=https://home.cern/science/physics/standard-model|title=The Standard Model|website=CERN|date=15 December 2023 }}

{{Unreferenced section|date=June 2021}}

{{See also|Quantum gravity|Gravity}}

File:Fundamental Interactions.png

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.{{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 }}{{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}} 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.{{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 }}

{{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.{{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}} 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.

{{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 interactions. 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 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 the weak and electromagnetic interactions become united into a single electroweak interaction at high energies.

{{See also|Strong interaction|Nuclear force|Quantum chromodynamics}}

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 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.

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.

{{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 }}

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.

{{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}}

{{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 constants have the values that we measure?
• Why are there three 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 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.

{{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

}} 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.

{{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

}} 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 symmetric extension of the Standard Model

{{cite journal

|author=P. Minkowski

|year=1977

|title=μ → e γ at a Rate of One Out of 10⁹ 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

}}

{{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

}} and in certain grand unified theories.

{{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

}} As long as new physics appears below or around 10¹⁴ 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.

{{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

}} 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.

{{cite arXiv|eprint=hep-ph/0606054|last1=Strumia|first1=Alessandro|title=Neutrino masses and mixings and...|year=2006}}

• 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 quantum gravity in which such fine tuning can be avoided.

{{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}} 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.

{{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

}}

• 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 asymmetry). The isotropy and homogeneity of the visible universe over large distances seems to require a mechanism like cosmic inflation, which would also constitute an extension of the Standard Model.

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

{{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
• Higgs mechanism: Higgs boson, Alternatives to the Standard Higgs Model
• Lagrangian
• Open questions: CP violation, Neutrino masses, QCD matter, Quantum triviality
• Quantum field theory
• Standard Model: Mathematical formulation of, Physics beyond the Standard Model
• Electron electric dipole moment

{{colend}}

{{NoteFoot}}

{{reflist}}

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}}

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}}

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• {{cite book

| author1=J.F. Donoghue

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}} Highlights dynamical and phenomenological aspects of the Standard Model.

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| author=Ken J. Barnes

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}}

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|year=2000

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}}

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|year=1999

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}}

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|page=3

|arxiv=astro-ph/0401347

|bibcode = 2004NuPhS.134....3W

|s2cid=28234516

}}

{{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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