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2.1 A Brief Tour of the Standard Model

The standard model of particle physics is a description of nature at very small distance scales, typically scales smaller than that of an atomic nucleus (). To the extent that the predictions of the theory can be calculated, the standard model provides a good description of all known phenomena in this regime.

Table 2.1: Particles of the Standard Model [3, pp. 1191--1195]

Mathematically, the standard model is a theory of interacting quantum fields. Excitations in these fields correspond to particles, and each separate field corresponds to a different type (or flavor) of particle. See Table 2.1 for a listing of the particle types of the standard model. These can be divided into three major groups: quarks, leptons, and gauge bosons. The quarks and leptons are all spin- particles, and thus obey the Pauli exclusion principle; they make up what is usually thought of as `matter'. Both the quarks and leptons are grouped into three generations of two particles each. The corresponding particles in each generation have similar properties, except for their masses, which increase with each successive generation. All `normal' matter (protons, neutrons, and electrons) is composed of particles from the first generation. Particles in higher generations can be produced in high-energy interactions (such as when cosmic rays hit the upper atmosphere), but they are unstable and ultimately decay into first generation particles or photons.

Each generation of leptons consists of one charged particle (the electron, muon, and tau) and an associated uncharged particle (the neutrinos). Experimentally, masses of the neutrinos are constrained to be quite small; the standard model assumes that they are zero. The charged leptons interact electromagnetically, but the neutrinos are affected only by the weak interaction (see below). This implies that for most purposes, neutrinos cannot be detected directly. Their presence must be inferred from an imbalance in the total measured momentum.

Quarks have two major features which qualitatively separate them from leptons. First, they have fractional electric charge --- either 1 / 3 or 2 / 3 the charge of an electron. Second, they are affected by the strong force, which binds quarks together inside nuclei, and is described in more detail below.

The particles of the third major class, the gauge bosons, are responsible for the interactions between particles. The equations of the standard model couple the fields of each gauge boson with fields of all the particles which feel that particular force. Interactions between two particles thus involve two couplings of the particles to the gauge boson; this can be viewed as a process in which the two particles exchange a virtual gauge boson.

Electromagnetism (`quantum electrodynamics' or `QED'), for example, is mediated by the photon, which couples to particles which have electric charge. An additional feature of electromagnetism is the fact that the coupling strength is not constant: it increases as the energy involved in the interaction increases. This is called a running coupling, and is a general feature of interactions in the standard model.

The weak interaction is mediated by the W and Z bosons. Unlike the photon, which is massless, the W and Z are quite heavy, with masses close to 100 GeV/. This implies that unlike electromagnetism, the weak force will operate only at rather small distance scales. One of the major features of the standard model is the fact that it treats the weak force and electromagnetism in a unified manner; these two forces are often referred to collectively as the `electroweak' force.

The strong force (`quantum chromodynamics' or `QCD') is mediated by gluons. Gluons couple to objects which possess `color' charge, which are the quarks plus the gluons themselves. A color charge has three possible values, conventionally called `red,' `green,' and `blue' (for quarks; antiquarks come in `anti-red,' `anti-green,' and `anti-blue'). As is the case for the electromagnetic interaction, the value of the strong coupling runs. However, the direction of the effect is different: as the energy of the interaction increases, the strength of the coupling gets smaller. This has the desirable consequence that at the high energies typical of modern high-energy experiments (), quarks behave nearly like free particles (`asymptotic freedom'), and the behavior of the strong force can be calculated using the same sort of perturbative techniques as are used for electromagnetism. However, at lower energies (such as would be typical of quarks bound in a nucleon) the coupling strength becomes large enough that perturbation theory breaks down. The behavior of such systems is presently not calculable from first principles.

The fact that the strength of the strong interaction increases as the energy of the interaction decreases, or equivalently, as the distance scale of the interaction increases, also ensures that at distance scales larger than a nucleon, quarks always appear in bound states. It is thought that these bound states are always arranged so that the color charges exactly cancel and have integral electric charge (either a quark and and its antiquark with the opposite color, or a mixture of all three colors).

In order to pull a quark out of a bound state such as a nucleon, one must expend sufficient energy to create a new quark-antiquark pair, one of which will pair with the removed quark, and the other of which will take the place of the removed quark. This means that if a quark is produced or knocked out of a nucleus in some interaction, it will rapidly `clothe' itself with other quarks which bind together to form a collection of composite particles. (This process is usually called fragmentation.) Experimentally, what one `sees' is not a single quark or gluon, but a collimated jet of many hadronic particles moving along directions close to that of the original quark.

The remaining force is gravity, and the particle which mediates it has been named the `graviton'. The bad news is that at present there is no workable theory of quantum gravity. The good news is that, since gravity is so much weaker than the other three forces, it is completely ignorable in almost all experiments of interest in high-energy physics.

    The remaining ingredient of the standard model is the Higgs boson. The standard method of introducing a new interaction into models like the standard model (by demanding a gauge symmetry) requires that the associated gauge bosons be massless. This is a problem for the case of the weak force, since the W and Z bosons must be quite massive in order to explain the observed low-energy behavior. The Higgs mechanism is a way around this problem; it introduces a new scalar particle which interacts with the W and Z in exactly the right way so that they acquire mass. The quarks and leptons can also acquire masses through this mechanism. If this description is correct, the Higgs should appear as a real, observable particle. To date, however, it has not been directly observed.

  Within the standard model, the top mass, the Higgs mass, and the ratio of the W and Z masses are interrelated, as shown in Figure 2.1. Although the dependence on the Higgs mass is weak (logarithmic), it is apparent that a sufficiently accurate measurement of the top mass can constrain the allowable range of Higgs masses.

Figure 2.1: The Standard Model relation between top mass and W mass, for different values of the Higgs mass. [4] Calculated using the LEP Z mass of 91.187 GeV/. The shaded band indicates a W mass of (from [3, p. 1191]).

For more information, there are many good texts which one can consult; for example, [5,6,7,8].

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Next: 2.2 Why Top Must Up: 2 The Top Quark Previous: 2 The Top Quark

Scott Snyder Fri May 19 19:19:46 CDT 1995