The Higgs Boson: Searching for the God Particle (18 page)

Other kinds of violations of
charge parity, less predictable
than the quantum-mechanical
mixing, should also occur in B
decays. The Cornell collider and
detector are being upgraded to
search for such effects. A number
of experiments on
B
physics
are also planned at proton accelerators
around the world. Both
types of colliders will provide crucial,
and complementary, pieces of evidence
on CP violation.

The
B
factories could definitively tell
researchers that the Standard Model
concept works and then help to determine
its remaining parameters. Alternatively,
they could show that the model’s
predictions cannot fit the data no matter
what the choice of parameters. Indeed,
the results could rule out entire classes
of models beyond the Standard Model,
thus helping theorists to zero in on a
successor. And if all goes well, we may
even come to understand why our world
is made exclusively of matter.

-Originally published: Scientific American 279(4), 76-81 (October 1998)

The Higgs Boson

by Martinus J. G. Veltman

The truly fundamental problems of physics can always be explained in simple terms without the help of complicated equations or mathematical arguments. At least this was once told to me by Victor F. Weisskopf, an eminent physicist who often engages in such explanations, and he may very well be right. It certainly holds for a proposed but undiscovered particle called the Higgs boson and the so-called Higgs field associated with it.

The Higgs boson, which is named after Peter W. Higgs of the University of Edinburgh, is the chief missing ingredient in what is now called the standard model of elementary processes: the prevailing theory that describes the basic constituents of matter and the fundamental forces by which they interact. According to the standard model, all matter is made up of quarks and leptons, which interact with one another through four forces: gravity, electromagnetism, the weak force and the strong force. The strong force, for instance, binds quarks together to make protons and neutrons, and the residual strong force binds protons and neutrons together into nuclei. The electromagnetic force binds nuclei and electrons, which are one kind of lepton, into atoms, and the residual electromagnetic force binds atoms into molecules. The weak force is responsible for certain kinds of nuclear decay. The influence of the weak force and the strong force extends only over a short range, no larger than the radius of an atomic nucleus; gravity and electromagnetism have an unlimited range and are therefore the most familiar of the forces.

In spite of all that is known about the standard model, there are reasons to think it is incomplete. That is where the Higgs boson comes in. Specifically,
it is held that the Higgs boson gives mathematical consistency to the standard model, making it applicable to energy ranges beyond the capabilities of the current generation of particle accelerators but that may soon be reached by future accelerators. Moreover,
the Higgs boson is thought to generate the masses of all the fundamental particles; in a manner of speaking,
particles "eat" the Higgs boson to gain weight.

The biggest drawback of the Higgs boson is that so far no evidence of its existence has been found. Instead a fair amount of indirect evidence already suggests that the elusive particle does not exist. Indeed, modern theoretical physics is constantly filling the vacuum with so many contraptions such as the Higgs boson that it is amazing a person can even see the stars on a clear night! Although future accelerators may well find direct evidence of the Higgs boson and show that the motivations for postulating its existence are correct, I believe things will not be so simple. I must point out that this does not mean the entire standard model is wrong. Rather, the standard model is probably only an approximation–albeit a good one–of reality.

Even though the only legitimate reason for introducing the Higgs boson is to make the standard model mathematically consistent, much attention has been given to the conceptually easier proposal that the particle generates the masses of all the fundamental particles. I shall therefore begin with that topic.

Central to an understanding of how the Higgs boson would generate mass is the concept of a field. A field is simply a quantity, such as temperature,
defined at every point throughout some region of space and time, such as the surface of a frying pan. In physics the term "field" is usually reserved for such entities as the gravitational field and the electromagnetic field. Fields generally make themselves felt by means of the exchange of a mediating particle; the particle that mediates the electromagnetic field, for example, is the photon, or quantum of light. The mediating particles of the gravitational field, the weak field and the strong field are respectively the graviton
(which has not yet been detected),
three weak vector bosons, called the
W+, W-
and
Z
⁰
particles, and eight gluons. In a somewhat analogous way the Higgs boson is the mediating particle of the proposed Higgs field.

It is now assumed that there is a constant Higgs field throughout all space,
that is, the vacuum of outer space is not empty but contains this constant field. The Higgs field is thought to generate mass by coupling to particles.
Depending on the coupling strength, a particle in space has a certain potential energy. By Einstein's famous equation,
E = mc
²
(energy equals mass multiplied by the square of the speed of light), the coupling energy is equivalent to a mass. The stronger the coupling,
the greater the mass.

The way particles are thought to acquire mass in their interactions with the Higgs field is somewhat analogous to the way pieces of blotting paper absorb ink. In such an analogy the pieces of paper represent individual particles and the ink represents energy, or mass. Just as pieces of paper of differing size and thickness soak up varying amounts of ink, different particles
"soak up" varying amounts of energy,
or mass. The observed mass of a particle depends on the particle's "energyabsorbing"
ability and on the strength of the Higgs field in space.

What are the characteristics of the proposed Higgs field? In order to endow particles with mass, the Higgs field, if it exists, would have to assume a uniform, nonzero value even in the vacuum. Moreover, the Higgsfield would be a scalar field, which is one of two kinds of field important in describing the interactions of particles.
A scalar field is a field in which each point has associated with it a single magnitude, or number. The other important field is a vector field: a 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.
The electromagnetic, weak and strong fields are all vector fields. (The gravitational field is a special entity called a tensor field.)

The proposed Higgs field must be a scalar field, because if it were a vector field, the mass of a particle would in general depend on the particle's alignment with the field. Stated in a somewhat oversimplified way, the mass of a person would change if he or she turned around while standing in the same place. In other words, the Higgs field is "spinless."

Because the Higgs field is spinless,
the Higgs boson must also be spinless.
Spin, as applied to elementary particles,
is a quantum-mechanical property roughly equivalent to the classical spin of a rotating ball. Elementary particles can take on only integer (0, 1, 2 and so on) and half-integer (1/2, 3/2 and so on) values of spin. Particles that have integral spin are called bosons and particles that have half-integral spin are called fermions. Bosons and fermions have sharply differing properties,
but I shall not delve into that topic here.

The Higgs boson is called a scalar boson because it has a spin of 0. Most other bosons associated with fields are thought to be vector bosons: particles that have a spin of l. The photon,
gluon and
W+, W-
and
Z
⁰
particles,
for instance, are spin-1 bosons.

Since vector bosons are typically associated with the fundamental forces of nature and the Higgs boson is a scalar boson, the force by which particles couple to the Higgs field must be a new force. It is introduced explicitly and solely as a mechanism to improve the mathematical consistency of the standard model. The Higgs force behaves mathematically in a similar manner to the recently publicized
"fifth force" reported by Ephraim Fischbach of Purdue University. Theproposed Higgs force is, however,
weaker and has a much shorter range than the "fifth force."

The Higgs force is not a universal force, because it couples differently to different particles. Specifically, if a particle is observed to have mass, the strength of the coupling to the Higgs field is assumed to be whatever quantity is necessary to generate precisely that mass. Presumably the Higgs field does not couple to the photon, since experiment shows the photon is massless.
But apparently it couples to the
W+, W-
and
Z
⁰
particles, because they do have mass. It should perhaps be noted that particles could have a mass of their own, in addition to what they are thought to acquire from the Higgs field. Curiously, however, in the standard model not a single particle could have a mass of its own without destroying the mathematical completeness of the theory.

From a physical point of view little is gained by proposing that the Higgs boson accounts for mass. It is not known, for example, why the Higgs field should couple more strongly to some particles than it does to others.
Nor do investigators understand how the mass of the Higgs boson itself
(which is not known) comes about, although it is generally presumed to be dominantly through a self-interaction with the Higgs field. In this sense ignorance about the origin of particle masses is replaced by ignorance about particle-Higgs couplings, and no real knowledge is gained.

Moreover, the introduction of the Higgs boson creates a significant problem with respect to the "holy" field of gravitation. The equivalence of mass and energy implies that the graviton,
which couples to anything that carries mass, should couple to anything that carries energy, including the Higgs field. The coupling of the graviton to the Higgs field–ever present in all space–would generate a huge "cosmological constant": it would curve the universe into an object roughly the size of a football. If the Higgs boson is assumed to have roughly the same massas the weak vector bosons, the energy density of the Higgs field in the vacuum would be 10 trillion times greater than the density of matter in an atomic nucleus. If the earth were compressed to this density, its volume would be approximately 500 cubic centimeters, or a bit more than the size of a soft-drink can. Needless to say, this is contrary to experiment.

The theorists' way out is really something. It is assumed that the
"true" vacuum (one without a Higgs field) is curved in a negative sense: it has a cosmological constant equal in magnitude but opposite in sign to the one generated by the Higgs field. The introduction of the Higgs field then flattens out space to make precisely the universe as we know it. This solution is, of course, not very satisfactory,
and many ingenious attempts have been made to solve the problem of the huge cosmological constant. None of the attempts has succeeded. If anything,
matters have grown wor.se because theorists keep dumping more particles and fields into the vacuum.Perhaps somehow the universe became flat from the dynamics of the big-bang explosion, which is believed to have created the universe some 15 to 20 billion years ago.

The theory as it stands, with one Higgs field, does not explicitly contradict observation, even if one must accept the incredible disappearance of the cosmological constant. Certain extensions of the theory proposed over the past decade often involve the introduction of additional Higgs fields. Although the arguments for such extensions are often compelling, the phenomena associated with these extra Higgs fields have either never been seen or contradict observed facts.

To account in an elegant way for certain symmetries observed in the strong interactions, for example, a second Higgs field was proposed by Helen R. Quinn of the Stanford Linear Accelerator Center (SLAC) and Roberto Peccei of the Deutsches Electronen-Synchrotron (DESY, the electron accelerator in Hamburg). The ensuing theory predicted a new and presumably very light particle called the axion. So far, in spite of extensive searches, the axion has not been found.
In addition the theory has dramatic cosmological consequences concerning a phenomenon known as "domain walls." In general a domain wall marks where two regions of differing properties meet each other. Domain walls are, for instance, found in permanent magnets, where one region of atoms whose spins are aligned in one direction meets another region of atoms whose spins are aligned in a different direction.

It is believed that certain Higgs fields would have given rise to domain walls in the early universe. When the universe was young, the temperature was extremely hot and no Higgs field is thought to have existed. At some time the universe would have cooled sufficiently to allow a background Higgs field to come into being. Unless the cooling were completely uniform,
the Higgs field would quite likely have exhibited different properties from one region in space to the next. To what extent the clash of such regions would result in visible or even violent phenomena depends on detailed properties of the Higgs fields, but one would expect some kind of clash in connection with the suggestive proposal of Quinn and Peccei.

The question is why domain walls between such regions have not been observed. It could mean that there is no Higgs field, or that nature has been careful in its use of the field. Alternatively, the walls could have disappeared early in the history of the universe. This is rather typical: one starts with an excellent argument, drags in a Higgs field and then things go wrong. It certainly inspires little faith in the mechanism altogether.

The introduction of an extra Higgs boson also creates difficulties in a model that is attracting considerable attention called the SU(5) grand unified theory. The goal of unified theories in general is to account for the four forces in terms of one fundamental force. A step toward achieving that goal was reached over the past two decades with the introduction and verification of the so-called electroweak theory. The theory holds that the electromagnetic force and the weak force are manifestations of the same underlying force: the electroweak force. The electroweak theory was dramatically confirmed in 1983 at CERN, the European laboratory for particle physics,
with the detection of the
W+, W-
and
Z
⁰
particles.

The SU(5) grand unified theory seeks to bind the strong force and the electroweak force into one common force; the designation SU(5) refers to the mathematical group of symmetries on which the theory is based. According to SU(5) theory, the strong, weak and electromagnetic forces, which behave quite differently under ordinary circumstances, become indistinguishable when particles interact with an energy of approximately 10
¹⁵
billion electron volts (GeV).