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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 gravity.

 Contents

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:

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)&timesU(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; it has a special status in the theory, and has been the subject of some controversy. 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. Amongst the proton, neutron, and electron, those fermions which constitute the vast majority of matter, the Standard Model considers only the electron a fundamental particle. The proton and neutron are aggregates of smaller particles known as quarks, which are held together by the strong interaction. The fundamental fermions in the Standard Model are given in the table.

Table

Left handed fermions in the Standard Model
Fermion (Left-handed) Symbol Electric charge Weak charge* Weak isospin Hypercharge Color charge* Mass**
Generation 1
Electron e -1 2 -1/2 -1/2 1 0.511 MeV
Electron neutrino νe 0 2 +1/2 -1/2 1 < 50 eV
Positron ec 1 1 0 1 1 0.511 MeV
Electron antineutrino $\nu_e^c$ 0 1 0 0 1 < 50 eV
Up quark u +2/3 2 +1/2 +1/6 3 ~5 MeV ***
Down quark d -1/3 2 -1/2 +1/6 3 ~10 MeV ***
Anti-up antiquark uc -2/3 1 0 -2/3 $\bar{3}$ ~5 MeV ***
Anti-down antiquark dc +1/3 1 0 +1/3 $\bar{3}$ ~10 MeV ***
Generation 2
Muon μ -1 2 -1/2 -1/2 1 105.6 MeV
Muon neutrino νμ 0 2 +1/2 -1/2 1 < 0.5 MeV
Anti-Muon μc 1 1 0 1 1 105.6 MeV
Muon antineutrino $\nu_\mu^c$ 0 1 0 0 1 < 0.5 MeV
Charm quark c +2/3 2 +1/2 +1/6 3 ~1.5 GeV
Strange quark s -1/3 2 -1/2 +1/6 3 ~100 MeV
Anti-charm antiquark cc -2/3 1 0 -2/3 $\bar{3}$ ~1.5 GeV
Anti-strange antiquark sc +1/3 1 0 +1/3 $\bar{3}$ ~100 MeV
Generation 3
Tau τ -1 2 -1/2 -1/2 1 1.784 GeV
Tau neutrino ντ 0 2 +1/2 -1/2 1 < 70 MeV
Anti-Tau τc 1 1 0 1 1 1.784 GeV
Tau antineutrino $\nu_\tau^c$ 0 1 0 0 1 < 70 MeV
Top quark t +2/3 2 +1/2 +1/6 3 178 GeV
Bottom quark b -1/3 2 -1/2 +1/6 3 ~4.7 GeV
Anti-top antiquark tc -2/3 1 0 -2/3 $\bar{3}$ 178 GeV
Anti-bottom antiquark bc +1/3 1 0 +1/3 $\bar{3}$ ~4.7 GeV

* - These are not ordinary Abelian charges which can be added together but 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 section rates. 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 set up a lattice model 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 here are pretty large. In fact, current QCD lattice models seem to suggest a significantly lower mass of these quarks from that of this table.

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 and unit electric charge, but the muon is about 200 times more massive.

The electron and the electron-neutrino, and their counterparts in the other generations, are called "leptons". Unlike the other fermions, they do not possess a quality called "color", and therefore their interactions (weak and electromagnetic) fall off rapidly with distance. On the other hand, the strong force between quarks gets stronger with distance, so that quarks are always found in colorless combinations called hadrons. These 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.

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 Value (GeV) Standard Model (GeV) Mass of W boson $80.4120\pm0.0420$ $80.3900\pm0.0180$ Mass of Z boson $91.1876\pm0.0021$ $91.1874\pm0.0021$

Challenges to the Standard Model

Although the Standard Model has had great success in explaining experimental results, it has never been accepted as 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&times 1032 years. This and other experiments have falsified numerous GUTs, including SU(5).

In addition, there are cosmological reasons why the standard model is believed to be incomplete. Within it, matter and antimatter are symmetric. 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, a consequence of its omission of gravity.

The Higgs boson, which is predicted by the Standard Model, has not been observed as of 2005 (though some phenomenon have been observed in the last days of the LEP collider, which could be related to the Higgs; one of the reasons to build the LHC is that the increase in energy is expected to make the Higgs observable).

The first experimental deviation from the Standard Model came in 1998, when Super-Kamiokande published results indicating neutrino oscillation. This implied the existence of non-zero neutrino masses since massless particles travel at the speed of light and so do not experience the passage of time. The Standard Model did not accommodate massive neutrinos, because it assumed the existence of only "left-handed" neutrinos, which have spin aligned counter-clockwise to their axis of motion. If neutrinos have non-zero mass, they necessarily travel slower than the speed of light. Therefore, it would be possible to "overtake" a neutrino, choosing a reference frame in which its direction of motion is reversed without affecting its spin (making it right-handed). Since then, physicists have revised the Standard Model to allow neutrinos to have mass, which make up additional 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.

Selected papers

• Y. Hayato et al., Search for Proton Decay through p → νK+ in a Large Water Cherenkov Detector. Phys. Rev. Lett. 83, 1529 (1999).
• S.F. Novaes, Standard Model: An Introduction, hep-ph:0001283