The Higgs Boson: Searching for the God Particle (2 page)

What rules govern the combinations of quarks that form hadrons?
Mesons are composed of a
quark and an antiquark.
Because each quark has a spin of 1/2, the net spin of a meson is 0 if its constituents spin in opposite directions and 1
if they spin in the same direction, although in their excited states mesons may have larger values of spin owing to the quarks'
orbital motion.
The other class of hadrons, the baryons, consist of three quarks each. Summing the constituent quarks'
possible spins and directions yields two possible values for the spin of the least energetic baryons:
1/2 and 3/2 . No other combinations of quarks have been observed;
hadrons that consist of two or four quarks seem to be ruled out.

The reason is linked with the answer another puzzle.
According to the exclusion principle of Wolfgang Pauli, no two particles occupying a
minute region of space and possessing halfintegral spins can have the same quantum number-the same values of momentum, charge and spin.
The Pauli exclusion principle accounts elegantly for the configurations of electrons that determine an element's place in the periodic table.
We should expect it to be a
reliable guide to the panoply of hadrons as well. The principle would seem to suggest, however, that exotic hadrons such as the delta plus plus and the omega minus particles, which materialize briefly following high-energy collisions, cannot exist.
They consist respectively of three
u
and three
s
quarks and possess a
spin of 3/2;
all three quarks in each of the hadrons must be identical in spin as well as in other properties and hence must occupy the same quantum state

Colors

To explain such observed combinations it is necessary to suppose the three otherwise identical quarks are distinguished by another trait:
a new kind of charge, whimsically termed color, on which the strong force acts.
Each flavor of quark can carry one of three kinds of color charge:
red, green or blue.
To a
red quark there corresponds an antiquark with a color charge of antired (which may be thought of as cyan); other antiquarks bear charges of antigreen (magenta)
and antiblue (yellow).

The analogy between this new kind of charge and color makes it possible to specify the rules under which quarks combine. Hadrons do not exhibit a color charge; the sum of the component quarks' colors must be white, or colorneutral.
Therefore the only allowable combinations are those of a quark and its antiquark, giving rise to mesons, and of a red, a green and a blue quark, yielding the baryons.

Colored states are never seen in isolation.
This concealment is consistent with the fact that free quarks, bearing a single color charge, have never been observed. The activity of the strong force between colored quarks must be extraordinarily powerful, perhaps powerful enough to confine quarks permanently within colorless, or colorneutral, hadrons. The description of violent electron-positron collisions according to the quark model, however, assumes the quarks that give rise to the observed jets of hadrons diverge freely during the first instant following the collision. The apparent independence of quarks at very short distances is known as asymptotic freedom; it was described in 1973 by David J. Gross and Frank Wilczek of Princeton University and by H. David Politzer, then at Harvard University.

Analogy yields an operational understanding of this paradoxical state of affairs, in which quarks interact only weakly when they are close together and yet cannot be separated. We may think of a hadron as a bubble within which quarks are imprisoned. Within the bubble the quarks move freely, but they cannot escape from it. The bubbles, of course, are only a metaphor for the dynamical behavior of the force between quarks, and a fuller explanation for what is known as quark confinement can come only from an examination of the forces through which particles interact.

The Fundamental Interactions

Nature contrives enormous complexity of structure and dynamics from the six leptons and six quarks now thought to be the fundamental constituents of matter. Four forces govern their relations: electromagnetism, gravity and the strong and weak forces. In the larger world we experience directly, a force can be defined as an agent that alters the velocity of a body by changing its speed or direction.
In the realm of elementary particles, where quantum mechanics and relativity replace the Newtonian mechanics of the larger world, a more comprehensive notion of force is in order, and with it a more general term, interaction. An interaction can cause changes of energy, momentum or kind to occur among several colliding particles;
an interaction can also affect a particle in isolation, in a spontaneous decay process.

Only gravity has not been studied at the scale on which elementary particles exist; its effects on such minute masses are so small that they can safely be ignored. Physicists have attempted with considerable success to predict the behavior of the other three interactions through mathematical descriptions known as gauge theories.

The notion of symmetry is central to gauge theories;. A symmetry, in the mathematical sense, arises when the solutions to a set of equations remain the same even though a characteristic of the system they describe is altered.
If a mathematical theory remains valid when a characteristic of the system is changed by an identical amount at every point in space, it can be said that the equations display a global symmetry with respect to that characteristic.
If the characteristic can be altered independently at every point in space and the theory is still valid, its equations display local symmetry with respect to the characteristic.

Each of the four fundamental forces is now thought to arise from the invariance of a law of nature, such as the conservation of charge or energy, under a local symmetry operation, in which a certain parameter is altered independently at every point in space.
An analogy with an ideal rubber disk may help to visualize the effect of the mathematics. If the shape of the rubber disk is likened to a natural principle and the d isplacement of a point within the disk is regarded as a local symmetry operation, the disk must
keep its shape even as each point within it is displaced independently. The displacements stretch the disk and introduce forces between points. Similarly, in gauge theories the fundamental forces are the inevitable consequences of local symmetry operations;
they are required in order to preserve symmetry.

Of the three interactions studied in the realm of elementary particles, only electromagnetism is the stuff of everyday experience, familiar in the form of sunlight, the spark of a static discharge and the gentle swing of a compass needle.
On the subatomic level it takes on an unfamiliar aspect. According to relativistic quantum theory, which links matter and energy, electromagnetic interactions are mediated by photons:
massless "force particles" that embody precise quantities of energy.
The quantum theory of electromagnetism, which describes the photonmediated interactions of electrically charged particles, is known as quantum electrodynamics (QED).

In common with other theories of the fundamental interactions, QED is a gauge theory. In QED the electromagnetic force can be derived by requiring that the equations describing the motion of a charged particle remain unchanged in the course of local symmetry operations. Specifically, if the phase of the wave function by which a charged particle is described in quantum theory is altered independently at every point in space, QED requires that the electromagnetic interaction and its mediating particle, the photon, exist in order to maintain symmetry.

QED is the most successful of physical theories. Using calculation methods developed in the 1940's by Richard P. Feynman and others, it has achieved predictions of enormous accuracy, such as the infinitesimal effect of the photons radiated and absorbed by an electron on the magnetic moment generated by the electron's innate spin. Moreover, QED's descriptions of the electromagnetic interaction have been verified over an extraordinary range of distances, varying from less than 10
^-18
meter to more than 10
⁸
meters.

Screening

In particular QED has explained the effective weakening of the electromagnetic charge with distance. The electric charge carried by an object is a fixed and definite quantity. When a charge is surrounded by other freely moving charges, however, its effects may be modified. If an electron enters a medium composed of molecules that have positively and negatively charged ends, for example, it will polarize the molecules. The electron will repel their negative ends and attract their positive ends, in effect screening itself in positive charge. The result of the polarization is to reduce the electron's effective charge by an amount that increases with d istance. Only when the electron is inspected at very close range – on a submolecular scale, within the screen of positive charges – is its full charge apparent.

Such a screening effect seemingly should not arise in a vacuum, in which there are no molecules to become polarized.
The uncertainty principle of Werner Heisenberg suggests, however, that the vacuum is not empty. According to the principle, uncertainty about the energy of a system increases as it is examined on progressively shorter time scales. Particles may violate the law of the conservation of energy for unobservably brief instants; in effect, they may materialize from nothingness.
In QED the vacuum is seen as a complicated and seething medium in which pairs of charged "virtual" particles, particularly electrons and positrons, have a fleeting existence. These ephemeral vacuum fluctuations are polarizable just as are the molecules of a gas or a liquid. Accordingly QED predicts that in a vacuum too electric charge will be screened and effectively reduced at large distances.

The strong interaction affecting quarks that is based on the color charge also varies with distance, although in a contrary manner: instead of weakening with d istance the color charge appears to grow stronger. Only at distances of less than about 10
^-13
centimeter, the diameter of a proton, does it diminish enough to allow mutually bound quarks a degree of independence.
Yet the explanation for this peculiar behavior is found in a theory that is closely modeled on QED. It is a theory called quantum chromodynamics
(QCD), the gauge theory of the strong interactions.

Like QED, QCD postulates force particles, which mediate interactions.
Colored quarks interact through the exchange of entities called gluons, just as charged particles trade photons.
Whereas QED recognizes only one kind of photon, however, QCD admits eight kinds of gluon. In contrast to the photons of QED, which do not alter the charge of interacting particles, the emission or absorption of a gluon can change a quark's color; each of the eight gluons mediates a different transformation.
The mediating gluon is itself colored, bearing both a color and an anticolor.

The fact that the gluons are colorcharged, in contrast to the electrically neutral photons of QED, accounts for the differing behaviors over distance of the electromagnetic and strong interactions.
In QCD two competing effects govern the effective charge:
screening, analogous to the screening of QED, and a new effect known as camouflage. The screening, or vacuum polarization, resembles that in electromagnetic interactions. The vacuum of QCD is populated by pairs of virtual quarks and antiquarks, winking into and out of existence. If a quark is introduced into the vacuum, virtual particles bearing contrasting color charges will be attracted to the quark; those bearing a like charge will be repelled.
Hence the quark's color charge will be hidden within a cloud of unlike colors, which serves to reduce the effective charge of the quark at greater distances.