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Wikipedia: Standard Model

For the Standard Model in Cryptography, see Standard Model (cryptography).

For the Standard Model in Cosmology, see the article on the Big Bang.

The Standard Model of particle physics is a theory which describes three of the four known fundamental interactions between the elementary particles that make up all matter. It is a quantum field theory developed between 1970 and 1973 which is consistent with both quantum mechanics and special relativity. To date, almost all experimental tests of the three forces described by the Standard Model have agreed with its predictions. However, the Standard Model falls short of being a complete theory of fundamental interactions, primarily because of its lack of inclusion of gravity, the fourth known fundamental interaction, but also because of the large number of numerical parameters (such as masses and coupling constants) that must be put "by hand" into the theory (rather than being derived from first principles).

The Standard Model of Fundamental Particles and Interactions

The Standard Model

In physics, the dynamics of both matter and energy in Nature is presently best understood in terms of the kinematics and interactions of fundamental particles. To date, science has managed to reduce the laws which seem to govern the behavior and interaction of all types of matter and energy we are aware of, to a small core of fundamental laws and theories. A major goal of physics is to find the 'common ground' that would unite all of these into one integrated model of everything, in which all the other laws we know of would be special cases, and from which the behavior of all matter and energy can 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." (Feynman's lectures on Physics, Vol 1. 2-7)

Within this, the Standard Model is a grouping of two major theories – quantum electroweak and quantum chromodynamics – which provides an internally consistent theory describing interactions between all experimentally observed particles. Technically, quantum field theory provides the mathematical framework for the Standard Model. The Standard Model describes each type of particle in terms of a mathematical field. For a technical description of the fields and their interactions, see Standard model (basic details).

For ease of description, the Standard Model can be divided into three parts – covering particles of matter, force mediating particles, and the Higgs boson.

Particles of Matter

The matter particles described by the Standard Model all have an intrinsic property known as 'spin' whose value is determined to be 1/2. In Standard Model terms, this means that all matter particles are fermions. For this reason, they follow the Pauli exclusion principle in accordance with the spin-statistics theorem, and it is this which causes their 'material' quality.^{[citation needed]} Apart from their antiparticle partners, a total of twelve different types of matter particles are known and accounted for by the Standard Model. Six of these are classified as quarks (up, down, strange, charm, top and bottom), and the other six as leptons (electron, muon, tau, and their corresponding neutrinos).

Organization of Fermions
	Generation 1		Generation 2		Generation 3
Quarks	Up	$u\,$	Charm	$c\,$	Top	$t\,$
Quarks	Down	$d\,$	Strange	$s\,$	Bottom	$b\,$
Leptons	Electron Neutrino	$\nu_e\,$	Muon Neutrino	$\nu_\mu\,$	Tau Neutrino	$\nu_\tau\,$
Leptons	Electron	$e\,$	Muon	$\mu\,$	Tau	$\tau\,$

Matter particles (as do mediating particles) also carry various charges which make them susceptible to the fundamental forces, which are in turn mediated as described in the next subsection.

Each quark can carry any one of three color charges – red, green or blue, enabling them to participate in strong interactions.
The up-type quarks (up, charm, and top quarks) carry an electric charge of +2/3, and the down-type quarks (down, strange, and bottom) carry an electric charge of –1/3, enabling both types to participate in electromagnetic interactions.
Leptons do not carry any color charge – they are color neutral, preventing them from participating in strong interactions.
The electron-type leptons (the electron, the muon, and the tau lepton) carry an electric charge of –1, enabling them to participate in electromagnetic interactions.
The neutrino-type leptons (the electron neutrino, the muon neutrino and the tau neutrino) carry no electric charge, preventing them from participating in electromagnetic interactions
Both quarks and leptons carry a handful of flavor charges, including the weak isospin, enabling all particles to interact via the weak nuclear interaction.

Pairs from each group (one up-type quark, one down-type quark, a down-type lepton and its corresponding neutrino) form what is known as a 'generation'. The corresponding particles between each generation are identical to each other, with the exception of their mass and a property known as their flavor.

Force-Mediating Particles

Summary of interactions between particles described by the Standard Model.

Forces in physics are the ways that particles interact and influence each other. At a macro level, for example, the electromagnetic force allows particles to interact with, and via magnetic fields, and the force of gravitation allows two particles with mass to attract one another in accordance with Newton's Law of Gravitation. The standard model explains such forces as resulting from matter particles exchanging other particles, known as force-mediating particles. When a force-mediating particle is exchanged, at a macro 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. Force-mediating particles are believed to be the reason why the forces and interactions between particles observed in the laboratory and in the universe exist.

The known force-mediating particles described by the Standard Model also all have spin (as did matter particles), but in their case, the value of the spin is 1, meaning that all force-mediating particles are bosons. As a result, they do not follow the Pauli Exclusion Principle. The different types of force mediating particles 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 W⁺, W^–, and Z⁰ gauge bosons mediate the weak nuclear interactions between particles of different flavors (all quarks and leptons). They are massive, with the Z⁰ being more massive than the $W \pm$ . The weak interactions involving the $W \pm$ act on exclusively left-handed particles and not the left-handed antiparticles. Furthermore, the $W \pm$ carry an electric charge of +1 and –1 and couple to the electromagnetic interactions. The electrically neutral Z⁰ boson interacts with both left-handed particles and antiparticles. These three gauge bosons along with the photons are grouped together which collectively mediate the electroweak interactions.

The eight gluons mediate the strong nuclear interactions between color charged particles (the quarks). Gluons are massless. The eightfold multiplicity of gluons is labeled by a combinations of color and an anticolor charge (i.e., Red-anti-Green).^[1] Because the gluon has an effective color charge, they can 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 in the illustration immediately above and to the right.

Force Mediating Particles
Electromagnetic Force		Weak Nuclear Force		Strong Nuclear Force
Photon	$γ$	W⁺, W^-, and Z Gauge Bosons	$W +$ , $W -$ , $Z$	Gluons	$g$

The Higgs Boson

Main article: Higgs Boson

The Higgs particle is a hypothetical massive scalar elementary particle predicted by the Standard Model, and the only fundamental particle predicted by that model which has not fully been observed as yet. This is partly because it requires an exceptionally large amount of energy to create and observe under laboratory circumstances. It has no intrinsic spin, and thus (like the force-mediating particles) is also classified as a boson.

The Higgs Boson plays a unique role in the Standard Model, and a key role in explaining the origins of the mass of other elementary particles, in particular the difference between the massless photon and the very heavy W and Z bosons. Elementary particle masses, and the differences between electromagnetism (caused by the photon) and the weak force (caused by the W and Z bosons), are critical to many aspects of the structure of microscopic (and hence macroscopic) matter; thus, if it is proven to exist, the Higgs boson has an enormous effect on the world around us.

As of 2007, no experiment has directly detected the existence of the Higgs boson, but there is some indirect evidence for it. It is hoped that upon the completion of the Large Hadron Collider, experiments conducted at CERN would bring experimental evidence confirming the existence for the particle.

List of Standard Model Fermions

This table is based in part on data gathered by the Particle Data Group (QuarksPDF (54.8 KiB)).

**Left handed fermions in the Standard Model**
Generation 1
Fermion (left-handed)	Symbol	Electric charge	Weak isospin	Hypercharge	Color charge *	Mass **
Electron	$e^-\,$	$-1\,$	$-1/2\,$	$-1/2\,$	$\bold{1}\,$	511 keV
Positron	$e^+\,$	$+1\,$	$0\,$	$+1\,$	$\bold{1}\,$	511 keV
Electron-neutrino	$\nu_e\,$	$0\,$	$+1/2\,$	$-1/2\,$	$\bold{1}\,$	< 2 eV
Up quark	$u\,$	$+2/3\,$	$+1/2\,$	$+1/6\,$	$\bold{3}\,$	~ 3 MeV ***
Up antiquark	$\bar{u}\,$	$-2/3\,$	$0\,$	$-2/3\,$	$\bold{\bar{3}}\,$	~ 3 MeV ***
Down quark	$d\,$	$-1/3\,$	$-1/2\,$	$+1/6\,$	$\bold{3}\,$	~ 6 MeV ***
Down antiquark	$\bar{d}\,$	$+1/3\,$	$0\,$	$+1/3\,$	$\bold{\bar{3}}\,$	~ 6 MeV ***

Generation 2
Fermion (left-handed)	Symbol	Electric charge	Weak isospin	Hypercharge	Color charge *	Mass **
Muon	$\mu^-\,$	$-1\,$	$-1/2\,$	$-1/2\,$	$\bold{1}\,$	106 MeV
Antimuon	$\mu^+\,$	$+1\,$	$0\,$	$+1\,$	$\bold{1}\,$	106 MeV
Muon-neutrino	$\nu_\mu\,$	$0\,$	$+1/2\,$	$-1/2\,$	$\bold{1}\,$	< 2 eV
Charm quark	$c\,$	$+2/3\,$	$+1/2\,$	$+1/6\,$	$\bold{3}\,$	~ 1.3 GeV
Charm antiquark	$\bar{c}\,$	$-2/3\,$	$0\,$	$-2/3\,$	$\bold{\bar{3}}\,$	~ 1.3 GeV
Strange quark	$s\,$	$-1/3\,$	$-1/2\,$	$+1/6\,$	$\bold{3}\,$	~ 100 MeV
Strange antiquark	$\bar{s}\,$	$+1/3\,$	$0\,$	$+1/3\,$	$\bold{\bar{3}}\,$	~ 100 MeV

Generation 3
Fermion (left-handed)	Symbol	Electric charge	Weak isospin	Hypercharge	Color charge *	Mass **
Tau lepton	$\tau^-\,$	$-1\,$	$-1/2\,$	$-1/2\,$	$\bold{1}\,$	1.78 GeV
Anti-tau lepton	$\tau^+\,$	$+1\,$	$0\,$	$+1\,$	$\bold{1}\,$	1.78 GeV
Tau-neutrino	$\nu_\tau\,$	$0\,$	$+1/2\,$	$-1/2\,$	$\bold{1}\,$	< 2 eV
Top quark	$t\,$	$+2/3\,$	$+1/2\,$	$+1/6\,$	$\bold{3}\,$	171 GeV
Top antiquark	$\bar{t}\,$	$-2/3\,$	$0\,$	$-2/3\,$	$\bold{\bar{3}}\,$	171 GeV
Bottom quark	$b\,$	$-1/3\,$	$-1/2\,$	$+1/6\,$	$\bold{3}\,$	~ 4.2 GeV
Bottom antiquark	$\bar{b}\,$	$+1/3\,$	$0\,$	$+1/3\,$	$\bold{\bar{3}}\,$	~ 4.2 GeV
Notes: * These are not ordinary abelian charges, which can be added together, but are labels of group representations of Lie groups. Mass is really a coupling between a left-handed fermion and a right-handed fermion. For example, the mass of an electron is really a coupling between a left-handed electron and a right-handed electron, which is the antiparticle of a left-handed positron. Also neutrinos show large mixings in their mass coupling, so it's not accurate to talk about neutrino masses in the flavor basis or to suggest a left-handed electron neutrino. ***** The masses of baryons and hadrons and various cross-sections are the experimentally measured quantities. Since quarks can't be isolated because of QCD confinement, the quantity here is supposed to be the mass of the quark at the renormalization scale of the QCD scale.

Log plot of masses in the Standard Model.

Tests and predictions

The Standard Model predicted the existence of W and Z bosons, the gluon, the top quark and the charm quark before these particles had been observed. Their predicted properties were experimentally confirmed with good precision.

The Large Electron-Positron Collider at CERN tested various predictions about the decay of Z bosons, and found them confirmed.

To get an idea of the success of the Standard Model a comparison between the measured and the predicted values of some quantities are shown in the following table:

Quantity	Measured (GeV)	SM prediction (GeV)
Mass of W boson	80.398±0.025	80.3900±0.0180
Mass of Z boson	91.1876±0.0021	91.1874±0.0021

Challenges to the Standard Model

Unsolved problems in physics: Parameters in the Standard Model: What gives rise to the Standard Model of particle physics? Why do its particle masses and coupling constants possess the values we have measured? Does the Higgs boson predicted by the model really exist? Why are there three generations of particles in the Standard Model?

The Standard Model of particle physics has been empirically determined through experiments over the past fifty years. Currently the Standard Model predicts that there is one more particle to be discovered, the Higgs boson. One of the reasons for building the Large Hadron Collider is that the increase in energy is expected to make the Higgs observable. However, as of 2007 there are only indirect experimental indications for the existence of the Higgs boson and it can not be claimed to be found.

The Standard Model is as yet unable to explain gravity in terms of particles.

There has been a great deal of both theoretical and experimental research exploring whether the Standard Model could be extended into a complete theory of everything. This area of research is often described by the term 'Beyond the Standard Model'. There are several facets of this question. For example, one line of inquiry attempts to explore why there are seemingly so many unrelated parameters of the theory – 29 in all. Research also focusses on the Hierarchy problem (why the weak scale and Planck scale are so disparate), and attempts to reconcile the emerging Standard Model of Cosmology with the Standard Model of particle physics. Many questions relate to the initial conditions that led to the presently observed Universe. Examples include: Why is there a matter/antimatter asymmetry? Why is the Universe isotropic and homogeneous at large distances?

The anthropic principle

Some claim that the vast majority of possible values for the parameters of the Standard Model are incompatible with the existence of life (see fine-tuned universe for more details).^[2] According to arguments based on the anthropic principle, the Standard Model in our universe has the parameters it has because the universe has to be based upon parameters able to support life, in order for life to emerge able to ask the question. Since we know life has emerged, the choice of universal parameters is not unrestricted, but is ipso facto limited to being selected from choices of parameters where life could emerge. In theory (goes the anthropic principle) there could be a hundred billion universes where life as we know it could not emerge, because of having parameters where life as we know it was not possible. (See also Conditional probability.)

Some physicists argue that if we knew the String theory landscape of possible theories and prior distribution of these theories and also know the probability that any given theory will give rise to life, we would be able to make a statistical prediction of the parameters of the Standard Model.^[2] Other physicists point out that it is difficult to see how you can predict the probability of life from any given theory. How can we know what kinds of life are possible?

Notes

^ 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.
^ ^a ^b V. Agrawal, S.M. Barr, J.F. Donoghue, D. Seckel (1998). "The anthropic principle and the mass scale of the Standard Model". Physical Review D 57 (9): 5480 - 5492.

References

Introductory textbooks

Griffiths, David J. (1987). Introduction to Elementary Particles. Wiley, John & Sons, Inc. ISBN 0-471-60386-4.

D.A. Bromley (2000). Gauge Theory of Weak Interactions. Springer. ISBN 3-540-67672-4.

Gordon L. Kane (1987). Modern Elementary Particle Physics. Perseus Books. ISBN 0-201-11749-5.

Advanced textbooks

Cheng, Ta Pei; Li, Ling Fong. Gauge theory of elementary particle physics. Oxford University Press. ISBN 0-19-851961-3.

— introduction to all aspects of gauge theories and the Standard Model.

Donoghue, J. F.; Golowich, E.; Holstein, B. R.. Dynamics of the Standard Model. Cambridge University Press. ISBN 0-521-47625-6.

— highlights dynamical and phenomenological aspects of the Standard Model.

O'Raifeartaigh, L.. Group structure of gauge theories. Cambridge University Press. ISBN 0-521-34785-8.

— highlights group-theoretical aspects of the Standard Model.

Journal articles

S.F. Novaes, Standard Model: An Introduction, hep-ph/0001283
D.P. Roy, Basic Constituents of Matter and their Interactions — A Progress Report, hep-ph/9912523
Y. Hayato et al., Search for Proton Decay through p → νK⁺ in a Large Water Cherenkov Detector. Phys. Rev. Lett. 83, 1529 (1999).
Ernest S. Abers and Benjamin W. Lee, Gauge theories. Physics Reports (Elsevier) C9, 1-141 (1973).

External links

General subfields within physics
Classical mechanics · Electromagnetism · Thermodynamics · Statistical mechanics · Quantum mechanics · Relativity · High energy physics · Condensed matter physics · Atomic, molecular, and optical physics

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