Standard Model

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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

1 The Standard Model
2 Tests and predictions
3 Challenges to the Standard Model
4 The anthropic principle
5 See also
6 Notes
7 References
- 7.1 Textbooks
- 7.2 Journal Articles
8 External links

[edit] The Standard Model

It is understood that the entire dynamics of the universe can be explained in terms of matter and by the forces that act on it. For pedagogical purposes, in this article, the Standard Model is divided in a similar manner: ordinary matter particles (fermions), force mediating particles (bosons), and the Higgs particle (also a boson).

Technically, quantum field theory provides the mathematical framework for the Standard Model. Consequently, each type of particle is described in terms of a mathematical field. For a technical description of the fields and their interactions, see Standard model (basic details).

[edit] Particles of Ordinary Matter

The matter particles described by the Standard Model all have an intrinsic spin whose value is determined to be 1/2, making them fermions. For this reason, they follow the Pauli Exclusion Principle. Apart from their antiparticle partners, a total of twelve different matter particles are known as of early 2007. 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 Quark	( $u\,$ )	Charm Quark	( $c\,$ )	Top Quark	( $t\,$ )
Quarks	Down Quark	( $d\,$ )	Strange Quark	( $s\,$ )	Bottom Quark	( $b\,$ )
Leptons	Electron Neutrino	( $\nu_e\,$ )	Muon Neutrino	( $\nu_\mu\,$ )	Tau Neutrino	( $\nu_\tau\,$ )
Leptons	Electron	( $e\,$ )	Muon	( $\mu\,$ )	Tau Lepton	( $\tau\,$ )

These particles carry charges which make them susceptible to the fundamental forces (described in the next subsection).

Each quark carries 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 down-type leptons (the electron, the muon, and the tau lepton) carry an electric charge of –1, enabling them to participate in electromagnetic interactions.
The up–type leptons (the neutrinos) carry no electric charge, preventing them from participating in electromagnetic interactions
Both, quarks and leptons carry a handful of flavor charges (see flavor), 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 quarks, a lepton and its corresponding neutrino) form a generation. Corresponding particles between each generation are identical to each other apart from their masses and flavors.

[edit] Spin and Chirality

Main article: Spin (physics)

All particles in the Standard Model have an intrinsic spin, allowing us to roughly visualize each particle as a miniature top spinning in space. Technically, we associate a quantum number to this property called spin, and is fixed for all matter particles (quarks and leptons, alike) at 1/2. Hence, all the particles carry the same internal angular momentum. The spin of all particles is described by a vector, $\mathbf{s}$ , with cartesian components $(s_x,\,s_y,\,s_z)$ whose length never changes. At length scales dominated by quantum mechanics, the orientation of the spin is limited in a very non-intuitive way. The component of $\mathbf{s}$ along any given direction (say, along the x-axis) is limited to take on one of two values: $s_x=+\textstyle\frac{1}{2}\hbar$ , in which case the particle is said to be "spin-up in the x-direction", or $s_x=\textstyle-\frac{1}{2}\hbar$ , in which case is "spin-down." Here, $\hbar$ is Planck's constant — a very tiny unit of angular momentum. Even more bizarre is that despite this limitation, any component of $\mathbf{s}$ may be in a mixture (superposition) between the spin-up case and the spin-down case. Only probing the particle would cause the value of the x-component of the spin to snap to exclusively one of the two allowed values.

There is nothing special about the x-, y- and the z-axis. In principle and in practice, one may be interested in the component of spin along a direction that lies between the x- and y-axis, or between the x- and z- axis, or between all three axis. The allowed values are still limited to $+\textstyle\frac{1}{2}\hbar$ and $-\textstyle\frac{1}{2}\hbar$ . Physicists are often interested in the particle's spin along its momentum, $p$ (direction of motion). The component of spin along the particle's momentum is chirality. As usual, a particles chirality are limited to $s_\mathbf{p}=+\textstyle\frac{1}{2}\hbar$ , in which case the particle is right-handed, or $s_\mathbf{p}=-\textstyle\frac{1}{2}\hbar$ , in which case the particle is left-handed. An understanding of chirality is crucial to understand the selective nature of the weak nuclear force.

[edit] Force Mediating Particles

Summary of interactions between particles described by the Standard Model.

The force mediating particles described by the Standard Model all have an intrinsic spin whose value is 1, making them bosons. As a result, they do not follow the Pauli Exclusion Principle. The different types of force mediating particles are described below.

The photons mediate the familiar electromagnetic force between electrically charged particles (these are the quarks, electrons, muons, tau, W⁺ and W^–). They are massless and are 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 equally massive W⁺ and W^–. An interesting feature of the weak force is that interactions involving the W⁺ and W^– gauge bosons act on exclusively left-handed particles (those particles whose chirality is $s_\mathbf{p}=-\textstyle\frac{1}{2}\hbar$ ). The right-handed particles are completely neutral to the W bosons. Furthermore, the W⁺ and W^– bosons carry an electric charge of +1 and –1 making those susceptible to electromagnetic interactions. The electrically neutral Z⁰ boson acts on particles of both chiralities, but preferentially on left-handed ones. The weak nuclear interaction is unique in that it is the only one that selectively acts on particles of different chiralities; the photons of electromagnetism and the gluons of the strong force act on particles without such prejudice. 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). They are massless. But, each of the eight carry combinations of color and an anticolor charge^[1] enabling them to 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 Z⁰ Gauge Bosons	$W +$ , $W -$ , $Z 0$	Gluons	$g$

[edit] The Higgs Boson

Main article: Higgs Boson

The Higgs particle described by the Standard Model has no intrinsic spin, and thus is also classified as a boson. As of February 2007, the experimental evidence for the Higgs boson has not been found; so far it is a theoretical particle. 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.

The Higgs boson plays a unique role in the Standard Model.

[edit] Table [1]

**Left handed fermions in the Standard Model**
Generation 1
Fermion (left-handed)	Symbol	Electric charge	Weak charge *	Weak isospin	Hypercharge	Color charge *	Mass **
Electron	$e\,$	$-1\,$	$\bold{2}\,$	$-1/2\,$	$-1/2\,$	$\bold{1}\,$	0.510999 MeV
Electron-neutrino	$\nu_e\,$	$0\,$	$\bold{2}\,$	$+1/2\,$	$-1/2\,$	$\bold{1}\,$	< 2 eV
Positron	$\bar{e}\,$	$+1\,$	$\bold{1}\,$	$0\,$	$+1\,$	$\bold{1}\,$	0.510999 MeV
Electron-antineutrino	$\bar{\nu_e}\,$	$0\,$	$\bold{1}\,$	$0\,$	$0\,$	$\bold{1}\,$	< 2 eV
Up quark	$u\,$	$+2/3\,$	$\bold{2}\,$	$+1/2\,$	$+1/6\,$	$\bold{3}\,$	~ 3 MeV ***
Down quark	$d\,$	$-1/3\,$	$\bold{2}\,$	$-1/2\,$	$+1/6\,$	$\bold{3}\,$	~ 6 MeV ***
Anti-up antiquark	$\bar{u}\,$	$-2/3\,$	$\bold{1}\,$	$0\,$	$-2/3\,$	$\bold{\bar{3}}\,$	~ 3 MeV ***
Anti-down antiquark	$\bar{d}\,$	$+1/3\,$	$\bold{1}\,$	$0\,$	$+1/3\,$	$\bold{\bar{3}}\,$	~ 6 MeV ***

Generation 2
Fermion (left-handed)	Symbol	Electric charge	Weak charge *	Weak isospin	Hypercharge	Color charge *	Mass **
Muon	$\mu\,$	$-1\,$	$\bold{2}\,$	$-1/2\,$	$-1/2\,$	$\bold{1}\,$	105.658 MeV
Muon-neutrino	$\nu_\mu\,$	$0\,$	$\bold{2}\,$	$+1/2\,$	$-1/2\,$	$\bold{1}\,$	< 2 eV
Antimuon	$\bar{\mu}\,$	$+1\,$	$\bold{1}\,$	$0\,$	$+1\,$	$\bold{1}\,$	105.658 MeV
Muon-antineutrino	$\bar{\nu_\mu}\,$	$0\,$	$\bold{1}\,$	$0\,$	$0\,$	$\bold{1}\,$	< 2 eV
Charm quark	$c\,$	$+2/3\,$	$\bold{2}\,$	$+1/2\,$	$+1/6\,$	$\bold{3}\,$	~ 1.3 GeV
Strange quark	$s\,$	$-1/3\,$	$\bold{2}\,$	$-1/2\,$	$+1/6\,$	$\bold{3}\,$	~ 100 MeV
Anti-charm antiquark	$\bar{c}\,$	$-2/3\,$	$\bold{1}\,$	$0\,$	$-2/3\,$	$\bold{\bar{3}}\,$	~ 1.3 GeV
Anti-strange antiquark	$\bar{s}\,$	$+1/3\,$	$\bold{1}\,$	$0\,$	$+1/3\,$	$\bold{\bar{3}}\,$	~ 100 MeV

Generation 3
Fermion (left-handed)	Symbol	Electric charge	Weak charge *	Weak isospin	Hypercharge	Color charge *	Mass **
Tau lepton	$\tau\,$	$-1\,$	$\bold{2}\,$	$-1/2\,$	$-1/2\,$	$\bold{1}\,$	1.777 GeV
Tau-neutrino	$\nu_\tau\,$	$0\,$	$\bold{2}\,$	$+1/2\,$	$-1/2\,$	$\bold{1}\,$	< 2 eV
Anti-tau lepton	$\bar{\tau}\,$	$+1\,$	$\bold{1}\,$	$0\,$	$+1\,$	$\bold{1}\,$	1.777 GeV
Tau-antineutrino	$\bar{\nu_\tau}\,$	$0\,$	$\bold{1}\,$	$0\,$	$0\,$	$\bold{1}\,$	< 2 eV
Top quark	$t\,$	$+2/3\,$	$\bold{2}\,$	$+1/2\,$	$+1/6\,$	$\bold{3}\,$	171.4 GeV
Bottom quark	$b\,$	$-1/3\,$	$\bold{2}\,$	$-1/2\,$	$+1/6\,$	$\bold{3}\,$	~ 4.2 GeV
Anti-top antiquark	$\bar{t}\,$	$-2/3\,$	$\bold{1}\,$	$0\,$	$-2/3\,$	$\bold{\bar{3}}\,$	170.9 GeV
Anti-bottom antiquark	$\bar{b}\,$	$+1/3\,$	$\bold{1}\,$	$0\,$	$+1/3\,$	$\bold{\bar{3}}\,$	~ 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 and a right-handed electron neutrino have the same mass as this table seems to suggest. ***** - What is actually measured experimentally are the masses of baryons and hadrons and various cross-sections. 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 phase transition. In order to compute this quantity, physicists have to compute the hadron spectrum using lattice gauge theory and try out various masses for the quarks until the model comes up with a close fit with experimental data. Since the masses of the first-generation quarks are significantly below the QCD scale, the uncertainties are pretty large. In fact, current lattice QCD models seem to suggest a significantly lower mass of these quarks from that of this table.

Log plot of masses in the Standard Model.

[edit] 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

[edit] 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? Is the Standard Model a good approximation to reality, or is it fatally flawed?

There is no experimental indication yet for the existence of the Higgs boson.

Although the Standard Model has had great success in explaining experimental results, it has two important defects:

1 - The model contains 19 free parameters, such as particle masses, which must be determined experimentally. Another 10 parameters are needed to include neutrino masses. These parameters cannot be independently calculated.

2 - Alain Connes has shown that the standard model can be derived from general relativity by generalizing Riemannian geometry to noncommutative geometry. The noncommutative standard model has fewer free parameters than the conventional one. However, despite the fact that noncommutative geometry is formulated in the language of quantum mechanics, quantum field theories in noncommutative geometries are still an open problem.

Since the completion of the Standard Model, many efforts have been made to address the first of these problems.

One attempt to address the first defect is known as grand unification. The so-called grand unified theories (GUTs) hypothesized that the SU(3), SU(2), and U(1) groups are actually subgroups of a single large symmetry group. At high energies (far beyond the reach of current experiments), the symmetry of the unifying group is preserved; at low energies, it reduces to SU(3)×SU(2)×U(1) by a process known as spontaneous symmetry breaking. The first theory of this kind was proposed in 1974 by Georgi and Glashow, using SU(5) as the unifying group. A distinguishing characteristic of these GUTs is that, unlike the Standard Model, they predict the existence of proton decay. In 1999, the Super-Kamiokande neutrino observatory reported that it had not detected proton decay, establishing a lower limit on the proton half-life of 6.7× 10³² years. This and other experiments have falsified numerous GUTs, including SU(5). Another effort to address the first defect has been to develop preon models which attempt to set forth a substructure of more fundamental particles than those set forth in the Standard Model.

In addition, there are cosmological reasons why the Standard Model is believed to be incomplete. In the Standard Model, matter and antimatter are related by the CPT symmetry, which suggests that there should be equal amounts of matter and antimatter after the Big Bang. While the preponderance of matter in the universe can be explained by saying that the universe just started out this way, this explanation strikes most physicists as inelegant. Furthermore, the Standard Model provides no mechanism to generate the cosmic inflation that is believed to have occurred at the beginning of the universe.

The Higgs boson, which is predicted by the Standard Model, has not been observed as of 2007 (though some phenomena were observed in the last days of the LEP collider that could be related to the Higgs). One of the reasons for building the Large Hadron Collider is that the increase in energy is expected to make the Higgs observable.

The first experimental deviation from the Standard Model (as proposed in the 1970's) came in 1998, when Super-Kamiokande published results indicating neutrino oscillation. Under the Standard Model, a massless neutrino cannot oscillate, so this observation implied the existence of non-zero neutrino masses. It was therefore necessary to revise the Standard Model to allow neutrinos to have mass; this may be simply achieved by adding 10 more free parameters beyond the initial 19.

A further extension of the Standard Model can be found in the theory of supersymmetry, which proposes a massive supersymmetric "partner" for every particle in the conventional Standard Model. Supersymmetric particles have been suggested as a candidate for explaining dark matter. Although supersymmetric particles have not been observed experimentally to date, the theory is one of the most popular avenues of research in theoretical particle physics.

[edit] 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 has the field content it does and the parameters it has because these are the values that are likely to give rise to the existence of lifeforms intelligent enough to be self-aware. Some physicists argue that if we knew the 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]

[edit] See also

The theoretical formulation of the standard model
Weak interactions, Fermi theory of beta decay and electroweak theory
Strong interactions, flavour, quark model and quantum chromodynamics
For open questions, see quark matter, CP violation and neutrino masses
Beyond the Standard Model
noncommutative standard model

[edit] 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.

[edit] References

[edit] 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.

[edit] 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).
J. Hucks, Global structure of the standard model, anomalies, and charge quantization, Phys. Rev. D 43, 2709–2717 (1991). [2]

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