The Higgs Boson: Searching for the God Particle (23 page)

A practical problem with performing
such tests is that we do not yet understand
the theories well enough to calculate
what masses the Higgs bosons themselves
should have, which makes searching
for them more difficult because one
must examine a range of masses. A combination
of theoretical reasoning and
data from experiments guides us about
roughly what masses to expect.

The Large Electron-Positron Collider
(LEP) at CERN, the European
laboratory for particle physics near Geneva,
operated over a mass range that
had a significant chance of including a
Higgs boson. It did not find one—although
there was tantalizing evidence
for one just at the limits of the collider’s
energy and intensity—before it was shut
down in 2000 to make room for constructing
a newer facility, CERN’s
Large Hadron Collider (LHC). The
Higgs must therefore be heavier than
about 120 proton masses. Nevertheless,
LEP did produce indirect evidence that
a Higgs boson exists: experimenters at
LEP made a number of precise measurements,
which can be combined with
similar measurements from the Tevatron
and the collider at the Stanford
Linear Accelerator Center. The entire
set of data agrees well with theory only

if certain interactions of particles with
the lightest Higgs boson are included
and only if the lightest Higgs boson is
not heavier than about 200 proton
masses. That provides researchers with
an upper limit for the mass of the Higgs
boson, which helps focus the search.

For the next few years, the only collider
that could produce direct evidence
for Higgs bosons will be the Tevatron.
Its energy is suffi cient to discover a Higgs
boson in the range of masses implied by
the indirect LEP evidence, if it can consistently
achieve the beam intensity it
was expected to have, which so far has
not been possible. In 2007 the LHC,
which is seven times more energetic and
is designed to have far more intensity
than the Tevatron, is scheduled to begin
taking data. It will be a factory for Higgs
bosons (meaning it will produce many of
the particles a day). Assuming the LHC
functions as planned, gathering the relevant
data and learning how to interpret
it should take one to two years. Carrying
out the complete tests that show in detail
that the interactions with Higgs fields
are providing the mass will require a
new electron-positron collider in addition
to the LHC (which collides protons)
and the Tevatron (which collides protons
and antiprotons).

Dark Matter

What is discovered about Higgs
bosons will not only test whether the
Higgs mechanism is indeed providing
mass, it will also point the way to how
the Standard Model can be extended to
solve problems such as the origin of dark
matter.

With regard to dark matter, a key
particle of the SSM is the lightest superpartner
(LSP). Among the superpartners
of the known Standard Model particles
predicted by the SSM, the LSP is the one
with the lowest mass. Most superpartners
decay promptly to lower-mass superpartners,
a chain of decays that ends
with the LSP, which is stable because it
has no lighter particle that it can decay
into. (When a superpartner decays, at
least one of the decay products should be
another superpartner; it should not decay
entirely into Standard Model particles.)
Superpartner particles would have
been created early in the big bang but
then promptly decayed into LSPs. The
LSP is the leading candidate particle for
dark matter.

The Higgs bosons may also directly
affect the amount of dark matter in the
universe. We know that the amount of
LSPs today should be less than the
amount shortly after the big bang, because
some would have collided and annihilated
into quarks and leptons and
photons, and the annihilation rate may
be dominated by LSPs interacting with
Higgs bosons.

As mentioned earlier, the two basic
SSM Higgs fields give mass to the Standard
Model particles and some mass to
the superpartners, such as the LSP. The
superpartners acquire more mass via additional
interactions, which may be with
still further Higgs fields or with fields
similar to the Higgs. We have theoretical
models of how these processes can happen,
but until we have data on the superpartners
themselves we will not know
how they work in detail. Such data are
expected from the LHC or perhaps even
from the Tevatron.

Neutrino masses may also arise from
interactions with additional Higgs or
Higgs-like fields, in a very interesting
way. Neutrinos were originally assumed
to be massless, but since 1979 theorists
have predicted that they have small
masses, and over the past decade several
impressive experiments have confirmed
the predictions. The neutrino masses are less than
a millionth the size of the next smallest
mass, the electron mass. Because neutrinos
are electrically neutral, the theoretical
description of their masses is more
subtle than for charged particles. Several
processes contribute to the mass of each
neutrino species, and for technical reasons
the actual mass value emerges from
solving an equation rather than just adding
the terms.

Thus, we have understood the three
ways that mass arises: The main form of
mass we are familiar with—that of protons
and neutrons and therefore of atoms—comes from the motion of quarks
bound into protons and neutrons. The
proton mass would be about what it is
even without the Higgs field. The masses
of the quarks themselves, however, and
also the mass of the electron, are entirely
caused by the Higgs field. Those masses
would vanish without the Higgs. Last,
but certainly not least, most of the
amount of superpartner masses, and
therefore the mass of the dark matter
particle (if it is indeed the lightest superpartner),
comes from additional interactions
beyond the basic Higgs one.

Finally, we consider an issue known
as the family problem. Over the past half
a century physicists have shown that the
world we see, from people to flowers to
stars, is constructed from just six particles:
three matter particles (up quarks,
down quarks and electrons), two force
quanta (photons and gluons), and Higgs
bosons—a remarkable and surprisingly
simple description. Yet there are four
more quarks, two more particles similar
to the electron, and three neutrinos. All
are very short-lived or barely interact
with the other six particles. They can be
classifi ed into three families: up, down,
electron neutrino, electron; charm,
strange, muon neutrino, muon; and top,
bottom, tau neutrino, tau. The particles
in each family have interactions identical
to those of the particles in other families.
They differ only in that those in the second
family are heavier than those in the
first, and those in the third family are
heavier still. Because these masses arise
from interactions with the Higgs field,
the particles must have different interactions
with the Higgs field.

Hence, the family problem has two
parts: Why are there three families when
it seems only one is needed to describe
the world we see? Why do the families
differ in mass and have the masses they
do? Perhaps it is not obvious why physicists
are astonished that nature contains
three almost identical families even if one
would do. It is because we want to fully
understand the laws of nature and the
basic particles and forces. We expect that
every aspect of the basic laws is a necessary
one. The goal is to have a theory in
which all the particles and their mass ratios
emerge inevitably, without making
ad hoc assumptions about the values of
the masses and without adjusting parameters.
If having three families is essential,
then it is a clue whose signifi cance is currently
not understood.

Tying It All Together

The standard model and the SSM
can accommodate the observed family
structure, but they cannot explain it.
This is a strong statement. It is not that
the SSM has not yet explained the family
structure but that it cannot. For me, the
most exciting aspect of string theory is
not only that it may provide us with a
quantum theory of all the forces but also
that it may tell us what the elementary
particles are and why there are three
families. String theory seems able to address
the question of why the interactions
with the Higgs fi eld differ among the
families. In string theory, repeated families
can occur, and they are not identical.
Their differences are described by properties
that do not affect the strong, weak,
electromagnetic or gravitational forces
but that do affect the interactions with
Higgs fields, which fits with our having
three families with different masses. Although
string theorists have not yet fully
solved the problem of having three families,
the theory seems to have the right
structure to provide a solution. String
theory allows many different family
structures, and so far no one knows why
nature picks the one we observe rather
than some other. Data on the quark and
lepton masses and on their superpartner
masses may provide major clues to teach
us about string theory.

One can now understand why it took
so long historically to begin to understand
mass. Without the Standard Model
of particle physics and the development
of quantum fi eld theory to describe particles
and their interactions, physicists
could not even formulate the right questions.
Whereas the origins and values of
mass are not yet fully understood, it is
likely that the framework needed to understand
them is in place. Mass could not
have been comprehended before theories
such as the Standard Model and its supersymmetric
extension and string theory
existed. Whether they indeed provide
the complete answer is not yet clear, but
mass is now a routine research topic in
particle physics.

-Originally published: Scientific American 293(1), 40-48 (July 2005)

Is Nature Supersymmetric?

by Howard E. Haber and Gordon L. Kane

About 25 centuries ago the Ionian Greeks argued that the apparent complexity of the universe could be understood in terms of a few simple underlying laws. Remarkable progress has been made toward realizing that goal. It appears that the basic constituents of matter have been identified. A few forces can account for the behavior of any form of matter, ranging from subatomic particles to galaxies. To complete the description of the laws of nature, however, further insight is still needed. For the past decade a large number of theoretical physicists have extensively explored an approach called supersymmetry. A supersymmetric theory incorporates and extends the successful discoveries of past years in an attempt to construct a new and more comprehensive theory. It also makes testable predictions.

Perhaps the most convenient point of entry into the concept of supersymmetry is the standard picture of the fundamental constituents of matter. All matter consists of molecules, which in turn consist of atoms. An atom consists of a number of protons and neutrons bound together in a nucleus, which is surrounded by a "cloud" of electrons. Individual elements are distinguished by their number of protons.

Until recently protons and neutrons were thought to be fundamental particles.
Experiments carried out with high-energy particle accelerators during the past two decades have revealed that they are not; protons and neutrons appear to be composed of elementary particles known as quarks. Quarks are observed to carry a fraction (+2/3 or
-1/3) of the electric charge of the proton. There are six "flavors," or types, of quarks. They are called up,
down, charm, strange, top and bottom.

An individual quark is not expected to be isolated, or observed alone;
quarks are always part of composite particles known as hadrons. Hundreds of hadrons have been identified and catalogued. They include the proton and neutron as well as the more exotic pion and kaon. A proton, for instance,
is composed of two up quarks and one down quark, and a neutron is composed of one up quark and two down quarks. For an appropriate analogy one can liken quarks to the ends of a string and hadrons to the entire string,
including the quarks. Suppose one tries to isolate a quark by colliding two hadrons.
If a quark tries to get out after the collision, it stretches the string, which breaks. The result is more strings, that is, more hadrons (mainly pions, since they are the lightest hadrons).

Unlike protons and neutrons, electrons do seem to be fundamental particles.
In fact, they are part of another family of so-called elementary particles known as leptons. There are six flavors of leptons too: the electron, the muon, the tau particle, the electron neutrino, the muon neutrino and the tau neutrino.

All interactions between leptons and quarks can be accounted for by four kinds of force: gravitation, electromagnetism,
the strong force and the weak force. The electromagnetic force binds electrons and nuclei to make atoms. The atoms, although they are electrically neutral, interact through a residual electromagnetic force to form molecules. The strong force binds quarks to make protons, neutrons and all other hadrons, and the resid ual strong force between protons and neutrons is the so-called nuclear force that binds them into nuclei. The weak force is responsible for such phenomena as some nuclear decays and aspects of the fusion process that releases energy from the sun. In reality there are only three fundamental forces: a great accomplishment of the past two decades has been the demonstration that the electromagnetic and weak forces are manifestations of the same force,
known as the electroweak force. The strengths of the forces vary widely.
The strength of the electromagnetic force between two protons, for instance,
is roughly 10
³⁶
times greater than the strength of the corresponding gravitational force.

The forces are transmitted by the exchange of a number of particles. The photon, the quantum of electromagnetic radiation, is the carrier of the electromagnetic force. Eight particles known as gluons mediate the strong force. The photon and the giuons can be interpreted as particles having zeromass. The weak force is mediated by three particles: the positively charged
W+
, the negatively charged
W-
and the neutral
Z
⁰
Unlike the photon and the gluons, these particles are heavy:
they have masses nearly 100 times the mass of the proton. All these carriers have been experimentally observed.
The mediating agent of the gravitational force, as yet only conjectured, is the graviton.

The theory that describes the quarks and the leptons and their interactions has come to be called the standard model. For the standard model to be mathematically consistent a so-called Higgs particle must exist. (The simplest version of the model contains an electrically neutral Higgs particle;
more general models allow for electrically charged Higgs particles as well.)
It is thought the masses of the
W+
, wand
Z
⁰
particles and of the quarks and the leptons are generated through interactions with the Higgs particle.
The standard model predicts how the Higgs particle should interact with the other particles, but the mass of the Higgs particle itself is not predicted.
The expected properties are such that so far no experiment could have found a Higgs particle, and since the mass is not known it is hard to plan experiments to search for it.

How have physicists made sense of the panoply of particles described in the standard model? First,
the particles can be divided into two fundamental classes: fermions and bosons. Leptons and quarks, the basic constituents of matter, are fermions.
The basic particles that mediate the four forces are bosons. Fermions behave as though they carry an intrinsic angular momentum, called spin, equal to half-integer units (1/2, 3/2 and so on) of Planck's constant, which is itself the fundamental unit of angular momentum in quantum theory. Bosons have spins that are integer units (0,
1, 2 and so on) of Planck's constant.
The effects of the half-integer spin difference between fermions and bosons are profound. Fermions are "antisocial"
and tend to occupy different energy states; bosons are "gregarious" and tend to clump together in the same energy states. All leptons and quarks are spin-1/2 fermions. The photon, the
W+
,
W-
and
Z
⁰
particles and the eight gluons are spin-1 bosons. The graviton is expected to be a spin-2 boson and the Higgs particle is expected to be a spin-0, or spinless, boson.

An important unifying element of the standard model is the concept of symmetry. The interactions among the various particles are symmetric (that is, invariant, or unchanged) in the face of a number of subtle interchanges.
Suppose, for example, several protons are arranged in close proximity to one another (as in a nucleus), so that the strong force among them is much greater than the repulsive electromagnetic force. Imagine that the strong forces acting among the protons are then measured. If one now replaces each proton with a neutron, the forces remain unchanged. In fact, mathematically one can imagine replacing each proton with a "mixture" of the proton and the neutron, and again the forces remain unchanged. This is an example of a symmetry where the same interchange is made at all points in space.

More generalized symmetries are those in which interchanges vary from point to point in space and time. Such symmetries are important elements of gauge theories. All interactions described by the standard model can be successfully accounted for by exploiting such generalized symmetries.

The stage is now set for supersymmetry.
It is apparent that in spite of the success of the standard model, physicists must look beyond it if they hope to understand completely the properties of matter; some aspects of the standard model are mysterious and suggest that more discoveries will come. First,
no one can explain why the standard model takes the form it does. The mathematical structure of the theory is elegant and surprisingly simple, and the observed interactions show many symmetries. Yet a number of other forms (different choices of symmetries)
would theoretically have been equally plausible and elegant. Second,
there is no understanding of the physical origin of the masses of the fundamental particles and the strength of the forces acting between them. Why do they have the values they do? Most particle physicists hope that eventually such parameters can be calculatedrather than just measured. Although there are no direct clues at present as to how to extend the standard model,
supersymmetry seems to many physicists to be a likely direction in which to look. In the past few years efforts have been under way to search for evidence of supersymmetry in nature.

The search for experimental evidence of supersymmetry centers on the discovery of new particles. The reason is that the theory requires that for every ordinary particle there exist a
"superpartner" with identical properties-
except its spin differs by half a unit. In other words, supersymmetry differs from all previous theories in that it relates the two fundamental classes of particles, fermions and bosons,
to each other. In addition the strengths of the interaction forcesamong the proposed superpartners are identical with the strengths of the interaction forces among the various normal particles.

The spin-0 superpartners of the fermions are named by adding the prefix s- to the normal particle name; for example,
the spin-1/2 electron and the quark have the spin-0 partners selectron and squark respectively. The spin-1/2 superpartners of the bosons are named by adding the suffix -ina to the root of the normal particle name; for example, the partner of the spin-1 photon is the spin-1/2 photino and the partner of the spin-1 gluon is the spin-1/2 gluino. (For the Higgs particle there is a minor technical complication.
The supersymmetric theory requires both electrically charged and neutral Higgs particles; a positively charged
H+
, a negatively charged
H
and three neutrals, collectively denoted as
H
⁰
, are needed.)

What advantages are gained by multiplying the number of elementary particles by 2? First, supersymmetry can solve a fundamental problem: it provides a mechanism by which a single theory can account for two important energies, or masses, that differ by many orders of magnitude. (As expressed by Einstein's famous equation
E=mc
²
, mass and energy are eq uivalent and can be referred to interchangeably.)
Those energies are the masses of the
W+, W-
and
Z
⁰
particles,
roughly 10
¹¹
electron-volt units of energy,
and the so-called Planck mass,
about 10
²⁸
electron volts. The Planck mass is an important quantity to include in any theory that tries to account for gravity in a unification of the four fundamental forces; if elementary particles with a mass of 10
²⁸
electron volts existed,
the strength of the gravitational force among them would be greater than the strength of each of the other fundamental forces.

Ordinarily one would expect that if the masses of the
W
and
Z
⁰
particles were computable in a fundamental theory that contained the Planck mass, they would turn out to be roughly the same order of magnitude as the Planck mass, rather than 10
¹⁷
times smaller. In the supersymmetric theory,
however, delicate cancellations occur that allow the W and
Z
⁰
masses to be many orders of magnitude smaller than the Planck mass, just as they are observed to be. These delicate cancellations are not contrived but are guaranteed by the mathematical structure of the supersymmetric theory.

We should point out, however, that not all widely separated energies are problematical. For example, existing theories can easily account for the energy levels observed in both hadrons
(such as protons and neutrons) and atoms,
even though the energy levels of the hadrons are roughly 10
⁹
electron volts and those of the atoms are roughly 10 electron volts. The reason is found in the hierarchy of structure: atoms are made up of nuclei and electrons,
nuclei are made up of protons and neutrons, and protons and neutrons are made up of quarks: If, however,
one wants to develop a theory of fundamental particles and interactions,
one no longer has recourse to such a hierarchy.

A second feature of supersymmetry is its close relation to Einstein's theory of gravity. Ever since Einstein introduced general relativity physicists have attempted, without much success,
to unify gravity and quantum mechanics.
It is now widely believed by theorists that a quantum-mechanical theory of gravity will be a supersymmetric one.

Although many physicists have contributed to the development of supersymmetry,
a mathematically consistent formulation of the theory was first made in the early 1970's by a number of different groups working independently:
Andre Neveu and John H.
Schwarz, then at Princeton University;
Pierre M. Ramond of the University of Florida; Yu. A. Gol'fond and E. P.
Likhtman of the Physics Institute of the U.S.S.R. Academy of Sciences;
V. P. Akulov and D. V. Volkov of the Ukrainian Physical-Technical Institute,
and Julius Wess of the University of Karlsruhe in West Germany and Bruno Zumino of the University of California at Berkeley.

If indeed nature is supersymmetric,
the super symmetry must be a "broken symmetry," that is, a symmetry that holds true approximately, or for parts of the theory only. Imagine what would happen if nature were exactly supersymmetric. Selectrons would have the same mass as electrons and would bind to protons by the electromagnetic force. The properties of atoms formed in such a way would be very different from those of normal atoms.
As fermions, electrons must occupy different energy levels in atoms;
as bosons, selectrons would occupy the same energy levels. If atoms contained selectrons instead of electrons, the structure of the periodic table of elements would be completely altered.
Since such atoms have not been observed,
the mass of the selectron (if the selectron exists) must be larger than the mass of the electron, and so the symmetry is broken.