The Higgs Boson: Searching for the God Particle (4 page)

In such a unification only one gauge to describe all the interactions of matter.
In a gauge theory each particle in a
set can be transformed into any other particle. Transformations
of quarks into other quarks and of leptons into other leptons, mediated by gluons and intermediate bosons, are familiar.
A unified theory suggests that quarks can change into leptons and vice versa. As in any gauge theory, such an interaction would be mediated by a
force particle:
a postulated X or Y
boson.
Like other gauge theories, the unified theory describes the variation over distance of interaction strengths.
According to the simplest of the unified theories, the separate strong and electroweak interactions converge and become a
single interaction at a
distance of 10
^-29
centimeter, corresponding to an energy of 10
²⁴
electron volts.

Such an energy is far higher than may ever be attained in an accelerator, but certain consequences of unification might be apparent even in the lowenergy world we inhabit.
The supposition that transformations can cross the boundary between quarks and leptons implies that matter, much of whose mass consists of quarks, can decay.
If, for example, the two u quarks in a proton were to approach each other closer than 10
^-29
centimeter, they might combine to form an
X
boson, which would disintegrate into a
positron and a
d
antiquark.
The antiquark would then combine with the one remaining quark of the proton, ad quark, to form a
neutral pion, which itself would quickly decay into two photons.
In the course of the process much of the proton's mass would be converted into energy.

The observation of proton decay would lend considerable support to a
unified theory.
It would also have interesting cosmological consequences.
The universe contains far more matter than it does antimatter.
Since matter and antimatter are equivalent in almost every respect, it is appealing to speculate that the universe was formed with equal amounts of both.
If the number of baryons – three-quark particles such as the proton and the neutron, which constitute the bulk of ordinary matter – can change, as the decay of the proton would imply, then the current excess of matter need not represent the initial state of the universe.
Originally matter and antimatter may indeed have been present in equal quantities, but during the first instants after the big bang, while the universe remained in a state of extremely high energy, processes that alter baryon number may have upset the balance.

A number of experiments have been mounted to search for proton decay.
The large unification energy implies that the mean lifetime of the proton must be extraordinarily long—10
³⁰
years or more.
To have a
reasonable chance of observing a single decay it is necessary to monitor an extremely large number of protons;
a key feature of proton-decay experiments has therefore been large scale.
The most ambitious experiment mounted to date is an instrumented tank of purified water 21 meters on a side in the Morton salt mine near Cleveland.
During almost three years of monitoring none of the water's more than 10
³³
protons has been observed to decay, suggesting that the proton's lifetime is even longer than the simplest unified theory predicts.
In some rival theories, however, the lifetime of the proton is considerably longer, and there are other theories in which protons decay in ways that would be difficult to detect in existing experiments. Furthermore, results from other experiments hint that protons can indeed decay.

Open Questions

Besides pointing the way to a possible unification the standard model, consisting of QCD and the electroweak theory, has suggested numerous sharp questions for present and future accelerators. Among the many goals for current facilities is an effort to test the predictions of QCD in greater detail. Over the next decade accelerators with the higher energies needed to produce the massive
W
and
Z
⁰
bosons in adequate numbers will also add detail to electroweak theory. It would be presumptuous to say these investigations will turn up no surprises. The consistency and experimental successes of the standard model at familiar energies strongly suggest, however, that to resolve fundamental issues we need to take a large step up in interact ion energy from the several hundred GeV (billion electron volts) attainable in the most powerful accelerators now being built.

Although the standard model is remarkably free of inconsistencies, it is incomplete; one is left hungry for further explanation. The model does not account for the pattern of quark and lepton masses or for the fact that although weak transitions usually observe family lines, they occasionally cross them. The family pattern itself remains to be explained. Why should there be three matched sets of quarks and leptons? Might there be more?

Twenty or more parameters, constants not accounted for by theory, are required to specify the standard model completely. These include the coupling strengths of the strong, weak and electromagnetic interactions, the masses of the quarks and leptons, and parameters specifying the interactions of the Higgs boson. Furthermore, the apparently fundamental constituents and force particles number at least 34: 15 quarks (five flavors, each in three colors), six leptons, the photon, eight gluons, three intermediate bosons and the postulated Higgs boson. By the criterion of simplicity the standard model does not seem to represent progress over the ancient view of matter as made up of earth, air, fire and water, interacting through love and strife.
Encouraged by historical precedent, many physicists account for the diversity by proposing that these seemingly fundamental particles are made up of still smaller particles in varying combinations.

There are two other crucial points at which the standard model seems to falter.
Neither the separate theories of the strong and the electroweak interactions nor the conjectured unification of the two takes any account of gravity.
Whether gravity can be described in a quantum theory and unified with the other fundamental forces remains an open question. Another basic deficiency of the standard model concerns the Higgs boson. The electroweak theory requires that the Higgs boson exist but does not specify precisely how the particle must interact with other particles or even what its mass must be, except in the broadest terms.

The Superconducting Supercollider

What energy must we reach, and what new instruments do we need, to shed light on such fundamental problems?
The questions surrounding the Higgs boson, although they are by no means the only challenges we face, are particularly well defined, and their answers will bear on the entire strategy of unification. They set a useful target for the next generation of machines.

It has been proposed that the Higgs boson is not an elementary particle at all but rather a composite object made up of elementary constituents analogous to quarks and leptons but subject to a new kind of strong interaction, often called technicolor, which would confine them within about 10
^-17
centimeter.
The phenomena that would reveal such an interaction would become apparent at energies of about 1 TeV
(trillion electron volts). A second approach to the question of the Higgs boson's mass and behavior employs a postulated principle known as supersymmetry, which relates particles that differ in spin. Supersymmetry entails the existence of an entirely new set of elusive, extremely massive particles.
The new particles would correspond to known quarks, leptons and bosons but would differ in their spins. Because of their mass, such particles would reveal themselves fully only in interactions taking place at very high energy, probably about 1 TeV.

Our best hope for producing interactions of fundamental particles at energies of 1 TeV is an accelerator known as the Superconducting Supercollider
(SSC). Formally recommended to the Department of Energy in 1983 by the High Energy Physics Advisory Panel, it would incorporate proved technology on an unprecedented scale. A number of designs have been put forward, but all envision a proton-proton or proton-antiproton collider. High-energy beams of protons are prod uced more readily with current technology than beams of electrons and positrons, although electron-positron collisions are generally simpler to analyze; because protons are composite particles, their collisions yield a larger variety of interactions than collisions of electrons and positrons. Another common feature of the designs is the use of superconducting magnets, first employed on a large scale in the Tevatron Collider at the Fermi National Accelerator Laboratory (Fermilab) in Batavia, Ill. The technology increases the field strength and lowers the power consumption of the magnets that bend and confine the beam.

One of the more compact designs incorporates niobium-titanium alloy magnets cooled to 4.4 degrees Celsius above absolute zero. If the magnets generated fields of five tesla (l00,000 times the strength of the earth's magnetic field), two counterrotating beams of protons accelerated to energies of 20 TeV (needed to produce 1-TeV interactions of the quarks and gluons within the protons) could be confined within a loop about 30 kilometers in diameter. In other designs magnetic fields are lower and the proposed facility is correspondingly larger.

It is believed such a device could be operational in 1994, at a cost of $3 billion. The Department of Energy has encouraged the establishment of a Central Design Group to formulate a specific construction proposal within three years and is currently funding the development of magnets for the SSC at several laboratories.

The SSC represents basic research at unprecedented cost on an unmatched scale. Yet the rewards will be proportionate.
The advances of the past decade have brought us tantalizingly close to a profound new understanding of the fundamental constituents of nature and their interactions. Current theory suggests that the frontier of our ignorance falls at energies of about 1 TeV.
Whatever clues about the unification of the forces of nature and the constituents of matter wait beyond that frontier, the SSC is likely to reveal them.

--Originally published: Scientific American 252(4), 84-95. (April 1985)

Gauge Theories of the Forces between Elementary Particles

by Gerard 't Hooft

An understanding of how the world is put together requires a theory of how the elementary particles of matter interact with one another. Equivalently, it requires a theory of the basic forces of nature. Four such forces have been identified, and until recently a different kind of theory was needed for each of them. Two of the forces, gravitation and electromagnetism, have an unlimited range; largely for this reason they are familiar to everyone. They can be felt directly as agencies that push or pull. The remaining forces, which are called simply the weak force and the strong force, cannot be perceived directly because their influence extends only over a short range, no larger than the radius of an atomic nucleus. The strong force binds together the protons and the neutrons in the nucleus, and in another context it binds together the particles called quarks that are thought to be the constituents of protons and neutrons. The weak force is mainly responsible for the decay of certain particles.

A long-standing ambition of physicists is to construct a single master theory that would incorporate all the known forces. One imagines that such a theory would reveal some deep connection between the various forces while accounting for their apparent diversity. Such a unification has not yet been attained, but in recent years some progress may have been made. The weak force and electromagnetism can now be understood in the context of a single theory. Although the two forces remain distinct, in the theory they become mathematically intertwined. What may ultimately prove more important, all four forces are now described by means of theories that have the same general form. Thus if physicists have yet to find a single key that fits all the known locks, at least all the needed keys can be cut from the same blank. The theories in this single favored class are formally designated non-Abelian gauge theories with local symmetry. What is meant by this forbidding label is the main topic of this article. For now, it will suffice to note that the theories relate the properties of the forces to symmetries of nature.

Symmetries and apparent symmetries in the laws of nature have played a part in the construction of physical theories since the time of Galileo and Newton.
The most familiar symmetries are spatial or geometric ones. In a snowflake,
for example, the presence of a symmetrical pattern can be detected at a glance. The symmetry can be defined as an invariance in the pattern that is observed when some transformation is applied to it. In the case of the snowflake the transformation is a rotation by 60 degrees, or one-sixth of a circle. If the initial position is noted and the snowflake is then turned by 60 degrees (or by any integer multiple of 60 degrees), no change will be perceived. The snowflake is invariant with respect to 60-degree rotations.
According to the same principle,
a square is invariant with respect to 90-degree rotations and a circle is said to have continuous symmetry because rotation by any angle leaves it unchanged.

Although the concept of symmetry had its origin in geometry, it is general enough to embrace invariance with respect to transformations of other kinds.
An example of a nongeometric symmetry is the charge symmetry of electromagnetism.
Suppose a number of electrically charged particles have been set out in some definite configuration and all the forces acting between pairs of particles have been measured. If the polarity of all the charges is then reversed,
the forces remain unchanged.

Another symmetry of the nongeometric kind concerns isotopic spin, a property of protons and neutrons and of the many related particles called hadrons,
which are the only particles responsive to the strong force. The basis of the symmetry lies in the observation that the proton and the neutron are remarkably similar particles. They differ in mass by only about a tenth of a percent, and except for their electric charge they are identical in all other properties. It therefore seems that all protons and neutrons could be interchanged and the strong interactions would hardly be altered. If the electromagnetic forces (which depend on electric charge) could somehow be turned off, the isotopic-spin symmetry would be exact; in reality it is only approximate.

Although the proton and the neutron seem to be distinct particles and it is hard to imagine a state of matter intermediate between them, it turns out that symmetry with respect to isotopic spin is a continuous symmetry, like the symmetry of a sphere rather than like that of a snowflake. I shall give a simplified explanation of why that is so. Imagine that inside each particle are a pair of crossed arrows, one representing the proton component of the particle and the other representing the neutron component.
If the proton arrow is pointing up (it makes no difference what direction is defined as up), the particle is a proton; if the neutron arrow is up, the particle is a neutron. Intermediate positions correspond to quantum-mechanical superpositions of the two states, and the particle then looks sometimes like a proton and sometimes like a neutron. The symmetry transformation associated with isotopic spin rotates the internal indicators of all protons and ne utrons everywhere in the universe by the same amount and at the same time. If the rotation is by exactly 90 degrees, every proton becomes a neutron and every neutron becomes a proton. Symmetry with respect to isotopic spin, to the extent it is exact,
states that no effects of this transformation can be detected.

All the symmetries I have discussed so far can be characterized as global symmetries;
in this context the word global means "happening everywhere at once."
In the description of isotopic-spin symmetry this constraint was made explicit:
the internal rotation that transforms protons into neutrons and neutrons into protons is to be carried out everywhere in the universe at the same time. In addition to global symmetries, which are almost always present in a physical theory,
it is possible to have a "local" symmetry,
in which the convention can be decided independently at every point in space and at every moment in time. Although
"local" may suggest something of more modest scope than a global symmetry,
in fact the requirement of local symmetry places a far more stringent constraint on the construction of a theory.
A global symmetry states that some law of physics remains invariant when the same transformation is applied everywhere at once. For a local symmetry to be observed the law of physics must retain its validity even when a different transformation takes place at each point in space and time.

Gauge theories can be constructed with either a global or a local symmetry
(or both), but it is the theories with local symmetry that hold the greatest interest today. In order to make a theory invariant with respect to a local transformation something new must be added: a force. Before showing how this comes about, however, it will be necessary to discuss in somewhat greater detail how forces are described in modern theories of elementary-particle interactions.

The basic ingredients of particle theory today include not only particles and forces but also fields. A field is simply a quantity defined at every point throughout some region of space and time. For example, the quantity might be temperature and the region might be the surface of a frying pan. The field then consists of temperature values for every point on the surface.

Temperature is called a scalar quantity,
because it can be represented by position along a line, or scale. The corresponding temperature field is a scalar field, in which each point has associated with it a single number, or magnitude.
There are other kinds of field as well, the most important for present p urposes being the vector field, where at each point a vector, or arrow, is drawn. A vector has both a magnitude, which is represented by the length of the arrow, and a direction, which in three-dimensional space can be specified by two angles;
hence three numbers are needed in order to specify the value of the vector. An example of a vector field is the velocity field of a fluid; at each point throughout the volume of the fluid an arrow can be drawn to show the speed and direction of flow.

In the physics of electrically charged objects a field is a convenient device for expressing how the force of electromagnetism is conveyed from one place to another. All charged particles are supposed to emanate an electromagnetic field; each particle then interacts with the sum of all the fields rather than directly with the other particles.

In quantum mechanics the particles themselves can be represented as fields.
An electron, for example, can be considered a packet of waves with some finite extension in space. Conversely, it is often convenient to represent a quantum-mechanical field as if it were a particle.
The interaction of two particles through their interpenetrating fields can then be summed up by saying the two particles exchange a third particle, which is called the quantum of the field. For example, when two electrons, each surrounded by an electromagnetic field, approach each other and bounce apart,
they are said to exchange a photon, the quantum of the electromagnetic field.

The exchanged quantum has only an ephemeral existence. Once it has been emitted it must be reabsorbed, either by the same particle or by another one,
within a finite period. It cannot keep going indefinitely, and it cannot be detected in an experiment. Entities of this kind are called virtual particles. The larger their energy, the briefer their existence.
In effect a virtual particle borrows or embezzles a quantity of energy, but it must repay the debt before the shortage can be noticed.

The range of an interaction is related to the mass of the exchanged quantum.
If the field quantum has a large mass,
more energy must be borrowed in order to support its existence, and the debt must be repaid sooner lest the discrepancy be discovered. The distance the particle can travel before it must be reabsorbed is thereby reduced and so the corresponding force has a short range.
In the special case where the exchanged quantum is massless the range is infinite.

The number of components in a field corresponds to the number of quantum-mechanical states of the field quantum.
The number of possible states is in turn related to the intrinsic spin angular momentum of the particle. The spin angular momentum can take on only discrete values; when the magnitude of the spin is measured in fundamental units, it is always an integer or a half integer.
Moreover, it is not only the magnitude of the spin that is quantized but also its direction or orientation. (To be more precise, the spin can be defined by a vector parallel to the spin axis, and the projections,
or components, of this vector along any direction in space must have values that are integers or half integers.)
The number of possible orientations, or spin states, is equal to twice the magnitude of the spin, plus one. Thus a particle with a spin of one-half, such as the e lectron, has two spin states : the spin can point parallel to the particle's direction of motion or antiparallel to it. A spin-one particle has three orientations,
namely parallel, antiparallel and transverse. A spin-zero particle has no spin axis; since all orientations are equivalent,
it is said to have just one spin state.

A scalar field, which has just one component
(a magnitude), must be represented by a field q uantum that also has one component, or in other words by a spin-zero particle. Such particles are therefore called scalar particles. Similarly,
a three-component vector field req uires a spin-one field quantum with three spin states: a vector particle. The electromagnetic field is a vector field,
and the photon, in conformity with these specifications, has a spin of one unit. The gravitational field is a more complicated structure called a tensor and has 10 components; not all of them are independent, however, and the quantum of the field, the graviton, has a spin of two units, which ordinarily corresponds to five spin states.

In the cases of electromagnetism and gravitation one further complication must be taken into account. Since the photon and the graviton are massless,
they must always move with the speed of light. Because of their velocity they have a property not shared by particles with a finite mass: the transverse spin states do not exist. Although in some formal sense the photon has three spin states and the graviton has five, in practice only two of the spin states can be detected.