The Higgs Boson: Searching for the God Particle

by Scientific American Editors

  At the outset all four of the fields in the Weinberg-Salam-Ward model are of infinite range and therefore must be conveyed by massless quanta; one field carries a negative electric charge, one carries a positive charge and the other two fields are neutral. The spontaneous symmetry breaking introduces four Higgs fields, each field represented by a scalar particle. Three of the Higgs fields are swallowed by Yang-Mills particles, so that both of the charged Yang-Mills particles and one of the ne utral ones take on a large mass. These particles are collectively named massive intermediate vector bosons, and they are designated W+, W- and Z0. The fourth Yang-Mills particle, which is a neutral one, remains massless: it is the photon of electromagnetism. Of the Higgs particles, the three that lend mass to the Yang-Mills particles become ghosts and are therefore unobservable, but the last Higgs particle is not absorbed, and it should be seen if enough energy is available to produce it.

  The most intriguing prediction of the model was the existence of the Z0, a particle identical with the photon in all respects except mass, which had not been included in any of the earlier, provisional accounts of the weak force. Without the Z0 any weak interaction would necessarily entail an exchange of electric charge. Events of this kind are called charged-weak-current events. The Z0 introduced a new kind of weak interaction, a neutral-weak-current event. By exchanging a Z0, particles would interact without any transfer of charge and could retain their original identities. Neutral weak currents were first observed in 1973 at CERN .

  The elaboration of a successful gauge theory of the strong interactions, which are uniq ue to hadrons, could not be undertaken until a fundamental fact about the hadrons was understood: they are not elementary particles. A model of hadrons as composite objects was proposed in 1963 by Murray Gell-Mann of the California Institute of Technology; a similar idea was introduced independently and at about the same time by Yuval Ne'eman of Tel Aviv University and George Zweig of Cal Tech. In this model hadrons are made up of the smaller particles Gell-Mann named quarks. A hadron can be built out of quarks according to either of two blueprints. Combining three q uarks gives rise to a baryon, a class of hadrons that includes the proton and the neutron. Bind ing together one quark and one antiq uark makes a meson, a class typified by the pions. Every known hadron can be accounted for as one of these allowed combinations of quarks.

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  QUARK MODEL describes all hadrons, indluding the proton and the nuetron, as being composite particles made up of the similar entitites called quarks. In the original form of the model the quarks were assumed to come in three "flavors," labled u, d and s, each of which is now said to have three possible "colors," red, green and blue. There are also antiquarks with the corresponding anticolors cyan, magenta and yellow. The interactions of the quarks are now described by means of a guage theory based on invariance with respect to local transformations of color. Sixteen fields are needed to hold this invariance. They are taken in pairs to make up eight massless vector bosons, called gluons, each bearing a combination of color and anticolor.

  Illustration by Allen Beechel

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  In the original model there were just three kinds of quark, designated "up," "down" and "strange." James D. Bjorken of the Stanford Linear Accelerator Center and Sheldon Lee Glashow of Harvard soon proposed adding a fourth quark bearing a property called charm. In 1971 a beautiful argument by Glashow, John Iliopoulos of Paris and Luciano Maiani of the University of Rome showed that a quark with charm is needed to cure a discrepancy in the gauge theory of weak interactions. Charmed quarks, it was concluded, must exist if both the gauge theory and the quark theory are correct. The discovery in 1974 of the J or psi particle, which consists of a charmed quark and a charmed antiquark, s upported the Weinberg-SalamWard model and persuaded many physicists that the quark model as a whole should be taken seriously. It now appears that at least two more "flavors," or kinds, of quark are needed; they have been labeled "top" and "bottom."

  The primary task of any theory of the strong interactions is to explain the peculiar rules for building hadrons out of quarks. The structure of a meson is not too difficult to account for: since the meson consists of a quark and an antiquark, it is merely necessary to assume that the quarks carry some property analogous to electric charge. The binding of a quark and an antiquark would then be explained on the principle that opposite charges attract, just as they do in the hydrogen atom. The structure of the baryons, however, is a deeper enigma. To explain how three quarks can form a bound state one must assume that three like charges attract.

  The theory that has evolved to explain the strong force prescribes exactly these interactions. The analogue of electric charge is a property called color (although it can have nothing to do with the colors of the visible spectrum). The term color was chosen because the rules for forming hadrons can be expressed succinctly by requiring all allowed combinations of quarks to be "white," or colorless. The quarks are assigned the primary colors red, green and blue; the antiq uarks have the complementary "anticolors" cyan, magenta and yellow. Each of the quark flavors comes in all three colors, so that the introduction of the color charge triples the number of distinct quarks.

  From the available quark pigments there are two ways to create white : by mixing all three primary colors or by mixing one primary color with its complementary anticolor. The baryons are made according to the first scheme: the three quarks in a baryon are required to have different colors, so that the three primary hues are necessarily represented. In a meson a color is always accompanied by its complementary anticolor.

  The theory devised to account for these baffling interactions is modeled directly on quantum electrodynamics and is called quant um chromodynamics. It is a non-Abelian gauge theory. The gauge symmetry is an invariance with respect to local transformations of quark color.

  It is easy to imagine a global color symmetry. The quark colors, like the isotopic-spin states of hadrons, might be indicated by the orientation of an arrow in some imaginary internal space. Successive rotations of a third of a turn would change a quark from red to green to blue and back to red again. In a baryon, then, there would be three arrows, with one arrow set to each of the three colors. A global symmetry transformation, by definition, must affect all three arrows in the same way and at the same time. For example, all three arrows might rotate clockwise a third of a turn. As a result of such a transformation all three quarks would change color, but all observable properties of the hadron would remain as before. In particular there would still be one quark of each color, and so the baryon would remain colorless.

  Quantum chromodynamics requires that this invariance be retained even when the symmetry transformation is a local one. In the absence of forces or interactions the invariance is obviously lost. Then a local transformation can change the color of one quark but leave the other quarks unaltered, which would give the hadron a net color. As in other gauge theories, the way to restore the invariance with respect to local symmetry operations is to introduce new fields. In quantum chromodynamics the fields needed are analogous to the electromagnetic field but are much more complicated; they have eight times as many components as the electromagnetic field has. It is these fields that give rise to the strong force.

  The quanta of the color fields are called gluons (because they glue the quarks together). There are eight of them, and they are all massless and have a spin angular momentum of one unit. In other words, they are massless vector bosons like the photon. Also like the photon the gluons are electrically neutral, but they are not color-neutral. Each gluon carries one color and one anticolor. There are nine possible combinations of a color and an anticolor, but one of them is equivalent to white and is excluded, leaving eight distinct gluon fields.

  The gluons preserve local color symmetry in the following way. A quark is free to change its color, and it can do so independently of all other quarks, but every color transformation must be accompanied by the emission of a gluon, just as an electron can shift its phase onl
y by emitting a photon. The gluon, propagating at the speed of light, is then absorbed by another quark, which will have its color shifted in exactly the way needed to compensate for the original change. Suppose, for example, a red quark changes its color to green and in the process emits a gluon that bears the colors red and antigreen. The gluon is then absorbed by a green quark, and in the ensuing reaction the green of the quark and the antigreen of the gluon annihilate each other, leaving the second quark with a net color of red. Hence in the final state as in the initial state there is one red quark and one green quark. Because of the continual arbitration of the gluons there can be no net change in the color of a hadron, even though the quark colors vary freely from point to point. All hadrons remain white, and the strong force is nothing more than the system of interactions needed to maintain that condition.

  In spite of the complexity of the gluon fields, quantum electrodynamics and quantum chromodynamics are remarkably similar in form. Most notably the photon and the gluon are identical in their spin and in their lack of mass and electric charge. It is curious, then, that the interactions of quarks are very different from those of electrons.

  Both electrons and quarks form bound states, namely atoms for the electrons and hadrons for the quarks. Electrons, however, are also observed as independent particles; a small quantity of energy suffices to isolate an electron by ionizing an atom. An isolated quark has never been detected. It seems to be impossible to ionize a hadron, no matter how much energy is supplied. The quarks are evidently bound so tightly that they cannot be pried apart; paradoxically, however, probes of the internal structure of hadrons show the quarks moving freely, as if they were not bound at all.

  Gluons too have not been seen directly in experiments. Their very presence in the theory provokes objections like those raised against the pure, massless Yang-Mills theory. If massless particles that so closely resemble the photon existed, they would be easy to detect and they would have been known long ago. Of course, it might be possible to give the gluons a mass through the Higgs mechanism. With eight gluons to be concealed in this way, however, the project becomes rather cumbersome. Moreover, the mass would have to be large or the gluons would have been produced by now in experiments with high-energy accelerators; if the mass is large, however, the range of the quarkbinding force becomes too small.

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  POLARIZATION OF THE VACUUM explains to some extent the peculiar force law that seems to allow quarks complete freedom of movement within a hadron but forbids the isolation of quarks or gluons. In quantum electrodynamics (below) pairs of virtual electrons and antielectrons surround any isolated charge, such as an electron. Because of electrostatic forces the positively charged antielectrons tend to remain nearer the negtive electron charge and thereby cancel part of it. The observed electron charge is the difference between the "bare" charge and the screening charge of virtual antielectrons. Similarly, pairs of virtual quarks diminish the strength of the force between a real quark and a real antiquark. In quantum chromodynamics, however, there is a competing effect not found in quantum electrodynamics. Because the gluon also has a color charge (whereas the photon has no electric charge), virtual gluons also have an influence on the magnitude of the color force between quarks. The gluons do not screen the quark charge but enhance it. As a result the color charge is weak and the quarks move freely as long as they are close. At long range infinite energy may be needed to separate two quarks.

  Illustration by Allen Beechel

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  Atentative resolution of this quandary has been discovered not by modifying the color fields but by examining their properties in greater detail. In discussing the renormalization of quantum electrodynamics I pointed out that even an isolated electron is surrounded by a cloud of virtual particles, which it constantly emits and reabsorbs. The virtual particles include not only neutral ones, such as the photon, but also pairs of oppositely charged particles, such as electrons and their antiparticles, the positrons. It is the charged virtual particles in this cloud that under ordinary circumstances conceal the "infinite" negative bare charge of the electron. In the vicinity of the bare charge the electron- positron pairs become slightly polarized: the virtual positrons, under the attractive influence of the bare charge, stay closer to it on the average than the virtual electrons, which are repelled. As a result the bare charge is partially neutralized; what is seen at long range is the difference between the bare charge and the screening charge of the virtual positrons. Only when a probe approaches to within less than about 10-10 centimeter do the unscreened effects of the bare charge become significant.

  It is reasonable to suppose the same process would operate among color charges, and indeed it does. A red quark is enveloped by pairs of quarks and antiquarks, and the antired charges in this cloud are attracted to the central quark and tend to screen its charge. In quantum chromodynamics, however, there is a competing effect that is not present in quantum electrodynamics. Whereas the photon carries no electric charge and therefore has no direct influence on the screening of electrons, gluons do bear a color charge. (This distinction expresses the fact that quantum electrodynamics is an Abelian theory and quantum chromodynamics is a non-Abelian one.) Virtual gluon pairs also form a cloud around a colored quark, but it turns out that the gluons tend to enhance the color charge rather than attenuate it. It is as if the red component of a gluon were attracted to a red quark and therefore added its charge to the total effective charge. If there are no more than 16 flavors of quark (and at present only six are known), the "antiscreening" by gluons is the dominant influence.

  This curious behavior of the gluons follows from rather involved calculations, and the interpretation of the results depends on how the calculation was done. When I calculate it, I find that the force responsible is the color analogue of the gluon's magnetic field. It is also significant, however, that virtual gluons can be emitted singly, whereas virtual quarks always appear as a quark and an antiquark. A single gluon, bearing a net color charge, enhances the force acting between two other color charges.

  As a result of this "antiscreening" the effective color charge of a quark grows larger at long range than it is close by. A distant quark reacts to the combined fields of the central quark and the reinforcing gluon charges; at close range, once the gluon cloud has been penetrated, only the smaller bare charge is effective. The quarks in a hadron therefore act somewhat as if they were connected by rubber bands: at very close range, where the bands are slack, the quarks move almost independently, but at a greater distance, where the bands are stretched taut, the quarks are tightly bound.

  The polarization of virtual gluons leads to a reasonably precise account of the close-range behavior of quarks. Where the binding is weak, the expected motion of the particles can be calculated successfully. The long-range interactions, and most notably the failure of quarks and gluons to appear as free particles, can probably be attributed to the same mechanism of gluon antiscreening. It seems likely that as two color charges are pulled apart the force between them grows stronger indefinitely, so that infinite energy would be needed to create a macroscopic separation. This phenomenon of permanent quark confinement may be linked to certain special mathematical properties of the gauge theory. It is encouraging that permanent confinement has indeed been found in some highly simplified models of the theory. In the full-scale theory all methods of calculation fail when the forces become very large, but the principle seems sound. Quarks and gluons may therefore be permanently confined in hadrons.

  If the prevailing version of quantum chromodynamics turns out to be correct, color symmetry is an exact symmetry and the colors of particles are completely indistinguishable. The theory is a pure gauge theory of the kind first proposed by Yang and Mills. The gauge fields are inherently long-range and formally are much like the photon field. The quantum-mechanical constraints on those fields are so strong, however, that the observed interactions are quite unlike those of electromagnetism and even lead to the imprison
ment of an entire class of particles.

  Even where the gauge theories are right they are not always useful. The calculations that must be done to predict the result of an experiment are tedious, and except in quantum electrodynamics high accuracy can rarely be attained. It is mainly for practical or technical reasons such as these that the problem of quark confinement has not been solved. The equations that describe a proton in terms of q uarks and gluons are about as complicated as the equations that describe a nucleus of medium size in terms of protons and neutrons. Neither set of equations can be solved rigorously.

  In spite of these limitations the gauge theories have made an enormous contribution to the understanding of elementary particles and their interactions. What is most significant is not the philosophical appeal of the principle of local symmetry, or even the success of the individual theories. Rather it is the growing conviction that the class of theories now under consideration includes all possible theories for any system of particles whose m utual interactions are not too strong. Experiment shows that if particles remain closer together than about 10-14 centimeter, their total interaction, including the effects of all forces whether known or not, is indeed small. (The quarks are a special case: although the interactions between them are not small, those interactions can be attributed to the effects of virtual particles, and the interactions of the virtual particles are only moderate.) Hence it seems reasonable to attempt a systematic fitting of the existing gauge theories to experimental data.