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{{Short description|Theory of forces and subatomic particles}}

{{Quantum book backlink|Quantum field theory}}
'''The Standard Model''' of [[Physics:Particle physics|particle physics]] is the [[Scientific theory|theory]] describing three of the four known fundamental forces ([[Electromagnetism|electromagnetic]], [[Physics:Weak interaction|weak]] and [[Physics:Strong interaction|strong interaction]]s – excluding [[Company:Gravity|gravity]]) in the [[Universe|universe]] and classifying all known [[Physics:Elementary particle|elementary particle]]s.
It was developed in stages throughout the latter half of the 20th century, through the work of many scientists worldwide,<ref name="Oerter2006">{{cite book |author=R. Oerter |title=The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics |publisher=Penguin Group |year=2006 |page=2 |isbn=978-0-13-236678-6}}</ref> with the current formulation finalized in the mid-1970s upon experimental confirmation of the existence of [[Company:Quark|quark]]s.
The Standard Model is a paradigm of a [[Quantum field theory|quantum field theory]], exhibiting phenomena such as [[Physics:Spontaneous symmetry breaking|spontaneous symmetry breaking]], [[Physics:Anomaly|anomalies]], and renormalization.<ref name="Mann2010">{{cite book |author=R. Mann |title=An Introduction to Particle Physics and the Standard Model |publisher=CRC Press |year=2010 |doi=10.1201/9781420083002-25}}</ref>

<div style="float:right; border:1px solid #ccc; padding:4px; background:#fff8dc; margin:0 0 1em 1em; width:420px;">
[[File:Standard_Model_overview.jpg|400px]]
<div style="font-size:90%;">Standard Model: unified description of strong, weak, and electromagnetic interactions in quantum field theory</div>
</div>

== Gauge structure ==

The Standard Model is defined by the gauge symmetry:

<math>SU(3) \times SU(2)_L \times U(1)_Y</math>

which corresponds to:

* <math>SU(3)</math> → [[Physics:Quantum chromodynamics|strong interaction]]
* <math>SU(2)_L \times U(1)_Y</math> → [[Physics:Electroweak interaction|electroweak interaction]]

This symmetry determines the allowed interactions and particle content.<ref name="YangMills1954">{{cite journal |author=C. N. Yang |author2=R. Mills |title=Conservation of Isotopic Spin and Isotopic Gauge Invariance |journal=Physical Review |year=1954 |volume=96 |pages=191–195}}</ref>

== Particle content ==

All particles can be classified into fermions and bosons.

=== Fermions ===

The Standard Model includes 12 fermions of spin <math>\frac{1}{2}</math>, grouped into three generations.<ref name="SLAC">{{cite web |title=The Standard Model |url=https://www-project.slac.stanford.edu/e158/StandardModel.html}}</ref>

* Quarks: up, down, charm, strange, top, bottom
* Leptons: electron, muon, tau and their neutrinos

Quarks carry [[Physics:Color charge|color charge]] and participate in the strong interaction, while leptons do not.

Fermions obey the [[Physics:Pauli exclusion principle|Pauli exclusion principle]] and constitute all ordinary matter.<ref name="Eisert2013">{{cite journal |author=Jens Eisert |title=Pauli Principle, Reloaded |journal=Physics |year=2013}}</ref>

=== Gauge bosons ===

Gauge bosons mediate the fundamental interactions:

* Photon → electromagnetic force
* Gluons → strong interaction
* W and Z bosons → weak interaction

These arise from the gauge symmetry of the theory and act as force carriers.<ref name="Jaeger2021">{{cite journal |author=Gregg Jaeger |title=Exchange Forces in Particle Physics |journal=Foundations of Physics |year=2021}}</ref>

=== Higgs boson ===

The Higgs boson is a scalar particle responsible for mass generation via the Higgs mechanism.<ref name="Higgs1964">{{cite journal |author=P. W. Higgs |title=Broken Symmetries and the Masses of Gauge Bosons |journal=Physical Review Letters |year=1964}}</ref><ref name="Englert1964">{{cite journal |author=F. Englert |author2=R. Brout |title=Broken Symmetry and the Mass of Gauge Vector Mesons |journal=Physical Review Letters |year=1964}}</ref><ref name="Guralnik1964">{{cite journal |author=G. S. Guralnik |author2=C. R. Hagen |author3=T. W. B. Kibble |title=Global Conservation Laws and Massless Particles |journal=Physical Review Letters |year=1964}}</ref>

The Higgs field acquires a vacuum expectation value:

<math>\langle \phi \rangle \neq 0</math>

which leads to:

* masses for W and Z bosons
* masses for fermions
* a massless photon

[[File:Standard_Model_infographic.jpg|thumb|300px|Overview of the Standard Model sectors and interactions]]
== Lagrangian structure ==

The Standard Model is formulated as a quantum field theory with a Lagrangian composed of several sectors:

* Quantum chromodynamics (QCD)
* Electroweak sector
* Higgs sector
* Yukawa interactions

Each sector respects gauge invariance and contributes to the dynamics of particles and interactions.<ref name="Weinberg2004">{{cite journal |author=S. Weinberg |title=The making of the Standard Model |journal=European Physical Journal C |year=2004}}</ref>

== Fundamental interactions ==

The Standard Model describes three fundamental interactions:

* Electromagnetism
* Weak interaction
* Strong interaction

These interactions arise from the exchange of gauge bosons between particles.<ref name="CERN_SM">{{cite web |title=The Standard Model |publisher=CERN |year=2023}}</ref>

Gravity is not included due to incompatibility with quantum field theory.<ref name="Ashtekar2005">{{cite journal |author=Abhay Ashtekar |title=Gravity and the quantum |journal=New Journal of Physics |year=2005}}</ref>

== Experimental confirmation ==

The Standard Model has been confirmed by numerous experiments, including:

* discovery of quarks
* observation of W and Z bosons
* discovery of the Higgs boson (2012)<ref name="CERN2012">{{cite web |title=Observation of a New Particle with a Mass of 125 GeV |publisher=CERN |year=2012}}</ref>

Its predictions agree with experimental data to high precision.<ref name="Gaillard1999">{{cite journal |author=Mary K. Gaillard |title=The Standard Model of Particle Physics |journal=Reviews of Modern Physics |year=1999}}</ref>

== Limitations ==

Despite its success, the Standard Model is incomplete:

* does not include gravity
* does not explain dark matter or dark energy
* does not explain matter–antimatter asymmetry
* originally did not include neutrino masses

These issues motivate theories beyond the Standard Model.<ref name="Overbye2023">{{cite news |last=Overbye |first=Dennis |title=Don't Expect a 'Theory of Everything' to Explain It All |date=2023}}</ref><ref name="Carroll2007">{{cite book |author=Sean Carroll |title=Dark Matter, Dark Energy: The Dark Side of the Universe |year=2007}}</ref>

== Historical development ==

The development of the Standard Model involved key contributions:

* Dirac equation (1928) introducing antimatter<ref name="Husain2024">{{cite web |title=The Dirac equation unifies quantum mechanics and relativity |publisher=APS |year=2024}}</ref>
* Yang–Mills theory (1954) extending gauge symmetry<ref name="YangMills1954"/>
* Electroweak unification (Glashow, Weinberg, Salam)<ref name="Glashow1961">{{cite journal |author=S. L. Glashow |title=Partial symmetries of weak interactions |journal=Nuclear Physics |year=1961}}</ref><ref name="Weinberg1967">{{cite journal |author=S. Weinberg |title=A Model of Leptons |journal=Physical Review Letters |year=1967}}</ref>
* Introduction of quarks (Gell-Mann, Zweig)<ref name="Greenberg2009">{{cite book |author=O. Greenberg |title=Color Charge Degree of Freedom in Particle Physics |year=2009}}</ref>
* Higgs mechanism (1964)<ref name="Higgs1964"/>
* Asymptotic freedom in QCD (1973)<ref name="Gross1973">{{cite journal |author=D. Gross |author2=F. Wilczek |title=Ultraviolet behavior of non-abelian gauge theories |journal=Physical Review Letters |year=1973}}</ref><ref name="Politzer1973">{{cite journal |author=H. Politzer |title=Reliable perturbative results for strong interactions |journal=Physical Review Letters |year=1973}}</ref>

These developments established the modern framework of particle physics.

== Conceptual role ==

The Standard Model represents the culmination of:

* gauge symmetry principles
* non-Abelian gauge theory
* quantum field theory

It unifies QED, QCD, and electroweak theory into a single framework describing fundamental interactions.<ref name="JaegerQFT2021">{{cite journal |author=Gregg Jaeger |title=The Elementary Particles of Quantum Fields |journal=Entropy |year=2021}}</ref>

=See also=
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}

==References==
{{reflist|3}}
{{Author|Harold Foppele}}

{{Sourceattribution|Standard Model|1}}

Physics:Quantum Standard Model - Revision history

imported>WikiHarold: Repair Quantum Collection B backlink template

imported>WikiHarold: Repair Quantum Collection B backlink template