The Higgs Boson: Searching for the God Particle (14 page)

The pattern of quark and lepton charges is generated as follows. The
TTT
combination, with rishon charges of 1/3 + 1/3 + 1/3, has a total charge of + 1 and therefore corresponds to the positron; similarly,
T
¹
T
¹
T
¹
has a total charge of -1 and is identified with the electron. The
VVV
and
V
¹
V
¹
V
¹
combinations are both electrically neutral and represent the neutrino and the antineutrino respectively. The remaining allowed combinations yield fractionally charged quarks.
TTV
, with a charge of
+2/3, is the
u
quark, and
TVV
, with a charge of + 1/3, is the
d
¹
antiquark. The analogous antirishon states
V
¹
V
¹
T
¹
and
V
¹
T
¹
T
¹
correspond to the
d
quark and the
u
antiquark.

The model also accounts successfully for the color of the composite systems.
A
T
rishon can have any of the three colors red, yellow and blue, whereas a
V
rishon has an anticolor. Combinations such as
T
¹
T
¹
T
¹
and
VVV
, which designate leptons, can be made colorless since they can include one rishon in each color or one in each anticolor. The other combinations, which yield quarks, must have a net color. For example, a
TTV
state might have the rishon colors red, blue and antiblue; the antiblue would cancel the blue, leaving the system with a net color of red. In this way the connection between color and electric charge, which was apparent but unexplained in the standard model, is readily understood. Because of the way electric charge and color are allotted to the rishons, all composite systems with fractional charge turn out to be colored, and all systems with an integer charge can be made colorless.

Other regularities of the standardmodel also lose their air of mystery when rishons are introduced. Consider the hydrogen atom, made up of a proton and an electron, or in terms of quarks and leptons two u quarks, a d quark and an electron. The total rishon content of the quarks is four
T
's, one
T
¹
, two
V
's and two
V
¹
's. The electric charge of the
T
¹
cancels the charge of one
T
rishon, and the
V
's and
V
¹
's also cancel (they have no charge in any case), leaving the proton with a net charge equal to that of a
TTT
system. The electron's rishon content is just the opposite:
T
¹
T
¹
T
¹
. Thus it is evident why the proton and the electron have charges of equal magnitude and why the hydrogen atom is neutral: the ultimate sources of the charge are pairs of matched particles and antiparticles.

The rishon model and many other models that explain the pattern of the first generation have difficulty accounting for the second and third generations.
It would seem that such models lend themselves well to the scheme of forming each particle in the higher generations as an excited state of the corresponding particle in the first generation.
The simplest idea would be to describe the muon, for example, as having the same prequark constituents as the electron, but in the muon the prequarks would have some higher-energy configuration.
It is an elegant idea but, regrettably, it appears to be unworkable. The scheme implies differences in energy between the successive excited states that are much larger than the actual differences.
The flaw is a fundamental one, and there seems to be no remedy.

Other possible mechanisms for creating multiple generations have been considered
. Several physicists have suggested that the higher-generation relatives of a given state might be created by adding a Higgs particle, the "extra" particle associated with the weak bosons in the standard model. Because a Higgs particle has no electric charge or color or even spin angular momentum, adding one to a composite system would alter only the mass. Hence an electron might be converted into a muon by adding one Higgs particle or into a tau by ading two or more Higgs particles. Seiberg and I have proposed another possible mechanism: a higher-generation particle could be formed by the addition of pairs of prequarks and antiprequarks.
All charges and other properties must cancel in such a pair, and so again only the mass would be affected.

These ideas are currently at the stage of unrestrained speculation. No one knows what distinguishes the three generations from one another, or why there are three or whether there may be more.
No explanation can be given of the mass difference between the generations. In short, the triplication of the generations is still a major unsolved puzzle.

A third kind of substructure model deserves mention. It tries to relate the possibility of quark and lepton structure to another fundamental problem : understanding the relativistic quantum theory of gravitation. Ideas of this kind have been explored by John Ellis, Mary K. Gaillard, Luciano Maiani and Bruno Zumino of CERN . One approach to their ideas is to consider the distances at which prequarks interact: the experimental limit is less than 10
^-16
centimeter, but the actual distance could be several orders of magnitude smaller still.
At about 10
^-34
centimeter the gravitational force becomes strong enough to have a significant effect on individual particles. If the scale of the prequark interactions is this small, gravitation cannot be neglected. Ellis, Gaillard, Maiani and Zumino have outlined an ambitious program that aims to unify all the forces, including gravitation, in a scheme that treats not only the quarks and leptons but also the gauge bosons as composite particles. Like other composite models, however, this one has serious flaws.

Any prequark model, regardless of its details, must supply some mechanism for binding the prequarks together.
There must be a powerful attractive force between them. One strategy is to postulate a new fundamental force of nature analogous in its workings to the color force of the standard model. To emphasize the analogy the new force is called the hypercolor force and the carrier fields are called hypergluons. The prequarks are assumed to have hypercolor, but they combine to form hypercolorless composite systems, just as quarks have ordinary color but combine to form colorless protons and neutrons.
The hyper color force presumably also gives rise to the property of confinement, again in analogy to the color force. Hence all hyper colored prequarks would, be trapped inside composite particles, which would explain why free prequarks are not seen in experiments.
An idea of this kind was first proposed by 't Hooft, who studied some of its mathematical implications but also expressed doubt that nature actually follows such a path.

The typical radius of hypercolor con-finement must be less than 10
^-16
centimeter.
Only when matter is probed
'at distances smaller than this would it be possible to see the hypothetical prequarks and their hypercolors. At a range of 10
^-14
or 10
^-15
centimeter hypercolor effectively disappears; the only objects visible at this scale of resolution (the quarks and leptons) are neutral with respect to hypercolor. At a range of 10
^-13
centimeter ordinary color likewise fades away, and the world seems to be made up entirely of objects that lack both color and hypercolor: protons, neutrons, electrons and so on.

The notion of hypercolor is well suited to a variety of prequark models, including the rishon model. In addition to their electric charge and color the rishons are assumed to have hypercolor and the antirishons to have antihypercolor.
Only combinations of three rishons or three antirishons are allowed because only those combinations are neutral with respect to hypercolor. A mixed three-particle system, such as
TTT
, cannot exist because it would not be hypercolorless. The assignment of hypercolors thereby explains the rule for forming composite rishon systems.
Similar rules apply in other hypercolor-based prequark models.

If the aim of a prequark model is to simplify the understanding of nature, postulating a new basic force does not seem very helpful. In the case of hypercolor, however, there may be some compensation.
Consider the neutrino: it has neither electric charge nor color, only weak charge. According to the standard
model, two neutrinos can act on each other only through the short-range weak force. If neutrinos are composites of hyper colored prequarks, however, there could be an additional source of interactions between neutrinos. When two neutrinos are far apart, there are practically no hypercolor forces between them, but when they are at close range, the hypercolored prequarks inside one neutrino are able to "see" the inner hypercolors of the other one. Complicated shortrange attractions and repulsions are the result. The mechanism, of course, is exactly the same as the one that explains the molecular force as a residue of the electromagnetic force and the strong force as a residue of the color force.

The conclusion may also be the same.
Seiberg and I, and independently Greenberg and Sucher, were the first to suggest that the short-range weak force may actually be a residual effect of the hypercolor force. According to this hypothesis, the weak bosons W+ , W- and
Z
⁰
must also be composite objects, presumably made up of certain combinations of the same prequarks that compose the quarks and leptons. If this idea is confirmed, the list of fundamental forces will still have four entries: gravitation, electromagnetism, color and hypercolor. It should be noted, however, that all these forces are long-range ones; the short-range molecular, strong and weak forces will have lost their fundamental status.

For now hyper color remains a conjecture, and so does the notion of explaining the weak force as a residue of the hypercolor force. It may yet turn out that the weak force is fundamental. A careful measurement of the mass, lifetime and other properties of the weak bosons should provide important clues in this matter.

Hypercolor is not the only candidate for a prequark bind ing force. Another intere sting possibility was suggested by Pati, Salam and Strathdee. Instead of introducing a new hypercolor force, they borrowed an idea that has long been familiar, namely the magnetic force, and adapted it to a new purpose. An ordinary magnet invariably has two poles, which can be thought of as opposite magnetic charges. For 50 years there have been theoretical reasons for supposing there could also be isolated magnetic charges, or monopoles. Pati, Salam and Strathdee have argued that the prequarks could be particles with charges resembling both magnetic and electric charges. If they are, the forces binding them may be of a new and interesting origin.

None of the ideas I have just described constitutes a theory of prequark dynamics. Indeed, there is a serious imped iment to the formulation of such a theory; it is the requirement that the prequarks be exceedingly small. The most stringent limit on their size is set indirectly by measurements of the magnetic moment of the electron, which agree with the calculations of quantum electrodynamics to an accuracy of 10 significant digits. In the calculations it is assumed that the electron is pointlike;
if it had any spatial extension or internal structure, the measured value would differ from the calculated one. Evidently any such discrepancy can at most affect the 11th digit of the result. It is this constraint that implies the characteristic distance scale of the electron's internal structure must be less than 10
^-16
centimeter.
Roughly speaking, that is the maximum radius of an electron, and any prequarks must stay within it. If they strayed any wider, their presence would already have been detected.

Why should the small size of the electron inhibit speculation about its internal structure? The uncertainty principle establishes a reciprocal relation between the size of a composite system and the kinetic energy of any components moving inside it. The smaller the system, the larger the kinetic energy of the constituents.
It follows that the prequarks must have enormous energy: more than 100 GeV (100 billion electron volts), and possibly much more. (One electron volt is the energy acquired by an electron when it is accelerated through a potential difference of one volt.) Because mass is fundamentally equivalent to energy, it can be measured in the same system of units. The mass of the electron, for example, is equivalent to .0005 GeV. There is a paradox here, which I call the energy mismatch: the mass of the composite system (if it is indeed composite) is much smaller than the energy of its constituents.

The oddity of the situation can be illuminated by considering the relations of mass and kinetic energy in other composite systems. In an atom the kinetic energy of a typical electron is smaller than the mass of the atom by many orders of magnitude. In hydrogen, for example, the ratio is roughly one part in 100 million. The energy needed to change the orbit of the electron and thereby put the atom into an excited state is likewise a negligible fraction of the atomic mass. In a nucleus the kinetic energy of the protons and neutrons is also small compared with the nuclear mass, but it is not completely negligible.
The motion of the particles gives them an energy equivalent to about 1 percent of the system's mass. The energy needed to create an excited state is also about 1 percent of the mass.

With the proton and its quark constituents the energy-mass relation begins to get curious. From the effective radius of the proton the typical energy of its component quarks can be calculated; it turns out to be comparable to the mass of the proton itself, which is a little less than 1 GeV. The energy that must be invested to create an excited state of the quark system is of the same order of magnitude: the hadrons identified as excited states of the proton exceed it in mass by from 30 to 100 percent. Nevertheless, the ratio of kinetic energy to total mass is still in the range that seems intuitively reasonable. Suppose one knew only the radius of the proton, and hence the typical energy of whatever happens to be inside it, and one were asked to guess the proton's mass. Since the energy of the constituents is generally a few hundred million electron volts, one would surely guess that the total mass of the system is at least of the same order of magnitude and possibly greater. The guess would be correct.