The Higgs Boson: Searching for the God Particle (22 page)

-Originally published: Scientific American 288(6), 68-75 (June 2003)

The Mysteries of Mass

by Gordon Kane

Most people think they know what mass is, but they understand only part of
the story. For instance, an elephant is clearly bulkier and weighs more than
an ant. Even in the absence of gravity, the elephant would have greater mass—
it would be harder to push and set in motion. Obviously the elephant is more massive
because it is made of many more atoms than the ant is, but what determines the masses
of the individual atoms? What about the elementary particles that make up the atoms—
what determines their masses? Indeed, why do they even have mass?

We see that the problem of mass has two independent aspects. First, we need to
learn how mass arises at all. It turns out mass results from at least three different
mechanisms, which I will describe below. A key player in physicists’ tentative theories
about mass is a new kind of field that permeates all of reality, called the Higgs field.
Elementary particle masses are thought to come about from the interaction with the
Higgs field. If the Higgs field
exists, theory demands that it
have an associated particle,
the Higgs boson. Using particle
accelerators, scientists are
now hunting for the Higgs.

The second aspect is that
scientists want to know why
different species of elementary
particles have their specific
quantities of mass. Their intrinsic
masses span at least 11
orders of magnitude, but we
do not yet know why that
should be so. For comparison,
an elephant and the smallest
of ants differ by about 11 orders
of magnitude of mass.

What Is Mass?

Isaac Newton presented
the earliest scientific definition
of mass in 1687 in his landmark
Principia
: “The quantity of matter is the measure
of the same, arising from its density and bulk conjointly.” That very basic definition
was good enough for Newton and other scientists for more than 200 years. They understood
that science should proceed first by describing how things work and later by
understanding why. In recent years, however, the why of mass has become a research
topic in physics. Understanding the meaning and origins of mass will complete and
extend the Standard Model of particle physics, the well-established theory that describes
the known elementary particles and their interactions. It will also resolve mysteries
such as dark matter, which makes up about 25 percent of the universe.

The foundation of our modern understanding of mass is far more intricate than
Newton’s definition and is based on the Standard Model. At the heart of the Standard
Model is a mathematical function called
a Lagrangian, which represents how the
various particles interact. From that
function, by following rules known as
relativistic quantum theory, physicists
can calculate the behavior of the elementary
particles, including how they come
together to form compound particles,
such as protons. For both the elementary
particles and the compound ones, we
can then calculate how they will respond
to forces, and for a force
F
, we can write
Newton’s equation
F = ma
, which relates
the force, the mass and the resulting acceleration.
The Lagrangian tells us what
to use for m here, and that is what is
meant by the mass of the particle.

But mass, as we ordinarily understand
it, shows up in more than just
F = ma
. For example, Einstein’s special
relativity theory predicts that massless
particles in a vacuum travel at the speed
of light and that particles with mass
travel more slowly, in a way that can be
calculated if we know their mass. The
laws of gravity predict that gravity acts
on mass and energy as well, in a precise
manner. The quantity
m
deduced from
the Lagrangian for each particle behaves
correctly in all those ways, just as we expect
for a given mass.

Fundamental particles have an intrinsic
mass known as their rest mass
(those with zero rest mass are called
massless). For a compound particle, the
constituents’ rest mass and also their kinetic
energy of motion and potential energy
of interactions contribute to the
particle’s total mass. Energy and mass
are related, as described by Einstein’s famous
equation,
E = mc
²
(energy equals
mass times the speed of light squared).

An example of energy contributing
to mass occurs in the most familiar kind
of matter in the universe—the protons
and neutrons that make up atomic nuclei
in stars, planets, people and all that we
see. These particles amount to 4 to 5 percent
of the mass-energy of the universe. The Standard
Model tells us that protons and neutrons
are composed of elementary particles
called quarks that are bound together by
massless particles called gluons. Although
the constituents are whirling
around inside each proton, from outside
we see a proton as a coherent object with
an intrinsic mass, which is given by adding
up the masses and energies of its
constituents.

The Standard Model lets us calculate
that nearly all the mass of protons and
neutrons is from the kinetic energy of
their constituent quarks and gluons (the
remainder is from the quarks’ rest mass).
Thus, about 4 to 5 percent of the entire
universe—almost all the familiar matter
around us—comes from the energy of
motion of quarks and gluons in protons
and neutrons.

The Higgs Mechanism

Unlike protons and neutrons, truly
elementary particles—such as quarks
and electrons—are not made up of smaller
pieces. The explanation of how they
acquire their rest masses gets to the very
heart of the problem of the origin of
mass. As I noted above, the account proposed
by contemporary theoretical physics
is that fundamental particle masses
arise from interactions with the Higgs
field. But why is the Higgs field present
throughout the universe? Why isn’t its
strength essentially zero on cosmic
scales, like the electromagnetic field?
What is the Higgs field?

The Higgs field is a quantum field.
That may sound mysterious, but the fact
is that all elementary particles arise as
quanta of a corresponding quantum
field. The electromagnetic field is also a
quantum field (its corresponding elementary
particle is the photon). So in this respect,
the Higgs field is no more enigmatic
than electrons and light. The Higgs
field does, however, differ from all other
quantum fields in three crucial ways.

The first difference is somewhat technical.
All fields have a property called
spin, an intrinsic quantity of angular momentum
that is carried by each of their
particles. Particles such as electrons have
spin ½ and most particles associated
with a force, such as the photon, have
spin 1. The Higgs boson (the particle of
the Higgs field) has spin 0. Having 0 spin
enables the Higgs field to appear in the
Lagrangian in different ways than the
other particles do, which in turn allows—and leads to—its other two distinguishing
features.

The second unique property of the
Higgs field explains how and why it has
nonzero strength throughout the universe.
Any system, including a universe,
will tumble into its lowest energy state,
like a ball bouncing down to the bottom
of a valley. For the familiar fields, such
as the electromagnetic fields that give us
radio broadcasts, the lowest energy state
is the one in which the fields have zero
value (that is, the fields vanish)—if any
nonzero field is introduced, the energy
stored in the fields increases the net energy
of the system. But for the Higgs
field, the energy of the universe is lower
if the field is not zero but instead has a
constant nonzero value. In terms of the
valley metaphor, for ordinary fields the
valley floor is at the location of zero field;
for the Higgs, the valley has a hillock at
its center (at zero field) and the lowest
point of the valley forms a circle around
the hillock.
The universe, like a ball, comes to rest
somewhere on this circular trench,
which corresponds to a nonzero value of
the field. That is, in its natural, lowest
energy state, the universe is permeated
throughout by a nonzero Higgs field.

The final distinguishing characteristic
of the Higgs field is the form of its interactions
with the other particles. Particles
that interact with the Higgs field
behave as if they have mass, proportional
to the strength of the field times the
strength of the interaction. The masses
arise from the terms in the Lagrangian
that have the particles interacting with
the Higgs field.

Our understanding of all this is not
yet complete, however, and we are not
sure how many kinds of Higgs fields
there are. Although the Standard Model
requires only one Higgs field to generate
all the elementary particle masses, physicists
know that the Standard Model
must be superseded by a more complete
theory. Leading contenders are extensions
of the Standard Model known as
Supersymmetric Standard Models
(SSMs). In these models, each Standard
Model particle has a so-called superpartner
(as yet undetected) with closely related
properties. With the Supersymmetric Standard
Model, at least two different kinds
of Higgs fields are needed. Interactions
with those two fields give mass to the
Standard Model particles. They also give
some (but not all) mass to the superpartners.
The two Higgs fields give rise to five
species of Higgs boson: three that are
electrically neutral and two that are
charged. The masses of particles called
neutrinos, which are tiny compared with
other particle masses, could arise rather
indirectly from these interactions or from
yet a third kind of Higgs field.

Theorists have several reasons for
expecting the SSM picture of the Higgs
interaction to be correct. First, without
the Higgs mechanism, the W and Z bosons
that mediate the weak force would
be massless, just like the photon (which
they are related to), and the weak interaction
would be as strong as the electromagnetic
one. Theory holds that the
Higgs mechanism confers mass to the W
and Z in a very special manner. Predictions
of that approach (such as the ratio
of the W and Z masses) have been confi
rmed experimentally.

Second, essentially all other aspects
of the Standard Model have been well
tested, and with such a detailed, interlocking
theory it is difficult to change
one part (such as the Higgs) without affecting
the rest. For example, the analysis
of precision measurements of W and
Z boson properties led to the accurate
prediction of the top quark mass before
the top quark had been directly produced.
Changing the Higgs mechanism
would spoil that and other successful
predictions.

Third, the Standard Model Higgs
mechanism works very well for giving
mass to all the Standard Model particles,
W and Z bosons, as well as quarks and
leptons; the alternative proposals usually
do not. Next, unlike the other theories,
the SSM provides a framework to
unify our understanding of the forces of
nature. Finally, the SSM can explain
why the energy “valley” for the universe
has the shape needed by the Higgs mechanism.
In the basic Standard Model the
shape of the valley has to be put in as a
postulate, but in the SSM that shape can
be derived mathematically.

Testing the Theory

Naturally, physicists want to
carry out direct tests of the idea that mass
arises from the interactions with the different
Higgs fields. We can test three key
features. First, we can look for the signature
particles called Higgs bosons. These
quanta must exist, or else the explanation
is not right. Physicists are currently
looking for Higgs bosons at the Tevatron
Collider at Fermi National Accelerator
Laboratory in Batavia, Ill.

Second, once they are detected we
can observe how Higgs bosons interact
with other particles. The very same
terms in the Lagrangian that determine
the masses of the particles also fix the
properties of such interactions. So we
can conduct experiments to test quantitatively
the presence of interaction terms
of that type. The strength of the interaction
and the amount of particle mass are
uniquely connected.

Third, different sets of Higgs fields,
as occur in the Standard Model or in the
various SSMs, imply different sets of
Higgs bosons with various properties, so
tests can distinguish these alternatives,
too. All that we need to carry out the
tests are appropriate particle colliders—ones that have sufficient energy to produce
the different Higgs bosons, suffi-
cient intensity to make enough of them
and very good detectors to analyze what
is produced.