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Standard Model

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**Standard Model**of particle physics is the theory describing three of the four known fundamental forces (the electromagnetic, weak, and strong interactions, and not including the gravitational force) in the universe, as well as classifying all known elementary particles. It was developed in stages throughout the latter half of the 20th century, through the work of many scientists around the world,BOOK

, R. Oerter

, 2006

, The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics

, 2

, Penguin Group

, Kindle

, 978-0-13-236678-6

, with the current formulation being finalized in the mid-1970s upon experimental confirmation of the existence of quarks. Since then, confirmation of the top quark (1995), the tau neutrino (2000), and the Higgs boson (2012) have added further credence to the Standard Model. In addition, the Standard Model has predicted various properties of weak neutral currents and the W and Z bosons with great accuracy.Although the Standard Model is believed to be theoretically self-consistentIn 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 applicable to current experiments are all self-consistent. For a further discussion see e.g. Chapter 25 of BOOK
, 2006

, The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics

, 2

, Penguin Group

, Kindle

, 978-0-13-236678-6

, R. Mann

, 2010

, An Introduction to Particle Physics and the Standard Model

, CRC Press

, 978-1-4200-8298-2

, and has demonstrated huge successes in providing experimental predictions, it leaves some phenomena unexplained and falls short of being a complete theory of fundamental interactions. It does not fully explain baryon asymmetry, incorporate the full theory of gravitationSean Carroll, Ph.D., Caltech, 2007, The Teaching Company, , 2010

, An Introduction to Particle Physics and the Standard Model

, CRC Press

, 978-1-4200-8298-2

*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..." as described by general relativity, or account for the accelerating expansion of the Universe as possibly described by dark energy. The model does not contain any viable dark matter particle that possesses all of the required properties deduced from observational cosmology. It also does not incorporate neutrino oscillations and their non-zero masses.The development of the Standard Model was driven by theoretical and experimental particle physicists alike. For theorists, the Standard Model is a paradigm of a quantum field theory, which exhibits a wide range of phenomena including spontaneous symmetry breaking, anomalies and non-perturbative behavior. It is used as a basis for building more exotic models that incorporate hypothetical particles, extra dimensions, and elaborate symmetries (such as supersymmetry) 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

{{See also|History of quantum field theory|History of subatomic physics}}In 1954, Chen Ning Yang 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.JOURNAL, Chen-Ning Yang, C. N., Yang, Robert Mills (physicist), R., Mills, Conservation of Isotopic Spin and Isotopic Gauge Invariance, Physical Review, 96, 1, 191â€“195, 1954, 10.1103/PhysRev.96.191, 1954PhRv...96..191Y, In 1961, Sheldon Glashow combined the electromagnetic and weak interactions.JOURNAL, S.L. Glashow

, 1961

, Partial-symmetries of weak interactions

, Nuclear Physics (journal), Nuclear Physics

, 22, 4, 579â€“588

, 1961NucPh..22..579G

, 10.1016/0029-5582(61)90469-2

, In 1967 Steven WeinbergJOURNAL
, 1961

, Partial-symmetries of weak interactions

, Nuclear Physics (journal), Nuclear Physics

, 22, 4, 579â€“588

, 1961NucPh..22..579G

, 10.1016/0029-5582(61)90469-2

, S. Weinberg

, 1967

, A Model of Leptons

, Physical Review Letters

, 19, 21, 1264â€“1266

, 1967PhRvL..19.1264W

, 10.1103/PhysRevLett.19.1264

, and Abdus SalamCONFERENCE
, 1967

, A Model of Leptons

, Physical Review Letters

, 19, 21, 1264â€“1266

, 1967PhRvL..19.1264W

, 10.1103/PhysRevLett.19.1264

, A. Salam

, N. Svartholm

, 1968

, Elementary Particle Physics: Relativistic Groups and Analyticity

, 367

, Nobel Symposium, Eighth Nobel Symposium

, Almquvist and Wiksell

, Stockholm

, incorporated the Higgs mechanismJOURNAL
, N. Svartholm

, 1968

, Elementary Particle Physics: Relativistic Groups and Analyticity

, 367

, Nobel Symposium, Eighth Nobel Symposium

, Almquvist and Wiksell

, Stockholm

, F. Englert, R. Brout, 1964

, Broken Symmetry and the Mass of Gauge Vector Mesons

, Physical Review Letters

, 13, 9, 321â€“323

, 1964PhRvL..13..321E

, 10.1103/PhysRevLett.13.321

, JOURNAL
, Broken Symmetry and the Mass of Gauge Vector Mesons

, Physical Review Letters

, 13, 9, 321â€“323

, 1964PhRvL..13..321E

, 10.1103/PhysRevLett.13.321

, G.S. Guralnik, C.R. Hagen, T.W.B. Kibble, 1964

, Global Conservation Laws and Massless Particles

, Physical Review Letters

, 13, 20, 585â€“587

, 1964PhRvL..13..585G

, 10.1103/PhysRevLett.13.585

, into Glashow's electroweak interaction, giving it its modern form.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,JOURNAL
, Global Conservation Laws and Massless Particles

, Physical Review Letters

, 13, 20, 585â€“587

, 1964PhRvL..13..585G

, 10.1103/PhysRevLett.13.585

, F.J. Hasert, etal,

, 1973

, Search for elastic muon-neutrino electron scattering

, Physics Letters B

, 46, 1, 121

, 1973PhLB...46..121H

, 10.1016/0370-2693(73)90494-2

, JOURNAL
, 1973

, Search for elastic muon-neutrino electron scattering

, Physics Letters B

, 46, 1, 121

, 1973PhLB...46..121H

, 10.1016/0370-2693(73)90494-2

, F.J. Hasert, etal,

, 1973

, Observation of neutrino-like interactions without muon or electron in the Gargamelle neutrino experiment

, Physics Letters B

, 46, 1, 138

, 1973PhLB...46..138H

, 10.1016/0370-2693(73)90499-1

, JOURNAL
, 1973

, Observation of neutrino-like interactions without muon or electron in the Gargamelle neutrino experiment

, Physics Letters B

, 46, 1, 138

, 1973PhLB...46..138H

, 10.1016/0370-2693(73)90499-1

, F.J. Hasert,

, 1974

, Observation of neutrino-like interactions without muon or electron in the Gargamelle neutrino experiment

, Nuclear Physics B

, 73, 1, 1

, 1974NuPhB..73....1H

, 10.1016/0550-3213(74)90038-8, etal,

WEB
, 1974

, Observation of neutrino-like interactions without muon or electron in the Gargamelle neutrino experiment

, Nuclear Physics B

, 73, 1, 1

, 1974NuPhB..73....1H

, 10.1016/0550-3213(74)90038-8, etal,

, D. Haidt

, 4 October 2004

, The discovery of the weak neutral currents

,weblink

, CERN Courier

, 8 May 2008

, the electroweak theory became widely accepted and Glashow, Salam, and Weinberg shared the 1979 Nobel Prize in Physics for discovering it. The WÂ± and Z0 bosons were discovered experimentally in 1983; and the ratio of their masses was found to be as the Standard Model predicted.JOURNAL, Gaillard, Mary K., Mary K. Gaillard, Grannis, Paul D., Sciulli, Frank J.,weblink The Standard Model of Particle Physics, January 1999, Reviews of Modern Physics, 10.1103/RevModPhys.71.S96, 71, 2, 2019-07-14, The theory of the strong interaction (i.e. quantum chromodynamics, QCD), to which many contributed, acquired its modern form in 1973â€“74 when asymptotic freedom was proposedJOURNAL
, 4 October 2004

, The discovery of the weak neutral currents

,weblink

, CERN Courier

, 8 May 2008

, D.J. Gross, F. Wilczek, 1973

, Ultraviolet behavior of non-abelian gauge theories

, Physical Review Letters

, 30, 26, 1343â€“1346

, 1973PhRvL..30.1343G

, 10.1103/PhysRevLett.30.1343

, JOURNAL
, Ultraviolet behavior of non-abelian gauge theories

, Physical Review Letters

, 30, 26, 1343â€“1346

, 1973PhRvL..30.1343G

, 10.1103/PhysRevLett.30.1343

, H.D. Politzer

, 1973

, Reliable perturbative results for strong interactions

, Physical Review Letters

, 30, 26, 1346â€“1349

, 1973PhRvL..30.1346P

, 10.1103/PhysRevLett.30.1346,weblink

, (a development which made QCD the main focus of theoretical research)Dean Rickles (2014).

JOURNAL
, 1973

, Reliable perturbative results for strong interactions

, Physical Review Letters

, 30, 26, 1346â€“1349

, 1973PhRvL..30.1346P

, 10.1103/PhysRevLett.30.1346,weblink

, (a development which 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., Aubert, J.

, 1974

, Experimental Observation of a Heavy Particle J

, Physical Review Letters

, 33, 23, 1404â€“1406

, 1974PhRvL..33.1404A

, 10.1103/PhysRevLett.33.1404, etal,

JOURNAL
, 1974

, Experimental Observation of a Heavy Particle J

, Physical Review Letters

, 33, 23, 1404â€“1406

, 1974PhRvL..33.1404A

, 10.1103/PhysRevLett.33.1404, etal,

, Augustin, J.

, 1974

, Discovery of a Narrow Resonance in e+eâˆ’ Annihilation

, Physical Review Letters

, 33, 23, 1406â€“1408

, 1974PhRvL..33.1406A

, 10.1103/PhysRevLett.33.1406

, etal,

The term "Standard Model" was first coined by Abraham Pais and Sam Treiman in 1975, with reference to the electroweak theory with four quarks.Cao, Tian Yu. , 1974

, Discovery of a Narrow Resonance in e+eâˆ’ Annihilation

, Physical Review Letters

, 33, 23, 1406â€“1408

, 1974PhRvL..33.1406A

, 10.1103/PhysRevLett.33.1406

, etal,

*Conceptual developments of 20th century field theories*. Cambridge University Press, 1998, p. 320.

## Overview

At present, matter and energy are best understood in terms of the kinematics and interactions of elementary particles. To date, physics has reduced the 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)."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. 2â€“7

## Particle content

The Standard Model includes members of several classes of elementary particles, which in turn can be distinguished by other characteristics, such as color charge.All particles can be summarized as follows:{{Elementary particles}}### Fermions

(File:Elementary particle interactions in the Standard Model.png|upright=1.5|thumb|right|Summary of interactions between particles described by the Standard Model)The Standard Model includes 12 elementary particles of spin {{1/2}}, known as fermions. According to the spinâ€“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 charges they carry). There are six quarks (up, down, charm, strange, top, bottom), and six leptons (electron, electron neutrino, muon, muon neutrino, tau, tau neutrino). Pairs from each classification are grouped together to form a 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 very strongly bound to one another, forming color-neutral composite particles (hadrons) containing either a quark and an antiquark (mesons) or three quarks (baryons). The familiar proton and neutron are the two baryons having the smallest mass. Quarks also carry electric charge and weak isospin. Hence they interact with other fermions both electromagnetically and via the weak interaction. The remaining six fermions do not carry color charge and are called leptons. The three neutrinos do not carry electric charge either, so their motion is directly influenced only by the 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 around atomic nuclei, ultimately constituted of up and down quarks. Second- and third-generation 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

(File:Standard Model Feynman Diagram Vertices.png|upright=1.5|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 is 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 bosons are defined as force carriers that mediate the strong, weak, and electromagnetic fundamental interactions.Interactions in physics are the ways that particles influence other particles. At a macroscopic level, electromagnetism allows particles to interact with one another via electric and 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 exchanging other particles, generally referred to as*force mediating particles*. 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 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 gauge bosons of the Standard Model all have spin (as do matter particles). The value of the spin is 1, making them bosons. As a result, they do not follow the Pauli exclusion principle that constrains fermions: 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.

- Photons mediate the electromagnetic force between electrically charged particles. The photon is massless and is well-described by the theory of quantum electrodynamics.
- The {{SubatomicParticle|W boson+}}, {{SubatomicParticle|W boson-}}, and {{SubatomicParticle|Z boson}} gauge bosons mediate the weak interactions between particles of different flavors (all quarks 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. Furthermore, the {{SubatomicParticle|W boson+-}} carries an electric charge of +1 and âˆ’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 gluons mediate the strong interactions between color charged particles (the quarks). Gluons are massless. The eightfold multiplicity of gluons is labeled by a combination of color and anticolor charge (e.g. redâ€“antigreen).{{NoteTag|Technically, there are nine such colorâ€“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.}} 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.

### Higgs boson

The Higgs particle is a massive scalar elementary particle theorized by Peter Higgs 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.JOURNAL, P.W. Higgs

, 1964

, Broken Symmetries and the Masses of Gauge Bosons

, Physical Review Letters

, 13, 16, 508â€“509

, 1964PhRvL..13..508H

, 10.1103/PhysRevLett.13.508

, JOURNAL
, 1964

, Broken Symmetries and the Masses of Gauge Bosons

, Physical Review Letters

, 13, 16, 508â€“509

, 1964PhRvL..13..508H

, 10.1103/PhysRevLett.13.508

, G.S. Guralnik

, 2009

, The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles

, International Journal of Modern Physics A

, 24, 14, 2601â€“2627

, 0907.3466

, 2009IJMPA..24.2601G

, 10.1142/S0217751X09045431

, It has no intrinsic 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 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 becomes visible{{clarify|reason=Isn't "apparent" or "manifest" needed here instead of "visible"?|date=July 2013}} at energies above {{val|1.4|ul=TeV}};JOURNAL
, 2009

, The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles

, International Journal of Modern Physics A

, 24, 14, 2601â€“2627

, 0907.3466

, 2009IJMPA..24.2601G

, 10.1142/S0217751X09045431

, B.W. Lee, C. Quigg, H.B. Thacker, 1977

, Weak interactions at very high energies: The role of the Higgs-boson mass

, Physical Review D

, 16, 5, 1519â€“1531

, 1977PhRvD..16.1519L

, 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.NEWS
, Weak interactions at very high energies: The role of the Higgs-boson mass

, Physical Review D

, 16, 5, 1519â€“1531

, 1977PhRvD..16.1519L

, 10.1103/PhysRevD.16.1519

, 11 November 2009

, Huge $10 billion collider resumes hunt for 'God particle'

,weblink

, CNN

, 2010-05-04

, On 4 July 2012, two of the experiments at the LHC (ATLAS and 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 {{val|10|e=-25|u=kg}}), which is "consistent with the Higgs boson".WEB
, NEWS
, Huge $10 billion collider resumes hunt for 'God particle'

,weblink

, CNN

, 2010-05-04

, 4 July 2012

, CERN experiments observe particle consistent with long-sought Higgs boson

,weblink

, CERN

, 2016-11-12

, WEB
, WEB
, WEB
, CERN experiments observe particle consistent with long-sought Higgs boson

,weblink

, CERN

, 2016-11-12

, 4 July 2012

,weblink

, Confirmed: CERN discovers new particle likely to be the Higgs boson

, YouTube

, Russia Today

, 2013-08-06

, NEWS
,weblink

, Confirmed: CERN discovers new particle likely to be the Higgs boson

, YouTube

, Russia Today

, 2013-08-06

, D. Overbye

, 4 July 2012

, A New Particle Could Be Physics' Holy Grail

,weblink

, The New York Times

, 2012-07-04

, It was later confirmed to be the searched-for Higgs boson.WEB,weblink LHC experiments delve deeper into precision, 11 July 2017, CERN, 2017-07-23, , 4 July 2012

, A New Particle Could Be Physics' Holy Grail

,weblink

, The New York Times

, 2012-07-04

## Theoretical aspects

### Construction of the Standard Model Lagrangian {| class"wikitable collapsible collapsed"

!colspan="5"|Parameters of the Standard Model! Symbol! Description! Renormalization scheme (point)! Value*m*e|Electron mass||511 keV

*m*Î¼|Muon mass||105.7 MeV

*m*Ï„|Tau mass||1.78 GeV

*m*u|Up quark mass

Î¼{{overline>MS}} = 2 GeV|1.9 MeV |

*m*d|Down quark mass

Î¼{{overline>MS}} = 2 GeV|4.4 MeV |

*m*s|Strange quark mass

Î¼{{overline>MS}} = 2 GeV|87 MeV |

*m*c|Charm quark mass

Î¼{{overline>MS}} = mc|1.32 GeV |

*m*b|Bottom quark mass

Î¼{{overline>MS}} = mb|4.24 GeV |

*m*t|Top quark mass| On shell scheme|173.5 GeV

*Î¸*12|CKM 12-mixing angle||13.1Â°

*Î¸*23|CKM 23-mixing angle||2.4Â°

*Î¸*13|CKM 13-mixing angle||0.2Â°

*Î´*|CKM CP violation Phase||0.995

*g*1 or

*g*{{'}}|U(1) gauge coupling

Î¼{{overline>MS}} = mZ|0.357 |

*g*2 or

*g*|SU(2) gauge coupling

Î¼{{overline>MS}} = mZ|0.652 |

*g*3 or

*g*s|SU(3) gauge coupling

Î¼{{overline>MS}} = mZ|1.221 |

*Î¸*QCD|QCD vacuum angle||~0

*v*|Higgs vacuum expectation value||246 GeV

*m*H|Higgs mass|

125.09 | u=GeV}} |

#### Quantum chromodynamics sector

The quantum chromodynamics (QCD) sector defines the interactions between quarks and gluons, which is a Yangâ€“Mills gauge theory with SU(3) symmetry, generated by {{mvar|Ta}}. 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
mathcal{L}_text{QCD} = sum_psi overline{psi}_i left( igamma^mu(partial_mudelta_{ij} - i g_s G_mu^a T^a_{ij}) - m_psi delta_{ij} right) psi_j - frac{1}{4} G^a_{munu} G^{munu}_a,

where
{{mvar|Ïˆ{{su|b=i}}}} is the Dirac spinor of the quark field, where

*i*= {r, g, b} represents color, {{mvar|Î³{{isup|Î¼}}}} are the Dirac matrices, {{mvar|G{{su|b=Î¼|p=a}}}} is the 8-component (a = 1, 2, dots, 8) SU(3) gauge field, {{mvar|T{{su|b=ij|p=a}}}} are the 3â€¯Ã—â€¯3 Gell-Mann matrices, generators of the SU(3) color group, {{mvar|G{{su|b=Î¼Î½|p=a}}}} represents the gluon field strength tensor, {{mvar|gs}} is the strong coupling constant.#### Electroweak sector

The electroweak sector is a Yangâ€“Mills gauge theory with the symmetry group U(1)â€¯Ã—â€¯SU(2)L,
mathcal{L}_text{EW} = sum_psi barpsi gamma^mu left(ipartial_mu - g' tfrac12 Y_text{W} B_mu - g tfrac12 vectau_text{L} vec W_muright)psi - tfrac{1}{4} W_a^{munu} W_{munu}^a - tfrac{1}{4} B^{munu} B_{munu},

where
{{mvar|BÎ¼}} is the U(1) gauge field,
{{math|

Notice that the addition of fermion mass terms into the electroweak lagrangian is forbidden, since terms of the form moverlinepsipsi do not respect U(1)â€¯Ã—â€¯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.*Y*W}} is the weak hypercharge â€“ the generator of the U(1) group, {{math|{{vec|*W*}}*Î¼*}} is the 3-component SU(2) gauge field, {{math|{{vec|*Ï„*L}}}} are the Pauli matrices â€“ infinitesimal generators of the SU(2) group â€“ 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^{amunu} (a = 1, 2, 3) and B^{munu} are the field strength tensors for the weak isospin and weak hypercharge fields.#### Higgs sector

In the Standard Model, the Higgs field is a complex scalar of the group SU(2)L:
varphi = frac{1}{sqrt 2} left(begin{array}{c}varphi^+ varphi^0end{array}right),

where the superscripts + and 0 indicate the electric charge ({{mvar|Q}}) of the components. The weak hypercharge ({{math|*Y*W}}) of both components is 1.Before symmetry breaking, the Higgs Lagrangian is

mathcal{L}_text{H} = varphi^dagger left(partial^mu - frac{i}{2} left( g'Y_text{W} B^mu + g vectau vec W^mu right)right) left(partial_mu + frac{i}{2} left( g'Y_text{W} B_mu + g vectau vec W_mu right)right)varphi - frac{lambda^2}{4} left(varphi^dagger varphi - v^2right)^2,

which up to a divergence term, (i.e. after partial integration) can also be written as
mathcal{L}_text{H} = left|left(partial_mu + frac{i}{2} left( g'Y_text{W} B_mu + g vectau vec W_mu right)right)varphiright|^2 - frac{lambda^2}{4} left(varphi^dagger varphi - v^2right)^2.

#### Yukawa sector

The Yukawa interaction terms are
mathcal{L}_text{Yukawa} = overline U_L G_u U_R phi^0 - overline D_L G_u U_R phi^- + overline U_L G_d D_R phi^+ + overline D_L G_d D_R phi^0 + hc,

where {{mvar|Gu,d}} are {{math|3â€¯Ã—â€¯3}} matrices of Yukawa couplings, with the {{mvar|ij}} term giving the coupling of the generations {{mvar|i}} and {{mvar|j}}.## Fundamental interactions

{{Expand section|date=October 2015}}The Standard Model describes three of the four fundamental interactions in nature; only gravity remains unexplained. In the Standard Model, 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 particlesweblink Official CERN website{| style="margin: 1em auto 1em auto;" class="wikitable floatcenter"The four fundamental interactions of natureHTTP://WWW.PHA.JHU.EDU/~DFEHLING/PARTICLE.GIF, Standard Model of Particles and Interactions, jhu.edu, Johns Hopkins University, August 18, 2016, .gif, dead,weblink March 4, 2016, ! style="" rowspan="2" | Property/Interaction! style="background-color:#8080BF" rowspan="2" |Gravitation! style="background-color:#BFA080" colspan="2" |Electroweak! style="background-color:#80BF80" colspan="2" |Strong! style="background-color:#BFBF80" |Weak! style="background-color:#BF8080" |Electromagnetic! style="background-color:#AAD4AA" |Fundamental! style="background-color:#D5EAD5" |ResidualNot yet observed(Graviton hypothesised) | W+, Wâˆ’ and Z0 | Î³ (photon) | Gluons | Pion | , Rho meson>Ï and Ï‰ mesons |

All particles | Left-handed fermions | Electrically charged | Quarks, gluons | Hadrons |

Mass, energy | Flavor | Electric charge | Color charge |

Planets, stars, galaxies, galaxy groups | n/a | Atoms, molecules | Hadrons | Atomic nuclei |

{{val | e=-41}} (predicted) | {{val | e=-4}} | 1 | 60 | Not applicable to quarks |

{{val | e=-36}} (predicted) | {{val | e=-7}} | 1 | Not applicable to hadrons | 20 |

## Tests and predictions

The Standard Model (SM) predicted the existence of the W and Z bosons, gluon, and the top and charm quarks and predicted many of their properties before these particles were observed. The predictions were experimentally confirmed with good precision.JOURNAL, Woithe, Julia, Wiener, Gerfried, Van der Veken, Frederik, Let's have a coffee with the Standard Model of particle physics!, Phys. Educ., 52, 3, 034001, 10.1088/1361-6552/aa5b25, 2017, 2017PhyEd..52c4001W, The SM also predicted the existence of the Higgs boson, found in 2012 at the Large Hadron Collider, as the last particle of the SM.ARXIV, 1407.2122, Altarelli, Guido, The Higgs and the Excessive Success of the Standard Model, hep-ph, 2014,## Challenges

{{See also|Physics beyond the Standard Model}}{hide}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?

, S. Weinberg

, 1979

, Baryon and Lepton Nonconserving Processes

, Physical Review Letters

, 43, 21, 1566â€“1570

, 1979PhRvL..43.1566W

, 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 ModelJOURNAL
, 1979

, Baryon and Lepton Nonconserving Processes

, Physical Review Letters

, 43, 21, 1566â€“1570

, 1979PhRvL..43.1566W

, 10.1103/PhysRevLett.43.1566

, P. Minkowski

, 1977

, Î¼ â†’ e Î³ at a Rate of One Out of 109 Muon Decays?

, Physics Letters B

, 67, 4, 421â€“428

, 1977PhLB...67..421M

, 10.1016/0370-2693(77)90435-X

, JOURNAL
, 1977

, Î¼ â†’ e Î³ at a Rate of One Out of 109 Muon Decays?

, Physics Letters B

, 67, 4, 421â€“428

, 1977PhLB...67..421M

, 10.1016/0370-2693(77)90435-X

, R.N. Mohapatra, G. Senjanovic, 1980

, Neutrino Mass and Spontaneous Parity Nonconservation

, Physical Review Letters

, 44, 14, 912â€“915

, 1980PhRvL..44..912M

, 10.1103/PhysRevLett.44.912

, and in certain grand unified theories.BOOK
, Neutrino Mass and Spontaneous Parity Nonconservation

, Physical Review Letters

, 44, 14, 912â€“915

, 1980PhRvL..44..912M

, 10.1103/PhysRevLett.44.912

, M. Gell-Mann, P. Ramond, R. Slansky

, yes, 1979

,

, 315â€“321

, Supergravity

, F. van Nieuwenhuizen, D.Z. Freedman, North Holland

, 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: , yes, 1979

,

, 315â€“321

, Supergravity

, F. van Nieuwenhuizen, D.Z. Freedman, North Holland

, 978-0-444-85438-4

- 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.

, A. Blumhofer, M. Hutter, 1997

, Family Structure from Periodic Solutions of an Improved Gap Equation

, Nuclear Physics

, B484

, 1, 80â€“96

, 10.1016/S0550-3213(96)00644-Xarxiv = 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.

ARXIV, hep-ph/0606054, Strumia, Alessandro, Neutrino masses and mixings and..., 2006, , Family Structure from Periodic Solutions of an Improved Gap Equation

, Nuclear Physics

, B484

, 1, 80â€“96

, 10.1016/S0550-3213(96)00644-Xarxiv = 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.

- 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.

- 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.

## See also

{{Wikipedia books|Particles of the Standard Model}}- Yang-Mills theory
- Fundamental interaction:
- Gauge theory: Nontechnical introduction to gauge theory
- Generation
- Higgs mechanism: Higgs boson, Higgsless model
- Lagrangian
- Open questions: CP violation, Neutrino masses, Quark matter, Quantum triviality
- Quantum field theory
- Standard Model: Mathematical formulation of, Physics beyond the Standard Model

## Notes

{{NoteFoot}}## References

{{Reflist}}## Further reading

- BOOK

, R. Oerter

, 2006

, The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics

, Plume

,

, , 2006

, The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics

, Plume

,

- BOOK

, B.A. Schumm

, 2004

, Deep Down Things: The Breathtaking Beauty of Particle Physics

, Johns Hopkins University Press

, 978-0-8018-7971-5

, registration

,weblink

,

, 2004

, Deep Down Things: The Breathtaking Beauty of Particle Physics

, Johns Hopkins University Press

, 978-0-8018-7971-5

, registration

,weblink

,

- WEB

,weblink

, The Standard Model of Particle Physics Interactive Graphic

, , The Standard Model of Particle Physics Interactive Graphic

- Introductory textbooks

- BOOK

, I. Aitchison

, A. Hey

, 2003

, Gauge Theories in Particle Physics: A Practical Introduction.

, Institute of Physics

, 978-0-585-44550-2

, , A. Hey

, 2003

, Gauge Theories in Particle Physics: A Practical Introduction.

, Institute of Physics

, 978-0-585-44550-2

- BOOK

, W. Greiner

, B. MÃ¼ller

, 2000

, Gauge Theory of Weak Interactions

, Springer

, 978-3-540-67672-0

, , B. MÃ¼ller

, 2000

, Gauge Theory of Weak Interactions

, Springer

, 978-3-540-67672-0

- BOOK

, G.D. Coughlan

, J.E. Dodd

, B.M. Gripaios

, 2006

, The Ideas of Particle Physics: An Introduction for Scientists

, Cambridge University Press

,

, , J.E. Dodd

, B.M. Gripaios

, 2006

, The Ideas of Particle Physics: An Introduction for Scientists

, Cambridge University Press

,

- BOOK

, D.J. Griffiths

, 1987

, Introduction to Elementary Particles

, John Wiley & Sons

, 978-0-471-60386-3

, , 1987

, Introduction to Elementary Particles

, John Wiley & Sons

, 978-0-471-60386-3

- BOOK

, G.L. Kane

, 1987

, Modern Elementary Particle Physics

, Perseus Books

, 978-0-201-11749-3

, , 1987

, Modern Elementary Particle Physics

, Perseus Books

, 978-0-201-11749-3

- Advanced textbooks

- BOOK

, T.P. Cheng

, L.F. Li

, 2006

, Gauge theory of elementary particle physics

, Oxford University Press

, 978-0-19-851961-4

, Highlights the gauge theory aspects of the Standard Model. , L.F. Li

, 2006

, Gauge theory of elementary particle physics

, Oxford University Press

, 978-0-19-851961-4

- BOOK

, J.F. Donoghue

, E. Golowich

, B.R. Holstein

, 1994

, Dynamics of the Standard Model

, Cambridge University Press

, 978-0-521-47652-2

, Highlights dynamical and phenomenological aspects of the Standard Model. , E. Golowich

, B.R. Holstein

, 1994

, Dynamics of the Standard Model

, Cambridge University Press

, 978-0-521-47652-2

- BOOK

, L. O'Raifeartaigh

, 1988

, Group structure of gauge theories

, Cambridge University Press

, 978-0-521-34785-3

, , 1988

, Group structure of gauge theories

, Cambridge University Press

, 978-0-521-34785-3

- BOOK,weblink Elementary Particle Physics: Foundations of the Standard Model, Volume 2, 978-3-527-64890-0, Nagashima, Yorikiyo, 2013, Wiley, 920 pages.
- BOOK,weblink Quantum Field Theory and the Standard Model, 978-1-107-03473-0, Schwartz, Matthew D., 2014, Cambridge University, 952 pages.
- BOOK,weblink The Standard Model and Beyond, 978-1-4200-7907-4, Langacker, Paul, 2009, CRC Press, 670 pages. Highlights group-theoretical aspects of the Standard Model.

- Journal articles

- JOURNAL

, E.S. Abers

, B.W. Lee

, 1973

, Gauge theories

, Physics Reports

, 9, 1

, 1â€“141

, 10.1016/0370-1573(73)90027-6, 1973PhR.....9....1A,

, B.W. Lee

, 1973

, Gauge theories

, Physics Reports

, 9, 1

, 1â€“141

, 10.1016/0370-1573(73)90027-6, 1973PhR.....9....1A,

- JOURNAL

, M. Baak, etal,

, 2012

, The Electroweak Fit of the Standard Model after the Discovery of a New Boson at the LHC

, The European Physical Journal C

, 72, 11, 2205

, 1209.2716

, 10.1140/epjc/s10052-012-2205-9, 2012EPJC...72.2205B

, , 2012

, The Electroweak Fit of the Standard Model after the Discovery of a New Boson at the LHC

, The European Physical Journal C

, 72, 11, 2205

, 1209.2716

, 10.1140/epjc/s10052-012-2205-9, 2012EPJC...72.2205B

- JOURNAL

, Y. Hayato, etal

,

, 1999

, Search for Proton Decay through

, Physical Review Letters

, 83, 8, 1529â€“1533

, hep-ex/9904020

, 1999PhRvL..83.1529H

, 10.1103/PhysRevLett.83.1529

, ,

, 1999

, Search for Proton Decay through

*p*â†’*Î½K*+ in a Large Water Cherenkov Detector, Physical Review Letters

, 83, 8, 1529â€“1533

, hep-ex/9904020

, 1999PhRvL..83.1529H

, 10.1103/PhysRevLett.83.1529

- ARXIV

, S.F. Novaes

, 2000

, Standard Model: An Introduction

, hep-ph/0001283

, , 2000

, Standard Model: An Introduction

, hep-ph/0001283

- ARXIV

, D.P. Roy

, 1999

, Basic Constituents of Matter and their Interactions â€“ A Progress Report

, hep-ph/9912523

, , 1999

, Basic Constituents of Matter and their Interactions â€“ A Progress Report

, hep-ph/9912523

- JOURNAL

, F. Wilczek

, 2004

, The Universe Is A Strange Place

, 10.1016/j.nuclphysbps.2004.08.001

, Nuclear Physics B: Proceedings Supplements

, 134

, 3

, astro-ph/0401347

, 2004NuPhS.134....3W

, , 2004

, The Universe Is A Strange Place

, 10.1016/j.nuclphysbps.2004.08.001

, Nuclear Physics B: Proceedings Supplements

, 134

, 3

, astro-ph/0401347

, 2004NuPhS.134....3W

## External links

- "The Standard Model explained in Detail by CERN's John Ellis" omega tau podcast.
- "The Standard Model" on the CERN web site explains how the basic building blocks of matter interact, governed by four fundamental forces.
- Particle Physics: Standard Model, Leonard Susskind lectures (2010).
- {{YouTube|K6i-qE8AigE|"Standard Model"}}

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