The mathematics of the gauge theories is rigid, but it does leave some freedom for adjustment. That is, the predicted magnitude of an interaction between particles depends not only on the structure of the theory but also on the values assigned to certain free parameters, which must be considered constants of nature. The theory remains consistent no matter what choice is made for these constants, but the experimental predictions depend strongly on what values are assigned to the constants. Although the constants can be measured by doing experiments, they can never be derived from the theory. Examples of such constants of nature are the charge of the electron and the masses of elementary particles such as the electron and the quarks.
The strength of the gauge theories is that they require comparatively few such free parameters: about 18 constants of nature must be supplied to account for all the known forces. The tangled phenomena of the strongly interacting particles, which seemed incomprehensible 15 years ago, can now be unraveled by means of a theory that includes only a handful of free parameters. Among these all but three are small enough to be safely ignored.
Even if the free parameters have been reduced to a manageable number, they remain an essential part of the theory. No explanation can be offered of why they assume the values they do. The fundamental questions that remain unanswered by the gauge theories center on these apparent constants of nature. Why do the quarks and the other elementary particles have the masses they do? What determines the mass of the Higgs particle? What determines the fundamental unit of electric charge or the strength of the color force? The answers to such questions cannot come from the existing gauge theories but only from a more comprehensive theory.
In the search for a larger theory it is natural to apply once more a recipe that has already proved successful. Hence the obvious program is to search for global symmetries and explore the consequences of making them local symmetries. This principle is not a necessary one, but it is worth trying. Just as Maxwell's theory combined electricity and magnetism and the Weinberg-Salam-Ward model linked electromagnetism and the weak force, so perhaps some larger theory could be found to embrace both the Weinberg-Salam-Ward model and quantum chromodynamics. Such a theory might in principle be constructed on the model of the existing gauge theories. A more sweeping symmetry of nature must be found; making this symmetry a local one would then give rise to the strong force, the weak force and electromagnetism. In the bargain yet more forces, exceedingly weak and so far unobserved, may be introduced.
Work on such theories is proceeding, and it has lately concentrated on symmetries that allow transformations between quarks and leptons, the class of particles that includes the electron. It is my belief the schemes proposed so far are not convincing. The grand symmetry they presuppose must be broken in order to account for the observed disparities among the forces, and that requires several Higgs fields. The resulting theory has as many arbitrary constants of nature as the less comprehensive theories it replaces.
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STANDARD MODEL of elementary-particle interactions describes the four forces of nature by means of three non-Abelian guage theories. The fundamental particles of matter are six leptons and six flavors of quark, each of the flavors being present in three colors. Electromagnetism and the weak force are mediated by the guage particles of the Weinberg-Salam-Ward model, namely the massless photon and a triplet of very massive vector bosons, the W+, W- and Z0. The strong force is attributed to the eight massless gluons of quantum chromodynamics. Gravitation results from the exchange of a massless spin-two particle, the graviton, which is described by another local guage theory: the general theory of relativity. In addition there is one surviving Higgs particle, which is massive and electrically neutral. In the coming years the search for the massive vector bosons and the Higgs particle will serve as tests of this synthesis.
Illustration by Allen Beechel
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A quite different and more ambitious approach to unification has recently been introduced under the terms "supersymmetry" and "supergravity. " It gathers into a single category particles with various quantities of angular momentum; up to now particles with different spins were always assigned to separate categories. The utility of the supersymmetric theories has yet to be demonstrated, but they hold much promise. They offer a highly restrictive description of some hundreds of particles, including the graviton, in terms of only a few adj ustable parameters. So far the results do not much resemble the known physical world, but that was also true of the first Yang-Mills theory in 1954.
The form of unification that has been sought longest and most ardently is a reconciliation of the various quantum field theories with the general theory of relativity. The gravitational field seems to lead inevitably to quantized theories that cannot be renormalized. At extremely small scales of distance (10-33 centimeter) and time (10-44 second) quantum fluctuations of space-time itself become important, and they call into question the very meaning of a space-time continuum. Here lie the present limits not merely of gauge theories but of all known physical theories.
-Originally published: Scientific American 242(6), 104-138. (June 1980)
The Number of Families of Matter
By Gary J. Feldman and Jack Steinberger
The universe around us consists of three fundamental particles. They are the "up" quark, the "down" quark and the electron. Stars, planets, molecules, atoms—and indeed, ourselves—are built from amalgamations of these three entities. They, together with the neutral and possibly massless partner of the electron, the electron neutrino, constitute the first family of matter.
Nature, however, is not so simple. It provides two other families that are like the first in every respect except in their mass. Why did nature happen to provide three replications of the same pattern of matter? We do not know. Our theories as yet give no indication. Could there be more than three families? Recent experiments have led to the conclusion that there are not.
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Illustration by Ian Warpole
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In the spring and summer of 1989, experiments were performed by teams of physicists working at the Stanford Linear Accelerator Center (SLAc) and the European laboratory for particle physics (CERN) near Geneva. The teams used machines of differing designs to cause electrons (e-) and positrons (e+) to collide and thus produce quantities of the Z particle (or Z0, pronounced "zee zero" or "zee naught").
The most massive elementary particle observed, the Z weighs about 100 times as much as a proton and nearly as much as an atom of silver. As we shall see, this mass is merely an average. The Z lifetime is so short that individual Z particles differ slightly in their mass. The spread in the mass values is called a mass width, a quantity that depends on the number of families of matter. Because this width can be measured experimentally, the number of families of matter can be inferred. In this article we describe the experiments by which the families of matter were numbered.
But let us first put this achievement into perspective. The past two and a half decades have witnessed a remarkable systematization of our knowledge of the elementary particles and their interactions with one another. The known particles can be classified either as fermions or as gauge bosons. Fermions are particles of spin 1/2, that is, they have an intrinsic angular momentum of 1/2h, where h is the Planck unit of action, 10-27 ergsecond. Fermions may be thought of as the constituents of matter. Gauge bosons are particles of spin 1, or angular momentum 1h. They can be visualized as the mediators of the forces between the fermions. In addition to their spins, these particles are characterized by their masses and by their various couplings with one another, such as electric charges.
All known couplings, or interactions, can be classified into three types: electromagnetic, weak and strong. (A fourth interaction, gravity, is negligible at the level of elementary particles, so it need not be considered here.) Although the three interactions appear to be different, their mathematical formulation is quite similar. They are all described by theories i
n which fermions interact by exchanging gauge bosons.
The electromagnetic interaction, as seen in the binding of electrons and nuclei to form atoms, is mediated by the exchange of photons-the electromagnetic gauge bosons. The weak interaction is mediated by the heavy W+, W- and Z bosons, whereas the strong interaction is mediated by the eight massless "gluons." The proton, for instance, is composed of three fermion quarks that are bound together by the exchange of gluons.
These interactions also describe the creation of particles in high-energy collisions. The conversion of a photon into an electron and a positron serves as an example. So does the annihilation of an electron colliding with a positron at immensely high energy to produce a Z particle.
The evolution of these gauge theories constitutes a strikingly beautiful advance in particle physics. The unification of electromagnetism with the weak interaction was put forward during the years 1968-1971. This "electroweak" theory predicted the neutral weak interaction, discovered at CERN in 1973, and the heavy intermediate bosons W+, W- and Z0, discovered 10 years later, also at CERN .
The gauge theory of the strong interaction was advanced in the early 1970s. This theory is called quantum chromodynarnics because it explains the strong force by which quarks interact on the basis of their "color." Despite its name, color is an invisible trait. It is to the strong interaction what charge is to the electrical one: a quantity that characterizes the force. But whereas electrodynamic charge has only one state–positive or negative–the color charge has three. Quarks come in red, green and blue; antiquarks come in antired, antigreen and antiblue.
Together these two gauge theories predict, often with quite high precision, all elementary phenomena that have so far been observed. But their apparent comprehensiveness does not mean that the model is complete and that we can all go home. Gauge theory predicts the existence of the so-called Higgs particle, which is supposed to explain the origin of particle mass. No physicist can be happy until it is spotted or a substitute for it is supplied. Gauge theory also includes a number of arbitrary physical constants, such as the coupling strengths of the interactions and the masses of the particles. A complete theory would explain why these particular values are found in nature.
Among the rules the electroweak theory does provide is one that requires fermions to come in pairs. The electron and electron neutrino are such a pair; they are called leptons because they are relatively light. Another rule is that each particle must have its antiparticle–against the electron is posed the positron; against the electron neutrino, the electron antineutrino. When particles and antiparticles collide, they can annihilate one another, producing secondary particles. Such reactions, as we shall see, underlie the experiments discussed here.
To avoid some subtle disasters in the theory, it is necessary to associate with a lepton pair a corresponding pair of quarks. The electron is the lightest charged lepton, and therefore it is associated with the lightest quarks, the u quark (or up quark) and the d quark (or down quark). Quarks have not been seen in the free state; they are only found bound to other quarks and antiquarks.
The proton, for example, is composed of two u quarks and a d quark, whereas the neutron is composed of two d quarks and a u quark. A complete second family and most of a third have been shown to exist in high-energy experiments. In each case, the particles are much more massive than the corresponding members of the preceding f amily (the neutrinos form a possible exception). The second f amily's two leptons are the muon and the muon neutrino; its quarks are the "charm," or c, quark, and the "strange," or s, quark. The third family's confirmed members are its two leptons-the tau lepton and the tau neutrino-and the "bottom," or b, quark . The remaining quark, called the "top," or t, quark , is crucial to the electroweak theory. The particle has not been discovered, but we and most other physicists believe it exists and presume it is simply too massive to be brought into existence by today's particle accelerators.
No members of the second and third families are stable (again, with the possible exception of the neutrinos). Their lifetimes range between a millionth and a ten-trillionth of a second, at the end of which they decay into particles of lower mass.
There are two substantial gaps in the electroweak theory's grouping of particles. First, although the theory requires that fermions come in pairs, it does not specify how many pairs constitute a family. There is no reason why each family should not have, in addition to its leptons and quarks, particles of another, still unobserved type. This possibility interests a great number of our colleagues, but so far no new particles have been observed. Second, the theory says nothing about the central question of this article: the number of families of matter. Might there be higher families made up of particles too massive for existing accelerators to produce?
At present, physicists can do nothing but insert observed masses into theories on an ad hoc basis. Some pattern can, however, be discerned. Within a given class of particle (say, a charged lepton or a quark of charge +2/3 or of -1/3), the mass increases considerably in each succeeding family. The smallest such increase is the nearly 17-fold jump from the muon in the second family to the tau lepton in the third.
Another striking feature is found within families. Leptons are always less massive than quarks, and in every pair of leptons the neutrino is always substantially the less massive particle. In fact, it is uncertain whether neutrinos have any masses at all: experimental evidence merely puts upper limits on the mass each variety can have.
This lightness of neutrinos is essential to the method reported here for counting the number of families of particles. Even if the quark and lepton members of a fourth, fifth or sixth family were far too massive to be created by existing accelerators, the likelihood is nonetheless great that their neutrinos would have little or no mass. Almost certainly the mass of such neutrinos would be less than half the mass of the Z boson. If such neutrinos exist, therefore, they would be expected to be among the decay products of the Z, the only particle that decays copiously into pairs of neutrinos.
Unfortunately, neutrinos are hard to detect because they do not engage in electromagnetic or strong interactions. They touch matter only through forces that are called "weak," with good reason: most neutrinos pass through the earth without interacting. In the experiments we shall describe, the existence of neutrinos is sought indirectly.
The process begins by creating Z particles. The Z can be produced by an electron-positron pair whose combined kinetic energies make up the difference between their rest masses (expressed in equivalent energy) and the rest mass of the . Because these leptons have tiny rest masses, the beams in which they travel must each be raised to the very high energy of 45.5 billion electron volts (eV), about half the Z mass.
Now if the Z were perfectly stable, the beam energy would have to equal this value precisely to conserve energy and momentum. But such perfect stability is impossible, for if the Z can be created from particles, then it must also be free to decay back into them. In fact, the Z has many "channels" in which to decay. Each decay channel shortens the life of the Z.
Near the beginning of this article, we mentioned that the Z's short life made its mass indeterminate and that the extent of the indeterminacy could be used to number the families of matter. Let us explain why this must be so. One form of the Heisenberg uncertainty principle stipulates that the shorter the duration of a state is, the more uncertain its energy must be. Because the Z is shortlived, its energy–or equivalently, its mass–will have a degree of uncertainty. What this means is the following: the mass of any individual Z can be measured quite precisely, but different Zs will have slightly different masses. If the measured masses of many Zs are plotted, the resulting graph has a characteristic bell-like shape. The width of this shape is proportional to the speed at which the Z decays.
The shape is measured by varying the collision energy and observing the number of Z particles produced. The measurements trace a curve that peaks, or resonates, at a combined beam energy of about 91 b
illion eV. This point, called the peak cross section, defines the average Z mass. The width of the resonance curve defines the particle's mass uncertainty.
The width equals the sum of partial widths contributed by each of the Z's decay channels. The known channels are the decays to particle and antiparticle pairs of all fermions with less than one half the Z mass: the three varieties of charged leptons, the five kinds of quarks and the three varieties of neutrinos. If there are other fermions whose masses are less than half the Z mass, the Z will decay to these as well, and these channels will also contribute to the Z width, making it larger.
The present experiments show that such decays to new, charged particles do not occur, so we can be sure that the particles do not exist or that their masses are larger than half the Z mass. If, however, higher-mass families do exist, then–as we argued before–their neutrinos would still be expected to have masses much smaller than half the Z mass. Therefore, the Z would also decay to these channels, and although the neutrinos would not be seen directly in these experiments, these neutrino species would contribute to the Z width and so be observable. This is the principle enabling the experiments reported here to number the families of matter.
The electroweak theory predicts the contributions of the known channels to an accuracy of about 1 percent, as follows: for the combined quark channels, 1.74 billion eV; for each charged lepton channel, 83.5 million eV; and for each neutrino channel, 166 million eV.
As the number of assumed neutrinos (and hence families) increases, the predicted Z width also increases. The predicted peak cross section, on the other hand, declines by the square of the width. One can consequently deduce the number of families either from the measured width or from the peak cross section. The latter is statistically the more powerful measurement. The establishment of the number of families by direct experimental measurement had to await the production of large numbers of Zs by the well-understood process of electron- positron annihilation.
The Higgs Boson: Searching for the God Particle Page 8
