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{{about|the Standard Model of particle physics|other uses|Standard model (disambiguation)}}
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{{hatnote|This article is a non-mathematical general overview of the Standard Model. For a mathematical description, see the article [[Standard Model (mathematical formulation)]].}}
 
[[Image:Standard Model of Elementary Particles.svg|thumb|375px|The Standard Model of [[elementary particle]]s, with the three [[Generation (particle physics)|generations of matter]], [[gauge boson]]s in the fourth column, and the [[Higgs boson]] in the fifth.]]
{{Standard model of particle physics}}
 
The '''Standard Model''' of [[particle physics]] is a theory concerning the [[Electromagnetism|electromagnetic]], [[Weak interaction|weak]], and [[Strong interaction|strong]] nuclear interactions, which mediate the dynamics of the known subatomic [[particle]]s.  It was developed throughout the latter half of the 20th century, as a collaborative effort of scientists around the world.<ref>
{{cite book
|author=R. Oerter
|year=2006
|title=The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics
|page=2
|publisher=[[Penguin Group]]
|edition=Kindle
|isbn=0-13-236678-9
}}</ref>  The current formulation was finalized in the mid-1970s upon experimental confirmation of the existence of [[quark]]s.  Since then, discoveries of the [[top quark]] (1995), the [[tau neutrino]] (2000), and more recently the [[Higgs boson]] (2013), have given further credence to the Standard Model.  Because of its success in explaining a wide variety of experimental results, the Standard Model is sometimes regarded as a "theory of almost everything". Mathematically, the standard model is a quantized [[Yang–Mills theory]].
 
The Standard Model falls short of being a [[theory of everything|complete theory of fundamental interactions]] because it makes certain simplifying [[axiom|assumptions]]. It does not incorporate the full theory of [[gravitation]]<ref name = DarkMatter> Sean Carroll, Ph.D., Cal Tech, 2007, The Teaching Company, ''Dark Matter, Dark Energy: The Dark Side of the Universe'', Guidebook Part 2 page 59, Accessed Oct. 7, 2013, "...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..."</ref> as described by [[general relativity]], or predict the accelerating expansion of the universe (as possibly described by [[dark energy]]). The theory does not contain any viable [[dark matter]] particle that possesses all of the required properties deduced from observational [[cosmology]]. It also does not correctly account for [[neutrino oscillation]]s (and their non-zero masses). Although the Standard Model is believed to be theoretically self-consistent<ref>In fact, 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 are all self-consistent. For a further discussion see e.g. Chapter 25 of {{cite book
|author=R. Mann
|year=2010
|title=An Introduction to Particle Physics and the Standard Model
|publisher=[[CRC Press]]
|isbn=978-1-4200-8298-2
}}</ref> and has demonstrated huge and continued successes in providing experimental predictions, it does leave some [[beyond the standard model|phenomena unexplained]].
 
The development of the Standard Model was driven by [[Theoretical physics|theoretical]] and [[Experimental physics|experimental]] particle physicists alike. For theorists, the Standard Model is a paradigm of a [[quantum field theory]], which exhibits a wide range of physics including [[spontaneous symmetry breaking]], [[Anomaly (physics)|anomalies]], non-perturbative behavior, etc. It is used as a basis for building more [[Physics beyond the Standard Model|exotic models]] that incorporate [[hypothetical particle]]s, [[extra dimensions (disambiguation)|extra dimensions]], and elaborate symmetries (such as [[supersymmetry]]) in an attempt to explain experimental results at variance with the Standard Model, such as the existence of dark matter and neutrino oscillations.
 
==Historical background==
The first step towards the Standard Model was [[Sheldon Lee Glashow|Sheldon Glashow]]'s discovery in 1961 of a way to combine 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 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
}}</ref> and [[Abdus Salam]]<ref>
{{cite conference
|author=A. Salam
|editor=N. Svartholm
|year=1968
|booktitle=Elementary Particle Physics: Relativistic Groups and Analyticity
|pages=367
|conference=[[Nobel Symposium|Eighth Nobel Symposium]]
|publisher=[[Almquvist and Wiksell]]
|location=Stockholm
}}</ref> incorporated the [[Higgs mechanism]]<ref name="Englert1964">
{{cite journal
|author=F. Englert, 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
}}</ref><ref name="Peter W. Higgs 1964 508-509" /><ref name="G.S. Guralnik, C.R. Hagen, T.W.B. Kibble 1964 585–587">
{{cite journal
|author=G.S. Guralnik, C.R. Hagen, 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
}}</ref> into Glashow's [[electroweak theory]], giving it its modern form.
 
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''et al.''
|coauthors=<!-- -->
|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 ''et al.''
|coauthors=<!-- -->
|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 ''et al.''
|coauthors=<!-- -->
|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
}}</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]]
|accessdate=8 May 2008
}}</ref> the electroweak theory became widely accepted and Glashow, Salam, and Weinberg shared the 1979 [[Nobel Prize in Physics]] for discovering it. The W and Z [[boson]]s were discovered experimentally in 1981, and their masses were found to be as the Standard Model predicted.
 
The theory of the [[strong interaction]], to which many contributed, acquired its modern form around 1973–74, when experiments confirmed that the [[hadron]]s were composed of fractionally charged quarks.
 
==Overview==
At present, [[matter]] and [[energy]] are best understood in terms of the [[kinematics]] and [[fundamental interaction|interactions]] of elementary particles. To date, physics has reduced the [[scientific law|laws]] governing the behavior and interaction of all known forms of matter and energy to a small set of fundamental laws and theories. A major goal of physics is to find the "common ground" that would unite all of these theories into one integrated [[theory of everything]], of which all the other known laws would be special cases, and from which the behavior of all matter and energy could be derived (at least in principle).<ref>"Details can be worked out if the situation is simple enough for us to  make an approximation, which is almost never, but often we can understand more or less what is happening." from ''[[The Feynman Lectures on Physics]]'', Vol 1. pp. 2–7</ref>
 
==Particle content==
The Standard Model has 61 elementary particles.<ref>
{{cite book
|author=S. Braibant, G. Giacomelli, M. Spurio
|year=2009
|title=Particles and Fundamental Interactions: An Introduction to Particle Physics
|url=http://books.google.com/?id=0Pp-f0G9_9sC&pg=PA314&lpg=PA314&dq=61+fundamental+particles#v=onepage&q=61%20fundamental%20particles&f=false
|pages=313–314
|publisher=[[Springer Science+Business Media|Springer]]
|isbn=978-94-007-2463-1
}}</ref>
 
[[File:Bosons-Hadrons-Fermions-RGB-png2.png|thumb|540px|Particle classification. (Note that [[meson]]s are [[boson]]s and [[hadron]]s; and [[baryon]]s are hadrons and [[fermion]]s).]]
 
{| class="wikitable" style="text-align:left;"
|+ Elementary Particles
|-
|
! scope="col" | [[Generation (particle physics)|Types]]
! scope="col" | [[Generation (particle physics)|Generations]]
! scope="col" | [[Antiparticle]]
! scope="col" | [[Color charge|Colors]]
! scope="col" | Total
|-
! scope="row" | [[Quark]]s
|2
|3
|Pair
|3
|36
|-
! scope="row" | [[Lepton]]s
|2
|3
|Pair
|None
|12
|-
! scope="row" | [[Gluon]]s
|1
|1
|Own
|[[Gluon#Eight_gluon_colors|8]]
|8
|-
! scope="row" | [[W and Z bosons|W]]
|1
|1
|Pair
|None
|2
|-
! scope="row" | [[W and Z bosons|Z]]
|1
|1
|Own
|None
|1
|-
! scope="row" | [[Photon]]
|1
|1
|Own
|None
|1
|-
! scope="row" | [[Higgs boson|Higgs]]
|1
|1
|Own
|None
|1
|-
!colspan="5" !scope="row"| Total
|'''61'''
|}
 
===Fermions===
 
[[File:Standard Model.svg|300px|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-½]] known as [[fermion]]s. According to the [[spin-statistics theorem]], fermions respect the [[Pauli exclusion principle]]. Each fermion has a corresponding [[antiparticle]].
 
The fermions of the Standard Model are classified according to how they interact (or equivalently, by what [[charge (physics)|charges]] they carry). There are six [[quark]]s ([[up quark|up]], [[down quark|down]], [[charm quark|charm]], [[strange quark|strange]], [[top quark|top]], [[bottom quark|bottom]]), and six [[lepton]]s ([[electron]], [[electron neutrino]], [[muon]], [[muon neutrino]], [[tau (particle)|tau]], [[tau neutrino]]). Pairs from each classification are grouped together to form a [[Generation (particle physics)|generation]], with corresponding particles exhibiting similar physical behavior (see table).
 
The defining property of the quarks is that they carry [[color charge]], and hence, interact via the [[strong interaction]]. A phenomenon called [[color confinement]] results in quarks being perpetually (or at least since very soon after the start of the [[Big Bang]]) bound to one another, forming color-neutral composite particles ([[hadron]]s) containing either a quark and an antiquark ([[meson]]s) or three quarks ([[baryon]]s). The familiar [[proton]] and the [[neutron]] are the two baryons having the smallest mass. Quarks also carry [[electric charge]] and [[weak isospin]]. Hence they interact with other fermions both [[electromagnetism|electromagnetically]] and via the [[weak interaction]].
 
The remaining six fermions do not carry colour charge and are called leptons. The three [[neutrino]]s do not carry electric charge either, so their motion is directly influenced only by the [[weak interaction|weak nuclear force]], which makes them notoriously difficult to detect. However, by virtue of carrying an electric charge, the electron, muon, and tau all interact electromagnetically.
 
Each member of a generation has greater mass than the corresponding particles of lower generations. The first generation charged particles do not decay; hence all ordinary (baryonic) matter is made of such particles. Specifically, all atoms consist of electrons orbiting [[atomic nucleus|atomic nuclei]] ultimately constituted of up and down quarks. Second and third generations charged particles, on the other hand, decay with very short half lives, and are observed only in very high-energy environments. Neutrinos of all generations also do not decay, and pervade the universe, but rarely interact with baryonic matter.
 
===Gauge bosons===
[[Image:Elementary particle interactions.svg|400px|thumb|right|Summary of interactions between particles described by the Standard Model.]]
 
[[Image:Standard Model Feynman Diagram Vertices.png|400px|thumb|right|The above interactions form the basis of the standard model. Feynman diagrams in the standard model are built from these vertices. Modifications involving Higgs boson interactions and neutrino oscillations are omitted. The charge of the W bosons are dictated by the fermions they interact with; the conjugate of each listed vertex (i.e. reversing the direction of arrows) is also allowed.]]
 
In the Standard Model, [[gauge boson]]s are defined as [[force carrier]]s that mediate the strong, weak, and electromagnetic [[fundamental interaction]]s.
 
Interactions in physics are the ways that particles influence other particles. At a [[Macroscopic scale|macroscopic level]], electromagnetism allows particles to interact with one another via [[electric]] and [[magnetic field|magnetic]] fields, and gravitation allows particles with mass to attract one another in accordance with Einstein's theory of [[general relativity]]. The Standard Model explains such forces as resulting from matter particles [[Static forces and virtual-particle exchange|exchanging other particles]], known as ''force mediating particles'' (strictly speaking, this is only so if interpreting literally what is actually an ''approximation method'' known as [[Perturbation theory (quantum mechanics)|perturbation theory]]){{Citation needed|date=August 2010}}. When a force-mediating particle is exchanged, at a macroscopic level the effect is equivalent to a force influencing both of them, and the particle is therefore said to have ''mediated'' (i.e., been the agent of) that force. The [[Feynman diagram]] calculations, which are a graphical representation of the 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 gauge bosons of the Standard Model all have [[spin (physics)|spin]] (as do matter particles). The value of the spin is 1, making them [[boson]]s. As a result, they do not follow the [[Pauli exclusion principle]] that constrains [[fermion]]s: thus bosons (e.g. photons) do not have a theoretical limit on their spatial density (number per volume). The different types of gauge bosons are described below.
 
*[[Photon]]s mediate the electromagnetic force between electrically charged particles. The photon is massless and is well-described by the theory of [[quantum electrodynamics]].
 
*The [[W and Z bosons|{{SubatomicParticle|W boson+}}, {{SubatomicParticle|W boson-}}, and {{SubatomicParticle|Z boson}}]] gauge bosons mediate the [[weak interaction]]s between particles of different flavors (all [[quark]]s and leptons). They are massive, with the {{SubatomicParticle|Z boson}} being more massive than the {{SubatomicParticle|W boson+-}}.  The weak interactions involving the {{SubatomicParticle|W boson+-}} exclusively act on ''left-handed'' particles and ''right-handed'' antiparticles only. Furthermore, 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 antiparticles. These three gauge bosons along with the photons are grouped together, as collectively mediating the [[electroweak]] interaction.
 
*The eight [[gluon]]s mediate the [[strong interaction]]s between [[color charge]]d particles (the quarks). Gluons are massless. The eightfold multiplicity of gluons is labeled by a combination of color and anticolor charge (e.g. red–antigreen).<ref group="nb">Technically, there are nine such color–anticolor combinations. However, there is one color-symmetric combination that can be constructed out of a linear superposition of the nine combinations, reducing the count to eight.</ref> Because the gluons have an effective color charge, they can also interact among themselves. The gluons and their interactions are described by the theory of [[quantum chromodynamics]].
 
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 [[Robert Brout]], [[François Englert]], [[Peter Higgs]], [[Gerald Guralnik]], [[C. R. Hagen]], and [[Tom W. B. Kibble|Tom Kibble]] in 1964 (see [[1964 PRL symmetry breaking papers]]) and is a key building block in the Standard Model.<ref name="Englert1964" /><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
}}</ref><ref name="G.S. Guralnik, C.R. Hagen, T.W.B. Kibble 1964 585–587"/><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
}}</ref> It has no intrinsic [[spin (physics)|spin]], and for that reason is classified as a [[boson]] (like the gauge bosons, which have [[integer]] spin).
 
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 would explain 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 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
|author=B.W. Lee, C. Quigg, 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 7 to 8 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]]
|accessdate=2010-05-04
}}</ref>
 
On 4 July 2012, the two main experiments at the LHC ([[ATLAS experiment|ATLAS]] and [[Compact Muon Solenoid|CMS]]) both reported independently that they found a new particle with a mass of about {{val|125|ul=GeV/c2}} (about 133 proton masses, on the order of 10<sup>−25</sup>&nbsp;kg), which is "consistent with the Higgs boson." Although it has several properties similar to the predicted "simplest" Higgs,<ref>
{{cite web
|author=M. Strassler
|date=10 July 2012
|title=Higgs Discovery: Is it a Higgs?
|url=http://profmattstrassler.com/articles-and-posts/the-higgs-particle/the-discovery-of-the-higgs/higgs-discovery-is-it-a-higgs
|accessdate=2013-08-06
}}</ref> they acknowledged that further work would be needed to conclude that it is indeed the Higgs boson, and exactly which version of the Standard Model Higgs is best supported if confirmed.<ref name=cern1207>
{{cite news
|date=4 July 2012
|title=CERN experiments observe particle consistent with long-sought Higgs boson
|url=http://press.web.cern.ch/press/PressReleases/Releases2012/PR17.12E.html
|publisher=[[CERN]]
|accessdate=2012-07-04
}}</ref><ref>
{{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]]
|accessdate=2012-07-05
}}</ref><ref>
{{cite web
|date=1 January 2006
|title=ATLAS Experiment
|url=http://www.atlas.ch/news/2012/latest-results-from-higgs-search.html
|publisher=[[ATLAS experiment|ATLAS]]
|accessdate=2012-07-05
}}</ref><ref>
{{cite web
|date=4 July 2012
|url=http://www.youtube.com/watch?v=vXZ-yzwlwMw
|title=Confirmed: CERN discovers new particle likely to be the Higgs boson
|work=[[YouTube]]
|publisher=[[Russia Today]]
|accessdate=2013-08-06
}}</ref><ref name="NYT-20120704">
{{cite news
|author=D. Overbye
|date=4 July 2012
|title=A New Particle Could Be Physics' Holy Grail
|url=http://www.nytimes.com/2012/07/05/science/cern-physicists-may-have-discovered-higgs-boson-particle.html
|newspaper=[[New York Times]]
|accessdate=2012-07-04
}}</ref>
 
On 14 March 2013 the Higgs Boson was tentatively confirmed to exist.<ref>
{{cite web
|date=14 March 2013
|title=New results indicate that new particle is a Higgs boson
|url=http://home.web.cern.ch/about/updates/2013/03/new-results-indicate-new-particle-higgs-boson
|publisher=[[CERN]]
|accessdate=2013-08-06
}}</ref>
 
==Theoretical aspects==
{{main|Standard Model (mathematical formulation)}}
 
===Construction of the Standard Model Lagrangian===
{| class="wikitable collapsible collapsed"
!colspan="5"|Parameters of the Standard Model
|-
! Symbol
! Description
! Renormalization<br /> scheme (point)
! Value
|-
|''m''<sub>e</sub>
|Electron mass
|
|511 keV
|-
|''m''<sub>μ</sub>
|Muon mass
|
|105.7 MeV
|-
|''m''<sub>τ</sub>
|Tau mass
|
|1.78 GeV
|-
|''m''<sub>u</sub>
|Up quark mass
|''μ''<sub>[[MSbar scheme|{{overline|MS}}]]</sub> = 2 GeV
|1.9 MeV
|-
|''m''<sub>d</sub>
|Down quark mass
|''μ''<sub>{{overline|MS}}</sub> = 2 GeV
|4.4 MeV
|-
|''m''<sub>s</sub>
|Strange quark mass
|''μ''<sub>{{overline|MS}}</sub> = 2 GeV
|87 MeV
|-
|''m''<sub>c</sub>
|Charm quark mass
|''μ''<sub>{{overline|MS}}</sub> = ''m''<sub>c</sub>
|1.32 GeV
|-
|''m''<sub>b</sub>
|Bottom quark mass
|''μ''<sub>{{overline|MS}}</sub> = ''m''<sub>b</sub>
|4.24 GeV
|-
|''m''<sub>t</sub>
|Top quark mass
|[[On-shell scheme]]
|172.7 GeV
|-
|''θ''<sub>12</sub>
|[[Cabibbo–Kobayashi–Maskawa matrix|CKM 12-mixing angle]]
|
|13.1°
|-
|''θ''<sub>23</sub>
|CKM 23-mixing angle
|
|2.4°
|-
|''θ''<sub>13</sub>
|CKM 13-mixing angle
|
|0.2°
|-
|''δ''
|CKM [[CP violation|CP-violating]] Phase
|
|0.995
|-
|''g''<sub>1</sub> or ''g'''
|U(1) gauge coupling
|''μ''<sub>{{overline|MS}}</sub> = ''m''<sub>Z</sub>
|0.357
|-
|''g''<sub>2</sub> or ''g''
|SU(2) gauge coupling
|''μ''<sub>{{overline|MS}}</sub> = ''m''<sub>Z</sub>
|0.652
|-
|''g''<sub>3</sub> or ''g''<sub>s</sub>
|SU(3) gauge coupling
|''μ''<sub>{{overline|MS}}</sub> = ''m''<sub>Z</sub>
|1.221
|-
|''θ''<sub>QCD</sub>
|QCD [[vacuum angle]]
|
|~0
|-
|''v''
|Higgs vacuum expectation value
|
|246 GeV
|-
|''m''<sub>H</sub>
|Higgs mass
|
|~ 125 GeV (tentative)
|}
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 (physics)|field]] that pervades [[space-time]].  The construction of the Standard Model proceeds following the modern method of constructing most field theories: by first postulating a set of symmetries of the system, and then by writing down the most general [[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 depend on 19 parameters, whose numerical values are established by experiment.  The parameters are summarized in the table above (note: with the Higgs mass is at 125 GeV, the Higgs self-coupling strength ''λ'' ~ 1/8).
 
====Quantum chromodynamics sector====
{{Main|Quantum chromodynamics}}
The quantum chromodynamics (QCD) sector defines the interactions between quarks and gluons, with SU(3) symmetry, generated by T<sup>a</sup>. 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>\mathcal{L}_{QCD} = i\overline U (\partial_\mu-ig_sG_\mu^a T^a)\gamma^\mu U + i\overline D (\partial_\mu-i g_s G_\mu^a T^a)\gamma^\mu D.</math>
<math>G_\mu^a</math> is the SU(3) gauge field containing the gluons, <math>\gamma^\mu</math> are the Dirac matrices, D and U are the Dirac spinors associated with up- and down-type [[quark]]s, and g<sub>s</sub> is the strong coupling constant.
 
====Electroweak sector====
{{Main|Electroweak interaction}}
The electroweak sector is a [[Yang–Mills theory|Yang–Mills gauge theory]] with the simple symmetry group U(1)×SU(2)<sub>L</sub>,
:<math>
\mathcal{L}_\mathrm{EW} =
\sum_\psi\bar\psi\gamma^\mu
\left(i\partial_\mu-g^\prime{1\over2}Y_\mathrm{W}B_\mu-g{1\over2}\vec\tau_\mathrm{L}\vec W_\mu\right)\psi</math>
 
where ''B''<sub>''μ''</sub> is the U(1) gauge field; ''Y''<sub>W</sub> is the [[weak hypercharge]]—the generator of the U(1) group; <math>\vec{W}_\mu</math> is the
three-component SU(2) gauge field; <math>\vec{\tau}_\mathrm{L}</math> are the [[Pauli matrices]]—infinitesimal generators of the SU(2) group. The subscript L indicates that they only act on left fermions; ''g''′ and ''g'' are coupling constants.
 
====Higgs sector====
{{Main|Higgs mechanism}}
In the Standard Model, the [[Higgs field]] is a complex [[spinor]] of the group [[SU(2)]]<sub>L</sub>:
:<math>
\varphi={1\over\sqrt{2}}
\left(
\begin{array}{c}
\varphi^+ \\ \varphi^0
\end{array}
\right)\;,
</math>
where the indices + and 0 indicate the electric charge (''Q'') of the components. The weak isospin (''Y''<sub>W</sub>) of both components is 1.
 
Before symmetry breaking, the Higgs Lagrangian is:
:<math>\mathcal{L}_\mathrm{H} = \varphi^\dagger
\left({\partial^\mu}-
{i\over2} \left( g'Y_\mathrm{W}B^\mu + g\vec\tau\vec W^\mu \right)\right)
\left(\partial_\mu + {i\over2} \left( g'Y_\mathrm{W}B_\mu
+g\vec\tau\vec W_\mu \right)\right)\varphi \ - \ {\lambda^2\over4}\left(\varphi^\dagger\varphi-v^2\right)^2\;,</math>
 
which can also be written as:
:<math>\mathcal{L}_\mathrm{H} = \left|
\left(\partial_\mu + {i\over2} \left( g'Y_\mathrm{W}B_\mu
+g\vec\tau\vec W_\mu \right)\right)\varphi\right|^2 \ - \ {\lambda^2\over4}\left(\varphi^\dagger\varphi-v^2\right)^2\;.</math>
 
==Tests and predictions==
{{Refimprove section|date=April 2008}}
The Standard Model (SM) predicted the existence of the [[W and Z bosons]], [[gluon]], and the [[top quark|top]] and [[charm quark]]s before these particles were observed. Their predicted properties were experimentally confirmed with good precision. To give an idea of the success of the SM, the following table compares the measured masses of the W and Z bosons with the masses predicted by the SM:
 
{| class="wikitable"
|-
! Quantity !! Measured (GeV) !! SM prediction (GeV)
|-
| Mass of W boson || 80.387 ± 0.019 ||80.390 ± 0.018
|-
| Mass of Z boson || 91.1876 ± 0.0021 || 91.1874 ± 0.0021
|}
The SM also makes several predictions about the decay of Z bosons, which have been experimentally confirmed by the [[Large Electron-Positron Collider]] at [[CERN]].
 
In May 2012 [[BaBar experiment|BaBar Collaboration]] reported that their recently analyzed data may suggest possible flaws in the Standard Model of particle physics.<ref>
{{cite web
|date=31 May 2012
|title=BABAR Data in Tension with the Standard Model
|url=http://www-public.slac.stanford.edu/babar/BaBar-BtoDtaunu.aspx
|publisher=[[SLAC]]
|accessdate=2013-08-06
}}</ref><ref>
{{cite journal
|author1=BaBar Collaboration
|coauthors=<!-- -->
|year=2012
|title=Evidence for an excess of {{overline|B}} → D<sup>(*)</sup> τ<sup>−</sup> ν<sub>τ</sub> decays
|journal=[[Physical Review Letters]]
|volume=109 |issue=10 |pages=101802
|arxiv=1205.5442
|bibcode=2012PhRvL.109j1802L
|doi=10.1103/PhysRevLett.109.101802
|authorlink1=BaBar experiment
}}</ref> These data show that a particular type of particle decay called "B to D-star-tau-nu" happens more often than the Standard Model says it should. In this type of decay, a particle called the B-bar meson decays into a D meson, an antineutrino and a tau-lepton.
While the level of certainty of the excess (3.4 sigma) is not enough to claim a break from the Standard Model, the results are a potential sign of something amiss and are likely to impact existing theories, including those attempting to deduce the properties of [[Higgs boson]]s.<ref>
{{cite web
|date=18 June 2012
|title=BaBar data hint at cracks in the Standard Model
|url=http://esciencenews.com/articles/2012/06/18/babar.data.hint.cracks.standard.model
|work=e! Science News
|accessdate=2013-08-06
}}</ref>
 
On December 13, 2012, [[physicists]] reported the constancy, over space and time, of a basic [[physical constant]] of nature that supports the ''standard model of physics''.  The scientists, studying [[methanol]] molecules in a distant [[galaxy]], found the change (∆μ/μ) in the [[proton-to-electron mass ratio]] μ to be equal to "(0.0 ± 1.0) × 10<sup>−7</sup> at [[redshift]] z = 0.89" and consistent with "a [[null result]]".<ref name="Science-20121213">
{{cite journal
|author=J. Bagdonaitel ''et al.''
|coauthors=<!-- -->
|year=2012
|title=A Stringent Limit on a Drifting Proton-to-Electron Mass Ratio from Alcohol in the Early Universe
|journal=[[Science (journal)|Science]]
|volume=339 |issue=6115 |pages=46
|bibcode=2013Sci...339...46B
|doi=10.1126/science.1224898
}}</ref><ref name="Space-20121213">
{{cite web
|author=C. Moskowitz
|date=13 December 2012
|title=Phew! Universe's Constant Has Stayed Constant
|url=http://www.space.com/18894-galaxy-alcohol-fundamental-constant.html
|publisher=[[Space.com]]
|accessdate=2012-12-14
}}</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? Is it even a new particle?
}}
Self-consistency of the Standard Model (currently formulated as a non-abelian gauge theory quantized through path-integrals) has not been mathematically proven.  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.web.cern.ch/press/PressReleases/Releases2010/PR08.10E.html
|publisher=[[CERN]]
|accessdate=2012-07-05
}}</ref> To accommodate this finding, the classic Standard Model can be modified to include neutrino mass.
 
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
|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
|bibcode=1977PhLB...67..421M
|doi=10.1016/0370-2693(77)90435-X
}}</ref><ref name="MohapatraSenjanovic1980" >
{{cite journal
|author=R. N. Mohapatra, 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
|author=M. Gell-Mann, P. Ramond and R. Slansky
|year=1979
|chapter=
|pages=315–321
|title=Supergravity
|editor=F. van Nieuwenhuizen and D. Z. Freedman
|publisher=[[North Holland]]
|isbn=0-444-85438-X
}}</ref> As long as new physics appears below or around 10<sup>14</sup>&nbsp;[[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:
* It does not attempt to explain [[gravitation]], although a theoretical particle known as a [[graviton]] would help explain it, and unlike for the strong and electroweak interactions of the Standard Model, there is no known way of describing [[general relativity]], the canonical theory of gravitation, consistently 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 consider it to be ''ad hoc'' and inelegant, requiring 19 numerical constants whose values are unrelated and arbitrary. 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;
* The Higgs mechanism gives rise to the [[hierarchy problem]] if any new physics (such as quantum gravity) is present at high energy scales. In order for the weak scale to be much smaller than the [[Planck scale]], severe fine tuning of Standard Model parameters is required;
* It should be modified so as to be consistent with the emerging "Standard Model of [[cosmology]]." In particular, the Standard Model cannot explain the observed amount of [[cold dark matter]] (CDM) and gives 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==
{{Portal|Mathematics}}
{{Wikipedia books|Particles of the Standard Model}}
 
*[[Fundamental interaction]]:
**[[Quantum electrodynamics]]
**[[Strong interaction]]: [[Color charge]], [[Quantum chromodynamics]], [[Quark model]]
**[[Weak interaction]]: [[Electroweak theory]], [[Fermi theory of beta decay]], [[Weak hypercharge]], [[Weak isospin]]
*[[Gauge theory]]: [[Nontechnical introduction to gauge theory]]
*[[Generation (particle physics)|Generation]]
*[[Higgs mechanism]]: [[Higgs boson]], [[Higgsless model]]
*[[John Clive Ward|J. C. Ward]]
*[[Sakurai Prize|J. J. Sakurai Prize for Theoretical Particle Physics]]
*[[Lagrangian]]
*Open questions: [[BTeV experiment]], [[CP violation]], [[Neutrino mass]]es, [[Quark matter]]
*[[Penguin diagram]]
*[[Quantum field theory]]
*Standard Model: [[Standard Model (mathematical formulation)|Mathematical formulation of]], [[Physics beyond the Standard Model]]
*[[Unparticle physics]]
 
==Notes and references==
{{Reflist|group=nb}}
 
==References==
 
{{Reflist|colwidth=35em}}
 
==Further reading==
*{{cite book
| author=R. Oerter
| year=2006
| title=The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics
| publisher=[[Plume (publisher)|Plume]]
| isbn=
}}
*{{cite book
| author=B.A. Schumm
| year=2004
| title=Deep Down Things:  The Breathtaking Beauty of Particle Physics
| publisher=[[Johns Hopkins University Press]]
| isbn=0-8018-7971-X
}}
 
;Introductory textbooks
*{{cite book
| author=I. Aitchison, A. Hey
| year=2003
| title=Gauge Theories in Particle Physics: A Practical Introduction.
| publisher=[[Institute of Physics]]
| isbn=978-0-585-44550-2
}}
*{{cite book
| author=W. Greiner, B. Müller
| year=2000
| title=Gauge Theory of Weak Interactions
| publisher=[[Springer (publisher)|Springer]]
| isbn=3-540-67672-4
}}
*{{cite book
| author=G.D. Coughlan, J.E. Dodd, B.M. Gripaios
| year=2006
|  title=The Ideas of  Particle Physics: An Introduction for Scientists
|  publisher=[[Cambridge University Press]]
|  isbn=
}}
*{{cite book
| author=D.J. Griffiths
| year=1987
| title=Introduction to Elementary Particles
| publisher=[[John Wiley & Sons]]
| isbn=0-471-60386-4
}}
*{{cite book
| author=G.L. Kane
| year=1987
| title=Modern Elementary Particle Physics
| publisher=[[Perseus Books]]
| isbn=0-201-11749-5
}}
 
;Advanced textbooks
*{{cite book
| author=T.P. Cheng, L.F. Li
| year=2006
| title=Gauge theory of elementary particle physics
| publisher=[[Oxford University Press]]
| isbn=0-19-851961-3
}} Highlights the [[gauge theory]] aspects of the Standard Model.
*{{cite book
| author=J.F. Donoghue, E. Golowich, 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=L. O'Raifeartaigh
| year=1988
| title=Group structure of gauge theories
| publisher=[[Cambridge University Press]]
| isbn=0-521-34785-8
}} Highlights [[finite group|group-theoretical]] aspects of the Standard Model.
 
;Journal articles
*{{cite journal
|author=E.S. Abers, B.W. Lee
|year=1973
|title=Gauge theories
|journal=[[Physics Reports]]
|volume=9 |pages=1–141
|doi=10.1016/0370-1573(73)90027-6
|bibcode = 1973PhR.....9....1A }}
*{{cite journal
|author=M. Baak ''et al.''
|coauthors=<!-- -->
|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=
|arxiv=1209.2716
|doi=10.1140/epjc/s10052-012-2205-9
|bibcode = 2012EPJC...72.2205B }}
*{{cite journal
|author=Y. Hayato ''et al.''
|coauthors=<!-- -->
|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 |page=1529
|arxiv = hep-ex/9904020
|bibcode=1999PhRvL..83.1529H
|doi=10.1103/PhysRevLett.83.1529
}}
*{{cite arxiv
|author=S.F. Novaes
|year=2000
|title=Standard Model: An Introduction
|class=hep-ph
|eprint=hep-ph/0001283
}}
*{{cite arxiv
|author=D.P. Roy
|year=1999
|title=Basic Constituents of Matter and their Interactions — A Progress Report
|class=hep-ph
|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 }}
 
==External links==
*"[http://omegataupodcast.net/2012/04/93-the-standard-model-of-particle-physics The Standard Model explained in Detail by CERN's John Ellis]" omega tau podcast.
*"[http://www.newscientist.com/article/dn21279-lhc-sees-hint-of-lightweight-higgs-boson.html LHC sees hint of lightweight Higgs boson]" "[[New Scientist]]".
*"[http://www.newscientist.com/news/news.jsp?id=ns9999404 Standard Model may be found incomplete,]" ''[[New Scientist]]''.
*"[http://www-cdf.fnal.gov/top_status/top.html Observation of the Top Quark]" at [[Fermilab]].
*"[http://cosmicvariance.com/2006/11/23/thanksgiving The Standard Model Lagrangian.]" After electroweak [[symmetry breaking]], with no explicit [[Higgs boson]].
*"[http://nuclear.ucdavis.edu/~tgutierr/files/stmL1.html Standard Model Lagrangian]" with explicit Higgs terms. PDF, PostScript, and LaTeX versions.
*"[http://particleadventure.org/ The particle adventure.]" Web tutorial.
*Nobes, Matthew (2002) "Introduction to the Standard Model of Particle Physics" on [[Kuro5hin]]: [http://www.kuro5hin.org/story/2002/5/1/3712/31700 Part 1,] [http://www.kuro5hin.org/story/2002/5/14/19363/8142 Part 2,] [http://www.kuro5hin.org/story/2002/7/15/173318/784 Part 3a,] [http://www.kuro5hin.org/story/2002/8/21/195035/576 Part 3b.]
*"[http://home.web.cern.ch/about/physics/standard-model The Standard Model]" The Standard Model on the CERN web site explains how the basic building blocks of matter interact, governed by four fundamental forces.
 
{{particles}}
{{Physics-footer}}
{{Use dmy dates|date=March 2011}}
 
[[Category:Standard Model|*]]
[[Category:Concepts in physics]]
[[Category:Particle physics]]

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