Standard Model

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The Standard Model of particle physics is a theory which describes the strong, weak, and electromagnetic fundamental forces, as well as the fundamental particles that make up all matter. Developed between 1970 and 1973, it is a quantum field theory, and 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 is not a complete theory of fundamental interactions, primarily because it does not describe the gravitational force.

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The Standard Model

The Standard Model contains both fermionic and bosonic fundamental particles. Fermions are particles which possess half-integer spin and obey the Pauli exclusion principle, which states that no fermions can share the same quantum state. Bosons possess integer spin and do not obey the Pauli exclusion principle. Informally speaking, fermions are particles of matter and bosons are particles that transmit forces. For a detailed description of the differences between fermions and bosons, see the article on identical particles.

In the Standard Model, the theory of the electroweak interaction (which describes the weak and electromagnetic interactions) is combined with the theory of quantum chromodynamics. All of these theories are gauge theories, meaning that they model the forces between fermions by coupling them to bosons which mediate (or "carry") the forces. The Lagrangian of each set of mediating bosons is invariant under a transformation called a gauge transformation, so these mediating bosons are referred to as gauge bosons. The bosons in the Standard Model are: Template:Unsolved

It turns out that the gauge transformations of the gauge bosons can be exactly described using a unitary group called a "gauge group". The gauge group of the strong interaction is SU(3), and the gauge group of the electroweak interaction is SU(2)×U(1). Therefore, the Standard Model is often referred to as SU(3)×SU(2)×U(1). The Higgs boson is the only boson in the theory which is not a gauge boson. The Higgs has never been observed in experiments, and finding it is a major goal of experimental particle physics today. Gravitons, the bosons believed to mediate the gravitational interaction, are not accounted for in the Standard Model.

There are twelve different types, or "flavours", of fermions in the Standard Model. The proton, neutron are made up of two of these: the up quark and down quark, bound together by the strong nuclear force. Together with the electron (bound to the nucleus in atoms by the electromagnetic force), those fermions constitute the vast majority of everyday matter. All of the fundamental fermions in the Standard Model are given in the table.

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Table

Left handed fermions in the Standard Model
Generation 1
Fermion (Left-handed) Symbol Electric charge Weak charge* Weak isospin Hypercharge Color charge* Mass**
Electron <math>e</math> −1 <math>\bold{2}</math> −1/2 −1/2 <math>\bold{1}</math> 0.511 MeV
Electron neutrino <math>\nu_e</math> 0 <math>\bold{2}</math> +1/2 −1/2 <math>\bold{1}</math> < 50 eV
Positron <math>e^c</math> +1 <math>\bold{1}</math> 0 +1 <math>\bold{1}</math> 0.511 MeV
Electron antineutrino <math>\nu_e^c</math> 0 <math>\bold{1}</math> 0 0 <math>\bold{1}</math> < 50 eV
Up quark <math>u</math> +2/3 <math>\bold{2}</math> +1/2 +1/6 <math>\bold{3}</math> ~5 MeV ***
Down quark <math>d</math> −1/3 <math>\bold{2}</math> −1/2 +1/6 <math>\bold{3}</math> ~10 MeV ***
Anti-up antiquark <math>u^c</math> −2/3 <math>\bold{1}</math> 0 −2/3 <math>\bold{\bar{3}}</math> ~5 MeV ***
Anti-down antiquark <math>d^c</math> +1/3 <math>\bold{1}</math> 0 +1/3 <math>\bold{\bar{3}}</math> ~10 MeV ***
 
Generation 2
Fermion (Left-handed) Symbol Electric charge Weak charge* Weak isospin Hypercharge Color charge* Mass**
Muon <math>\mu</math> −1 <math>\bold{2}</math> −1/2 −1/2 <math>\bold{1}</math> 105.6 MeV
Muon neutrino <math>\nu_\mu</math> 0 <math>\bold{2}</math> +1/2 −1/2 <math>\bold{1}</math> < 0.5 MeV
Anti-Muon <math>\mu^c</math> +1 <math>\bold{1}</math> 0 +1 <math>\bold{1}</math> 105.6 MeV
Muon antineutrino <math>\nu_\mu^c</math> 0 <math>\bold{1}</math> 0 0 <math>\bold{1}</math> < 0.5 MeV
Charm quark <math>c</math> +2/3 <math>\bold{2}</math> +1/2 +1/6 <math>\bold{3}</math> ~1.5 GeV
Strange quark <math>s</math> −1/3 <math>\bold{2}</math> −1/2 +1/6 <math>\bold{3}</math> ~100 MeV
Anti-charm antiquark <math>c^c</math> −2/3 <math>\bold{1}</math> 0 −2/3 <math>\bold{\bar{3}}</math> ~1.5 GeV
Anti-strange antiquark <math>s^c</math> +1/3 <math>\bold{1}</math> 0 +1/3 <math>\bold{\bar{3}}</math> ~100 MeV
 
Generation 3
Fermion (Left-handed) Symbol Electric charge Weak charge* Weak isospin Hypercharge Color charge* Mass**
Tau lepton <math>\tau</math> −1 <math>\bold{2}</math> −1/2 −1/2 <math>\bold{1}</math> 1.784 GeV
Tau neutrino <math>\nu_\tau</math> 0 <math>\bold{2}</math> +1/2 −1/2 <math>\bold{1}</math> < 70 MeV
Anti-Tau <math>\tau^c</math> +1 <math>\bold{1}</math> 0 +1 <math>\bold{1}</math> 1.784 GeV
Tau antineutrino <math>\nu_\tau^c</math> 0 <math>\bold{1}</math> 0 0 <math>\bold{1}</math> < 70 MeV
Top quark <math>t</math> +2/3 <math>\bold{2}</math> +1/2 +1/6 <math>\bold{3}</math> 173 GeV
Bottom quark <math>b</math> −1/3 <math>\bold{2}</math> −1/2 +1/6 <math>\bold{3}</math> ~4.7 GeV
Anti-top antiquark <math>t^c</math> −2/3 <math>\bold{1}</math> 0 −2/3 <math>\bold{\bar{3}}</math> 173 GeV
Anti-bottom antiquark <math>b^c</math> +1/3 <math>\bold{1}</math> 0 +1/3 <math>\bold{\bar{3}}</math> ~4.7 GeV

* - 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.

Image:Particle chart Log.jpg

The fermions can be arranged in three generations, the first one consisting of the electron, the up and down quarks, and the electron neutrino. All ordinary matter is made from first-generation particles; the higher-generation particles decay quickly into the first-generation ones and can only be generated for a short time in high-energy experiments. The reason for arranging them in generations is that the four fermions in each generation behave almost exactly like their counterparts in the other generations; the only difference is in their masses. For example, the electron and the muon both have half-integer spin, unit electric charge and do not participate in the strong interaction, but the muon is about 200 times more massive than the electron.

The electron and the electron neutrino, and their counterparts in the other generations, are called "leptons". Unlike the quarks, they do not possess a quality called "color", and their interactions are only weak and electromagnetic, and fall off with distance. On the other hand, the strong or "color" force between quarks gets stronger with distance, so that quarks are always found in colorless combinations called hadrons, a phenomenon known as quark confinement. These colorless combinations are either fermionic baryons composed of three quarks (the proton and neutron being the most familiar example) or bosonic mesons composed of a quark-antiquark pair (such as pions). The mass of such aggregates exceeds that of the components due to their binding energy.

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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:

Quality Measured (GeV) SM prediction (GeV)
Mass of W boson 80.4120±0.0420 80.3900±0.0180
Mass of Z boson 91.1876±0.002191.1874±0.0021
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Challenges to the Standard Model

Although the Standard Model has had great success in explaining experimental results, it cannot be a complete theory of fundamental physics. This is because it has two important defects:

  1. The model contains 19 free parameters, such as particle masses, which must be determined experimentally (plus another 10 for neutrino masses). These parameters cannot be independently calculated.
  2. The model does not describe the gravitational interaction.

Since the completion of the Standard Model, many efforts have been made to address 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 2006 (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 LHC 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.

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See also


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References

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Textbooks

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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).
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