# Standard Model

Template:Quantum field theory The Standard Model of particle physics is a theory that describes three of the four known fundamental interactions between the elementary particles that make up all matter. It unifies the electroweak theory and quantum chromodynamics into a structure denoted by the gauge groups SU(3)×SU(2)×U(1). It is a quantum field theory 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 eighteen numerical parameters (such as masses and coupling constants) that must be put "by hand" into the theory (rather than being derived from first principles).

## Historical background

The formulation of the unification of the electromagnetic and weak interactions in the Standard Model is due to Steven Weinberg, Abdus Salam and, subsequently, Sheldon Glashow. The unification model was initially proposed by Steven Weinberg in 1967,[1] and completed integrating it with the proposal by Peter Higgs of spontaneous symmetry breaking[2][3][4] which gives origin to the masses of all particles described in the model.

After the discovery, made at CERN of the existence of neutral weak currents,[5][6][7][8] mediated by the [[Z boson|Template:SubatomicParticle boson]], foreseen in the Standard Model, Glashow, Salam, and Weinberg received the Nobel Prize in physics in 1979.

## Overview

File:Particle chart.svg

This image is a candidate for speedy deletion. It will be deleted after Thursday, 15 May 2008.

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)

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 (mathematical formulation).

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 ½, i.e. 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, charm, strange, 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
Template:SubatomicParticle Charm
Template:SubatomicParticle Top
Template:SubatomicParticle
Down
Template:SubatomicParticle Strange
Template:SubatomicParticle Bottom
Template:SubatomicParticle
Leptons Electron
Neutrino
Template:SubatomicParticle Muon
Neutrino
Template:SubatomicParticle Tau
Neutrino
Template:SubatomicParticle
Electron Template:SubatomicParticle Muon Template:SubatomicParticle Tau
Template:SubatomicParticle

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

File:Elementary particle interactions.svg
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, the electromagnetic force allows particles to interact with one another 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 do 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 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 an anticolor charge (e.g., Red-anti-Green).[9] 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 Template:SubatomicParticle Template:SubatomicParticle, Template:SubatomicParticle, and Template:SubatomicParticle<br\> Gauge Bosons Template:SubatomicParticle, Template:SubatomicParticle, Template:SubatomicParticle Gluons Template:SubatomicParticle

### The 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 been directly 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, which also have integral spin) 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. In electroweak theory it generates the masses of the massive leptons (electron, muon and tau); and also of the quarks.

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 of the particle.

Science, a journal of original scientific research, has reported: "...experimenters may have already overlooked a Higgs particle, argues theorist Chien-Peng Yuan of Michigan State University in East Lansing and his colleagues. They considered the simplest possible supersymmetric theory. Ordinarily, theorists assume that the lightest of theory's five Higgses is the one that drags on the W and Z. Those interactions then feed back on Higgs and push its mass above 121 times the mass of the proton, the highest mass searched for at CERN's Large Electron-Positron (LEP) collider, which ran from 1989 to 2000. But it's possible that the lightest Higgs weighs as little as 65 times the mass of a proton and has been missed, Yuan and colleagues argue in a paper to be published in Physical Review Letters`."[10]

### 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
Weak
hypercharge
Color
charge
*
Mass **
Electron ${\displaystyle e^{-}\,}$ ${\displaystyle -1\,}$ ${\displaystyle -1/2\,}$ ${\displaystyle -1\,}$ ${\displaystyle {\mathbf {1}}\,}$ 511 keV
Positron ${\displaystyle e^{+}\,}$ ${\displaystyle +1\,}$ ${\displaystyle 0\,}$ ${\displaystyle +2\,}$ ${\displaystyle {\mathbf {1}}\,}$ 511 keV
Electron-neutrino ${\displaystyle \nu _{e}\,}$ ${\displaystyle 0\,}$ ${\displaystyle +1/2\,}$ ${\displaystyle -1\,}$ ${\displaystyle {\mathbf {1}}\,}$ < 2 eV ****
Up quark ${\displaystyle u\,}$ ${\displaystyle +2/3\,}$ ${\displaystyle +1/2\,}$ ${\displaystyle +1/3\,}$ ${\displaystyle {\mathbf {3}}\,}$ ~ 3 MeV ***
Up antiquark ${\displaystyle {\bar {u}}\,}$ ${\displaystyle -2/3\,}$ ${\displaystyle 0\,}$ ${\displaystyle -4/3\,}$ ${\displaystyle {\mathbf {\bar {3}}}\,}$ ~ 3 MeV ***
Down quark ${\displaystyle d\,}$ ${\displaystyle -1/3\,}$ ${\displaystyle -1/2\,}$ ${\displaystyle +1/3\,}$ ${\displaystyle {\mathbf {3}}\,}$ ~ 6 MeV ***
Down antiquark ${\displaystyle {\bar {d}}\,}$ ${\displaystyle +1/3\,}$ ${\displaystyle 0\,}$ ${\displaystyle +2/3\,}$ ${\displaystyle {\mathbf {\bar {3}}}\,}$ ~ 6 MeV ***

Generation 2
Fermion
(left-handed)
Symbol Electric
charge
Weak
isospin
Weak
hypercharge
Color
charge *
Mass **
Muon ${\displaystyle \mu ^{-}\,}$ ${\displaystyle -1\,}$ ${\displaystyle -1/2\,}$ ${\displaystyle -1\,}$ ${\displaystyle {\mathbf {1}}\,}$ 106 MeV
Antimuon ${\displaystyle \mu ^{+}\,}$ ${\displaystyle +1\,}$ ${\displaystyle 0\,}$ ${\displaystyle +2\,}$ ${\displaystyle {\mathbf {1}}\,}$ 106 MeV
Muon-neutrino ${\displaystyle \nu _{\mu }\,}$ ${\displaystyle 0\,}$ ${\displaystyle +1/2\,}$ ${\displaystyle -1\,}$ ${\displaystyle {\mathbf {1}}\,}$ < 2 eV ****
Charm quark ${\displaystyle c\,}$ ${\displaystyle +2/3\,}$ ${\displaystyle +1/2\,}$ ${\displaystyle +1/3\,}$ ${\displaystyle {\mathbf {3}}\,}$ ~ 1.3 GeV
Charm antiquark ${\displaystyle {\bar {c}}\,}$ ${\displaystyle -2/3\,}$ ${\displaystyle 0\,}$ ${\displaystyle -4/3\,}$ ${\displaystyle {\mathbf {\bar {3}}}\,}$ ~ 1.3 GeV
Strange quark ${\displaystyle s\,}$ ${\displaystyle -1/3\,}$ ${\displaystyle -1/2\,}$ ${\displaystyle +1/3\,}$ ${\displaystyle {\mathbf {3}}\,}$ ~ 100 MeV
Strange antiquark ${\displaystyle {\bar {s}}\,}$ ${\displaystyle +1/3\,}$ ${\displaystyle 0\,}$ ${\displaystyle +2/3\,}$ ${\displaystyle {\mathbf {\bar {3}}}\,}$ ~ 100 MeV

Generation 3
Fermion
(left-handed)
Symbol Electric
charge
Weak
isospin
Weak
hypercharge
Color
charge *
Mass **
Tau lepton ${\displaystyle \tau ^{-}\,}$ ${\displaystyle -1\,}$ ${\displaystyle -1/2\,}$ ${\displaystyle -1\,}$ ${\displaystyle {\mathbf {1}}\,}$ 1.78 GeV
Anti-tau lepton ${\displaystyle \tau ^{+}\,}$ ${\displaystyle +1\,}$ ${\displaystyle 0\,}$ ${\displaystyle +2\,}$ ${\displaystyle {\mathbf {1}}\,}$ 1.78 GeV
Tau-neutrino ${\displaystyle \nu _{\tau }\,}$ ${\displaystyle 0\,}$ ${\displaystyle +1/2\,}$ ${\displaystyle -1\,}$ ${\displaystyle {\mathbf {1}}\,}$ < 2 eV ****
Top quark ${\displaystyle t\,}$ ${\displaystyle +2/3\,}$ ${\displaystyle +1/2\,}$ ${\displaystyle +1/3\,}$ ${\displaystyle {\mathbf {3}}\,}$ 171 GeV
Top antiquark ${\displaystyle {\bar {t}}\,}$ ${\displaystyle -2/3\,}$ ${\displaystyle 0\,}$ ${\displaystyle -4/3\,}$ ${\displaystyle {\mathbf {\bar {3}}}\,}$ 171 GeV
Bottom quark ${\displaystyle b\,}$ ${\displaystyle -1/3\,}$ ${\displaystyle -1/2\,}$ ${\displaystyle +1/3\,}$ ${\displaystyle {\mathbf {3}}\,}$ ~ 4.2 GeV
Bottom antiquark ${\displaystyle {\bar {b}}\,}$ ${\displaystyle +1/3\,}$ ${\displaystyle 0\,}$ ${\displaystyle +2/3\,}$ ${\displaystyle {\mathbf {\bar {3}}}\,}$ ~ 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 antineutrino.
• *** 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.
• **** The Standard Model assumes that neutrinos are massless. Despite it several contemporary experiments prove that neutrinos oscillate between their flavour states and it wouldn't happen if they were all massless. [11] It is straightforward to extend the model to fit these data but there is plenty of possibilities and the mass eigenstates are still an open question. See Neutrino#Mass.
File:Particle chart Log.svg
Log plot of masses in the Standard Model.

## Tests and predictions

Template:Refimprovesect 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

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 – 21 in all (18 parameters in the core theory, plus G, c and h; there are believed to be an additional 7 or 8 parameters required for the neutrino masses although neutrino masses are outside the standard model and the details are unclear). Research also focuses 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?

## Notes

1. S. Weinberg Phys. Rev.Lett. 19 1264-1266 (1967).
2. P. W. Higgs Phys. Lett. 12 132 (1964), Broken Symmetries, Massless Particles and Gauge Fields
3. P. W. Higgs Phys. Rev. Lett. 13 508 (1964), Broken Symmetries and the Masses of Gauge Bosons
4. "Peter Higgs: the man behind the boson". Physicsworld.com. 2004-07-10. Retrieved 2008-05-08.
5. F. J. Hasert et al. Phys. Lett. 46B 121 (1973).
6. F. J. Hasert et al. Phys. Lett. 46B 138 (1973).
7. F. J. Hasert et al. Nucl. Phys. B73 1(1974).
8. "The discovery of the weak neutral currents". CERN courier. 2004-10-04. Retrieved 2008-05-08.
9. 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.
10. "Higgs Hiding in Plain Sight?". ScienceNOW. 2008-01-23. Retrieved 2008-05-08.

## 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.

• 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 978-0521476522.
— 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).