THE NUMBER OF FAMILY OF MATTER

The Number of Families of Matter

According to the currently accepted theory of fundamental particles and their interactions, three generations, or families, of elementary particles exist in nature. The most familiar of these families is the first generation, which includes the electron and the “up” and “down” quarks that form the protons and neutrons in the nucleus of an atom. German-born American physicist and Nobel laureate Jack Steinberger and American physicist Gary J. Feldman participated in experiments in the late 1980s that confirmed the existence of only three families of elementary particles. They described their work in a 1991 Scientific American article. Since the article was published, scientists have verified the existence of the top quark.

The Number of Families of Matter

How experiments at cern and slac, using electron-positron collisions, showed that there are only three families of fundamental particles in the universe

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.

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 fe 1/2[h/2p], where [h/2p] is the Planck unit of action, 10^-27 erg-second. Fermions may be thought of as the constituents of matter. Gauge bosons are particles of spin 1, or angular momentum 1[h/2p]. 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 in 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 chromodynamics 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 family (the neutrinos form a possible exception). The second family'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 Z. 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 short-lived, 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 billion 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.

Researchers at cern attacked the problem by developing the Large Electron-Positron (lep) Collider, a traditional storage-ring design built on an unprecedented scale. The ring, which measures 27 kilometers in circumference, is buried between 50 and 150 meters under the plain that stretches from Geneva to the French part of the Jura Mountains. Resonance cavities accelerate the two beams with radio-frequency power. The beams move in opposite directions through a roughly circular tube. Electromagnets bend the beams around every curve and direct them to collisions in four areas, each of which is provided with a large detector.

The ring design has the advantage of storing the particles indefinitely, so that they can continue to circulate and collide. It has the disadvantage of draining the beams of energy in the form of synchroton radiation, an emission made by any charged particle that is diverted by a magnetic field. Such losses, which at these energies appear as X rays, increase as the fourth power of the beam's energy and are inversely proportional to the ring's radius. Designers can therefore increase the power of their beams by either pouring in more energy or building larger rings, or both. If optimal use is made of resources, the cost of such storage rings scales as the square of beam energy. The lep is thought to approach the practical economic limit for accelerators of this kind.

At Stanford, the problem of making electrons and positrons collide at high energy was attacked in a novel way in the Stanford Linear Collider (slc). The electrons and positrons are accelerated in a three-kilometer-long linear accelerator, which had been built for other purposes. They are sent into arcs a kilometer long, brought into collision and then dumped. The electrons and positrons each lose about 2 percent of their energy because of synchrotron radiation in the arcs, but this loss is tolerable because the particles are not recirculated. A single detector is placed at the point of collision.

The lep is an efficient device: when the electron and positron beams recirculate, about 45,000 collisions per second occur. The slc beams collide, at the most, only 120 times per second. Thus, the slc must increase its efficiency. This task can be accomplished by reducing the beam's cross section to an extremely small area. The smaller the cross section of the area becomes, the more likely it is that an electron will collide head-on with a positron. The slc has produced beam diameters of four-millionths of a meter, about one fifth the thickness of a human hair.

One of the main justifications for building the slc was that it would serve as a prototype for this new kind of collider. Indeed, the slc has shown that useful numbers of collisions are obtainable in linear colliders, and it has thus encouraged developmental research in this direction, both at slac and at cern. The present Z production rates at the slc are, however, still more than 100 times smaller than those at the lep.

Large teams of physicists analyze the collision products in big detectors. The slc's detector is called Mark II, and the lep's four detectors are called Aleph, Opal, Delphi and L3. The slac team numbers about 150 physicists; each of the cern teams numbers about 400 people, drawn from research institutes and universities of two dozen countries.

The function of a detector is to measure the energies and directions of as many as possible of the particles constituting a collision event and to identify their nature, particularly that of the charged leptons. Detectors are made in onionlike layers, with tracking devices on the inside and calorimeters on the outside. Tracking devices measure the angles and momenta of charged particles. The trajectories are located by means of the ionization trails the collision products leave behind in a suitable gas. Other media, such as semiconductor detectors and light-emitting plastic fibers, are also used.

The tracking devices are generally placed in strong magnetic fields that bend the particles' trajectories inversely with respect to their momenta. Measurement of the curves yields the momenta, which in turn provide close estimates of the energy. (At the energies encountered in these experiments, the energy and the momentum of a particle differ very little.)

Calorimeters measure the energies of both neutral and charged particles by dissipating these energies in successive secondary interactions in some dense medium. This energy is then sampled in a suitable way and localized as precisely as the granularity of the calorimeter allows. Calorimeters perform their function in a number of ways. The most common method uses sandwiches of thin sheets of dense matter, such as lead, uranium or iron, which are separated by layers of track-sensitive material.

Particles leave their mark in such materials by knocking electrons from their atoms. Argon, either in liquid form or as a gas combined with organic gases, is the usual medium. Plastic scintillators work differently: when a reaction particle traverses them, it produces a flash of light whose intensity is then measured. The calorimeter usually has two layers, an inner one optimized for the measurement of electrons and photons and an outer one optimized for hadrons.

To gather all the reaction products, the ideal detector would cover the entire solid angle surrounding the interaction point. Such detectors were pioneered in the 1970s at slac. In the lep's Aleph detector the tracking of the products from the annihilation of a positron and an electron proceeds in steps.

A silicon-strip device adjoining the reaction site fixes the forward end point of each trajectory to within ten-millionths of a meter (about half the breadth of a human hair). Eight layers of detection wires then track the trajectory through an inner chamber 60 centimeters in diameter. Finally, a so-called time-projection chamber, 3.6 meters in diameter, uses a strong electric field to collect electrons knocked from gas molecules by the traversing particles. The field causes the electrons to drift to the cylindrical chambers' two ends, where they are amplified and detected on 50,000 small pads. Each electron's point of origin is inferred from the place it occupies on the pads and the time it takes to get there.