The Structure of Quarks and Leptons

They have been , considered the elementary particles ofmatter, but instead they may consist of still smaller entities confjned within a volume less than a thousandth the size of a proton

by Haim Harari

n the past 100 years the search for the the quark model that brought relief. In imagination: they suggest a way of I ultimate constituents of matter has the initial formulation of the model all building a complex world ou t of a few penetrated four layers of structure. hadrons could be explained as combina­ simple parts. All matter has been shown to consist of tions of just three kinds of quarks. atoms. The atom itself has been found Now it is the qu arks and leptons Any theory of the elementary particles to have a dense nucleus surrounded by a themselves whose proliferation is begin­ fl. of matter must also take into ac­ cloud of electrons. The nucleus in turn ning to stir interest in the possibility of a count the forces that act between them has been broken down into its compo­ simpler-scheme. Whereas the original and the la ws of nature that govern the nent protons and neutrons. More recent­ model had three quarks, there are now forces. Little would be gained in simpli­ ly it has become apparent that the pro­ thought to be at least 18, as well as six fying the spectrum of particles if the ton and the neutron are also composite leptons and a dozen other particles that number of forces and laws were thereby particles; they are made up of the small­ act as carriers of forces. Three dozen increased. As it happens, there has been er entities called quarks. What comes basic units of matter are too many for a subtle interplay between the list of par­ next? It is entirely possible that the pro­ the taste of some physicists, and there is ticles and the list of forces throughout gression of orbs within orbs has at last no assurance that more quarks and'lep­ the history of physics. reached an end and that quarks cannot tons will not be discovered. Postulating In about 1800 four forces were be more finely divided. The leptons, the a still deeper level of organization is per­ thought to be fundamental: gravitation, class of particles that includes the elec­ haps the most straightforward way to electricity, magnetism and the short­ tron, could also be elementary and indi­ reduce the roster. All the quarks and range force between molecules that is visible. Some physicists, however, are leptons would then be composite ob­ responsible for the cohesion of matter. not at all sure the innermost kernel of jects, just as atoms and hadrons are, and A series of remarkable experimental matter has been exposed. They have be­ would owe their variety to the number and theoretical discoveries then led to gun to wonder whether the quarks and of ways a few smaller constituents can the recognition that electricity and mag­ leptons too might .not have some inter­ be brought together. The currently ob­ netism are actually two manifestations nal composition. served diversity of nature would be not of the same basic force, which was soon The main impetus for considering still intrinsic but combinatorial. given the name electromagnetism. The another layer of structure is the convic­ It should be emphasized that as yet discovery of atomic structure brought tion (or perhaps prej udice) that there there is no evidence q uar ks and leptons a further revision. Although an atom is should be only a few fundamental build­ have an inter nal structure of any kind. ing blocks of matter. Economy of means In the case of the leptons, experiments ATOM has long been a gu iding. principle of have probed to within 10-16 centimeter physics, and it has served well up to and found nothing to contradict the as­ /' now. The list of the ba sic constituents sumption that leptons are pointlike and /' / of matter first grew implausibly long structureless. As ·for the qu arks, it has /' /' toward the end of the 19th century, not been possible to examine a quark in ,.. ,.. when the number of chemical elements, isolation, much less to discern any possi­ ,.. and hence the number of species of at­ ble internal feat ures. Even as a strictly • oms, was approaching 100. The resolu­ theoretical conception, the subparticle NUCLEUS tion of atomic structure solved the prob­ idea has run into difficulty: no one has lem, and in about 1935 the number of been able to devise a consistent descrip­ " elementary particles stood at four: the tion of how the subparticles might move " proton, the ' neutron, the electron and inside a quark or a lepton and how they x 10,000 the neutrino. This parsimonious view of might interact with one another. They the world was spoiled iruthe 1950's and _' would have, to_be . almost unimaginably 1960's;, it turned out that tBe proton and small: if an atom were magnified to the the neutron are representatives ofa very size of the earth, its innermost constitu­ 10-8 CENTIMETER large family of particles, the family now ents could be no larger than a grapefruit. called hadrons. By the mid-1960's the Nevertheless, models of quark and lep­ HIERARCHY OF PARTICLES in the struc­ number of fundamental forms of matter ton substructure make a powerful ap­ ture of matter currently has four levels. All was again roughly 100. This time it was peal to the aesthetic sense and to the matter is made up of atoms; the atom con-

56 © 1983 SCIENTIFIC AMERICAN, INC electrically neutral overall, its constitu­ near, the colored quarks in one proton particles, and it is not understood in ents are charged, and the sh ort-range "see" the color charges in the other pro­ terms of microscopic events. For the molecular force came to be understood ton. The short-range attractions and re­ other three forces successful theories as a complicated residual effect of elec­ pulsions that result have been identified have been developed and are now wide­ tromagnetic interactions of positive nu­ with the effects of the strong force. In ly accepted. The three theories are dis­ clei and negative electrons. When two other words, just as the short-range mo­ tinct, but they are consistent with one neutral atoms are far apart, there are lecular force became a residue of the another; taken to gether they constitute practically no elect romagnetic forces long-range electromagnetic force, so the a comprehensive model of elementary between them. When they are near each short-range strong force has become a particles and their interactions, which I other, however, the charged constitu­ residue of the long-range color force. shall refer to as the standard model. ents of one atom are able to "see" and One more chapter can be added to this In the standard model the indivisible influence the inner charges of the other, abbreviated history of the forces of na­ constituents of matter are the quarks leading to various short-range attrac­ ture. A deep and beautiful connection and the leptons. It is convenient to dis­ tions and repulsions. has been found between electromagnet­ cuss the leptons first. There are six of As a result of these developments ism and the weak force, bringing them them: the electron and its co mpanion physics was left with only two basic almost to the point of full uni fication. the electron-type neutrino, the muon forces. The unification of electricity and They are clearly related, but the connec­ and the muon-type neutrino and the magnetism had reduced the number by tion is not quite as close as it is in the tau and the tau-type neutrino. The elec­ one, and the molecular interaction had case of electricity and magnetism, and tron, the muon and the tau have an been demoted from the rank of a funda­ so they must still be counted as sepa­ electric charge of -1; the three neu­ mental force to that of a derivative one. rate forces. Therefore the current list trinos are electrically ne u tral. The two remaining fundamental for­ of fundamental forces still has four en­ There are also six basic kinds of ces, gravitation and electromagnetism, tries: the long-range gravitational, elec­ quark, which have been given the names were both long-range. The exploration tromagnetic and color for ces and the up, down, charmed, strange, top and of nuclear structure, however, soon in­ short-range weak force. Within the lim­ bottom, or u, d, C, s, t and b. (The top trod uced two new short-range forces. its of present knowledge all natural quark has not yet been detected experi­ The strong force binds protons and neu­ phenomena can be understood through mentally, and neither has the tau-type trons together in the nucleus, and the these forces and their resid ual effects. neutrino, but few theorists doubt their weak force mediates certain transfor­ The evolution of ideas about particles existence.) The u, C and t quarks have an mations of one particle into another, as and that of ideas about forces are clearly electric charge of +2/3, the d, sa nd b in the beta decay of a radioactive nucle­ interdependent. As new basic particles quarks a charge of -1/3. In addition us. Thus there were again four forces. are found, old ones turn out to be com­ each quark type has three possible col­ The development of the quark model posite objects. As new forces are discov­ ors, which I shall designate red, yellow and the accompanying theory of quark ered, old ones are unified or red uced to and blue. Thus if each colored qu ark is interactions was the next occasion for resid ual status. The lists of particles and counted as a separate particle, there revising the list of forces. The quarks in forces are revised from time to time as are 18 qu ark varieties alto gether. Note a proton or a neutron are thought to be matter is explored at smaller scale and that each quark carries both color and held together by a new long-range fun­ as theoretical understanding progresses. electric charge, but none of the leptons damental force called the color force, Any change in one list inevitably leads are colored. which acts on the quarks because they to a modification of the other. The re­ For each particle in this scheme there bear a new kind of charge called color. cent speCUlations about quark and lep­ is an antiparticle with the same mass but (Neither the force nor the charge has ton structure are no exception; they too with opposite values of electric charge any relation to ordinary colors.) Just call for chan ges in the complement of and color. The antiparticle of the elec­ as an atom is made up of electrical­ forces. Whether the changes represent a tron is the positron, which has a charge ly charged constituents but is itself neu­ simplification remains to be seen. of +1. The antiparticle of a red u quark, tral, so a proton or a neutron is made with a charge of +2/3, is an antired u up of colored quarks but is itself color­ f the four established fundamental antiquark, with a charge of -2/3. less. When two colorless protons are O forces, gravitation must be put in a The color property of the quarks is far apart, there are essentially no color category apart. It is too feeble even to be analogous in many ways to electric forces between them, bu t when they are detected in the interactions of individual charge, but because there are three pos-

NUCLEUS PROTON QUARK PROTONS AND NEUTRONS � ,/ / / ,/ ,/ / ,/ ,/ ,/ ,/ • QUARK ,/ ./ / ------./ / ,/ HYPOTH ETICAL • PRE QUARKS

• ...... x 10 x 1,000 OR MORE

10 12 CE NTIMETER 10-'3 CEN TIMETER 10 '6 CEN TIMETER OR LESS sists of a nucleus surrounded by electrons; the nucleus is composed el: the quark might be a composite of hypothetical finer constituents, of protons and neutrons; each proton and Jleutron is thought to be which. can be generically called pre quarks. The leptons, the class of composed of three quarks. Recent speculations might add a fifth lev- particles that includes the electron, could also consist of prequarks.

© 1983 SCIENTIFIC AMERICAN, INC 57 sible colors it is apprecia bly more com­ second way to form a neutral state: any sic quantum-mechanical unit of angular plicated. Electrically charged particles composite system with eq ual quantities momentum. When a particle witJ:t a spin can be brought to gether to form an of all three colors or of all three anti­ of 1!2 moves along a straight line, its electrically neutral system in only one colors is also color less. For this reason intrinsic rotation can be either clockwise way: by combining equal quantities of a proton consisting of one red quark, or counterclockwise when the particle is positive and negative charge. A color­ one yellow quark and one blu e quark viewed along the direction of motion. If less composite particle can be formed has no net color. the spin is clockwise, the particle is said out of colored quarks in much the same One further property of the q uar ks to be right-handed, because when the way, namely by combining a colored and leptons should be mentioned: each fingers of the right hand curl in the same quark and an anticolored antiq uark. In particle has a spin, or intrinsic angular direction as the spin, the thumb indi­ the case of color, however, there is a momentum, equal to one-half the ba- cates the direction of motion. For a par-

GRAVITATIONAL ELECTRI C MAGNETIC MOLECULAR

2

GRAVITATI ONAL ELECTROMAGNETIC MOLECULAR

3 MOLECULAR

GRAVITATIONAL

4 MOLECULAR

GRAVITATIONAL WEAK STRONG

5 STRONG

GRAVITATIONAL WEAK

6 MOLECULAR STRONG

GRAVITATIONAL' COLOR

7 MOLECULAR WEAK STRONG GRAVITATIONAL ELECTROMAGNETIC J HYPERCOLOR COLOR

FUNDAMENTAL FORCES OF NATURE can be classified in a weak and the strong. In the quark model, however, the strong force scheme that has evolved together with the list of elementary particles. becomes a residue of a new long-range force called the color force. Here long-range forces are shown in gray and short-range ones in Furthermore, a deep relation has been found between the weak force color. Early in the 19th centnry three long-range forces were thought and electromagnetism, so that they can be considered partially uni­ to be fundamental: the gravitational, the electric and the magnetic. fied. The sixth row of the chart represents the ·forces of nature as One short-range force, the molecular force responsible for the cohe­ they are now understood in the "standard model" of elementary-par­ sion of matter, also had fundamental status. James Clerk Maxwell ticle physics. A successful model of quark and lepton structure could unified electricity and magnetism, and with the discovery of atomic bring a further revision. In some models, for example, there is a new structure it became apparent that the molecular force is not funda­ long-range force called hypercolor, and the weak force is a residne mental but instead is a residual-effect of electromagnetism. The dis­ of it. In models of this kind all the fundamental forces of nature are covery of the atomic nucleus introduced two short-range forces, the long-range ones. Such modelS, however, are still highly speCUlative.

58 © 1983 SCIENTIFIC AMERICAN, INC ticle with the opposite sense of spin a QUARKS LEPTONS left-hand rule describes the motion, and so the particle is said to be left-handed. (ELECTRON- FIRST (UP) (DOWN) (ELECTRON) TYPE u d e Ve NEUTRINO) n the standard model the three forces (/) z I that act on the quarks and leptons are 0 (MUON-TYPE described by essentially the same math­ � SECOND (CHARMED) (STRANGE) Ii (MUON) a: c s vii NEUTRINO) ematical structure. It is known as a w z gauge-invariant field theory or simply w a gauge theory. Each force is transmit­ CJ THIRD (BOTTOM) (TAU) (TAU-TYPE ted from one particle to another by car­ t (TOP) b T VT NEUTRINO) rier fields, which in turn are embodied in carrier particles, or gauge bosons. The gauge theory of the electromag­ netic force, called quantum electrody­ ELECTRIC -1 0 namics or QED, is the earliest and sim­ (/) +2/3 -1/3 plest of the three theories. It was devised w CJ in the 1940's by Richard P. Feynman, a: « Julian S. Schwinger and Sin-Itiro Tomo­ I () COLORLESS COLORLESS naga. QED describes the interactions COLOR of electrically charged particles, most notably the electron and the positron. There is one kind of gauge boson to me­ diate the interactions; it is the photon, the familiar quantum of electromagnet­ COLOR ic radiation, and it is massless and has no. electric charge of its own. QED is prob­ (/) w ably the most accurately tested theory in () ELECTRO­ a: MAGNETIC physics. For example, it correctly pre­ o dicts the magnetic moment of the elec­ u. tron to at least 10 significant digits. The theory of the color force was WEAK formulated by analogy to QED and is called quantum chromodynamics or QCD. It was developed over a period of STANDARD MODEL of elementary particles includes three "generations" of quarks and lep­ almost two decades through the efforts tons, although all ordinary matter can be constructed out of the particles of the first generation of many theoretical physicists. In QCD alone. The quarks are distinguished by fractional values of electric charge and by a property particles interact by virtue of their color that is fancifully called color: each quark type comes in red, yellow and blue versions. The lep­ rather than their electric charge. The tons have integer units of electric charge and are colorless. The two classes of particles also dif­ gauge bosons of QCD, which are re­ fer in their response to the various forces. Only the quarks are subject to the color force, and sponsible for binding quarks inside a as a result they may be permanently confined inside composite particles such as the proton. hadron, are called gluons. Like the pho­ ton, the gluons are massless, but where­ as there is just one kind of photon, there isolation. I must stress that although the with respect to the weak force. What is are eight species of gluons. A further idea of color confinement is now wide­ odder still, the weak charge is not con­ difference between the photon and the ly accepted, it has not been proved to served in nature: a unit of charge can be gluons turns out to be even more impor­ follow from QCD. There may still be created out of nothing or can disappear tant. Although the photon is the inter­ surprises in store. into the vacuum. In contrast, the net mediary of the electromagnetic force, it The weak force is somewhat different quantity of electric charge in an isolated has no electric charge and hence gives from the other two, but it can nonethe­ system of particles can never be altered, rise to no electromagnetic for ces of its less be described by a gauge theory of and neither can the net color. The weak own (or at least none of significant mag­ the same general kind. The theory was force is also distinguished by its exceed­ nitude). The gluons, in contrast, are not worked out, and the important connec­ ingly short range; its effects extend only colorless. They transmit the color force tion between the weak force and elec­ to a distance of about 10-16 centimeter, between quarks but they also have col­ tromagnetism was established, in the or roughly a thousandth of the diameter or of their own and respond to the color 1960's and the 'early 1970's by a large of a proton. force. This reflexiveness, whereby the number of investigators. Notable con­ carrier of the force acts on itself, makes tributions were made (in chronological n the gauge theory of the weak force a complete mathematical analysis of the order) by Sheldon Lee Glashow of Har­ I both the failure of the weak charge to color force exceedingly difficult. vard University, Steven Weinberg of be conserved and the short range of One peculiarity that seems to be in­ the University of Texas at Austin, Ab­ the force are attributed to a mechanism herent in QCD is the phenomenon of dus Salam of the International Centre called spontaneous symmetry bre ak­ color confinement. It is thought that the for Theoretical Physics in Trieste and ing, which I shall disc uss in greater de­ color force somehow traps colored ob­ Gerard 't Hooft of the University of tail below. For now it is sufficient to jects (such as quarks and gluons) inside Utrecht. note that the symmetry-breaking mecha­ composite objects that are invariably Curiously, the charges on which the nism implies that the weak charge, and colorless (such as protons and neutrons). weak force acts are associated with the the associated handedness of particles, The colored particles can never escape handedness of a particle. Among both should be conserved at extremely high (although they can form new colorless quarks and leptons left-handed particles energy, where a particle's mass is a neg­ combinations). It is because of color and right-handed antiparticles have a ligible fraction of its kinetic energy. confinement, physicists suppose, that a weak charge, but right-handed particles Spontaneous symmetry breaking also quark or a gluon has never been seen in and left-handed antiparticles are neutral requires that the gauge bosons of the

59 © 1983 SCIENTIFIC AMERICAN, INC weak force be massive particles; indeed, cently reported by a group of experi­ forces. For some unknown reason, how­ they have masses approxir.lately 100 menters at CERN, the European Labo­ ever, the s quark is roughly 20 .times as times the mass of the proton. In the stan­ ratory for Particle Physics in Geneva. heavy as the d quark, and the b quark is dard model there are three such bosons: In the next several years new particle ac­ approximately 600 times as heavy as the two of them, designated W+ and W-, celerators and more sensitive detecting d. The mass ratios of the other quarks carry electric charge as well as weak apparatus will test the remaining pre­ and of the charged leptons are likewise charge; the third, designated zo, is elec­ dictions of the model. Most physicists large and unexplained. (The masses of trically neutral. The large mass of the are quite certain they will be confirmed. the neutrinos are too small to have been weak bosons accounts for the short If the standard model has proved so measured; it is not yet known whether range of the force. According to the un­ successful, why would anyone consider the neutrinos are merely very light or certainty principle of quantum mechan­ more elaborate theories? The primary are entirely massless.) ics, the range of a force is inversely motivation is not a suspicion that the The presence of three generations of proportional to the mass of the parti­ standard model is wrong but rather a quarks and leptons begs for an explana­ cle that transmits it. Thus elect romag­ feeling that it is less than fully satisfying. tion. Why does nature repeat itself? The netism and the color force, being carried Even if the model gives correct answers pattern of particle masses is also myste­ by massless gauge bosons, are effective­ for all the questions it addresses, ma ny rious. In the standard model the masses ly infinite in range, whereas the weak questions are left unanswered and many are determined by approximately 20 force has an exceedingly small sphere regularities in nature remain coinciden­ "free" parameters that can be assigned of influence. Spontaneous symmetry tal or arbitrary. In short, the model itself any values the theorist chooses; in prac­ breaking has still another consequence: stands in need of explanation. tice the values are generally based on it predicts the existence of at least one experimental findings. Is it possible the additional massive particle, separate he strongest hint of some organizing 20 parameters are all unrelated? Are from the weak bosons. It is called the Tprinciple beyond the standard mod­ they fundamental constants of nature Higgs particle after Peter Higgs of the el is the proliferation of elementary par­ with the same status as the velocity of University of Edinburgh, who made an ticles. The known properties of matter light or the electric charge of the important contribution to the theory of are not so numerous or diverse that 24 electron? Pr obably not. spontaneous symmetry breaking. particles are needed to represent them A further tantalizing regularity can be In the past 10 years the succ esses of all. Indeed, there seems to be a great perceived in the electric charges of the the standard model have given physi­ deal of repetition in the spectrum of quarks and lepton s: they are all related cists a good deal of self-confidence. All quarks and leptons. There are three lep­ by simple ratios and are all integer mul­ known forms of matter can be con­ tons with an electric charge of -1, three tiples of one-third the electron charge. ' structed out of the 18 colored quarks neutral leptons, three quarks with a The standard model supplies no reason; and the six leptons of the model. All charge of +2/3 and three quarks with a in principle the charge ratios could have observed interactions of matter can be charge of -1/3. Everything is triplicat­ any values. It can be ded uced from ob­ explained as exchanges of the 12 gauge ed, and for no apparent reason. A world servation that the ratios of one-third and bosons included in the model: the pho­ constructed by choosing one particle two-thirds that define the quark charges ton, the eight gluons and the three weak from each of the four groups would are not approximations. The proton bosons. The model seems to be internal­ seem to have all the necessary variety. consists of two u quarks and a d qua rk, ly consistent; no one part is in conflict As it turns out, all ordinary matter can with charges of 2/3 + 213 -1/3, or with any other part, and all measurable indeed be formed from a subset that in­ +1. If these values were not exact and quantities are predicted to have a plausi­ cludes just the u quark, the d quark, the the quarks instead had charges of, say, ble, finite value. Internal consistency is electron and the electron-type neutrino. +.617 and -.383, the magnitude of not a trivial achievement in a conceptual These four particles and their antipar­ the proton's charge would not be exactly system of such wi de scope. So far the ticles make up the "firstge neration" equal to that of the electron's, and or­ model is also consistent with all experi­ of quarks and leptons. The remaining dinary atoms would not be electrically mental results, that is to say, no clea r quarks and leptons merely repeat the neutral. Since atoms can be bro ught prediction of the model has yet been same pattern in two additional genera­ together in enormous numbers, even a contradicted by experiment. To be sure, tions without seeming to add anything slight departure from neutrality could there are some important predictions new. Corresponding particles in differ­ be readily detected. that have not yet been fully verified; ent generations are identical in all re­ If the particles and antiparticles that most notably, the tau-type neutrino, the spects except one: they have different make up a single generation are ar­ top quark, the weak bosons and the masses. The d, sand b quarks, for exam­ ranged according to their charge, it is Higgs particle must be found. The first ple, respond in precisely the same way found that every value from -1 to + 1 direct evidence of W bosons was re- to the electromagnetic, color and weak in intervals of one-third is occupied by one particle (or, in he case of zero charge, by two particles, namely the ELECTRIC CHARGE neutrino and the antineutrino). The pat­ +1 +2/3 +1/3 o -1/3 -2/3 -1 tern formed raises still more questions. Why has nature favored these values of ANTILEPTONS electric charge but no others, such as +4/3 or -5/3? It is appar ent that all QUARKS u d particles with integral charge are color­ less and all those with fractional charge ANTI QUARKS d are colored. Is there some rela tion be­ tween the electric charge of a particle

LEPTONS e and its color or between the quarks and the leptons? The standard model implies no such relations, but they seem to exist. FIRST GENERATION of quarks and leptons forms an orderly pattern when the particles are Another motivation for look ing be­ arranged according to their electric charge. All values of charge from + 1 to -1 in intervals of 1/3 are represented. All colored 'particles have fractional charge and all colorless ones have yond the standard model is the contin­ integral charge. The pattern is an arbitrary feature of the standard model, where charge and uing desire to unify the fundamental color are independent, but it might have some explanation if quarks and leptons are composite. forces, or at lea st to findsome relation

60 © 1983 SCIENTIFIC AMERICAN, INC among them. The cause of pars imony ELECTRIC GENERATION would be served, for example, if two PREON CHARGE COLOR NUMBER of the .forces could be consolidated, as en z " +1/2 COLORLESS a electricity and magnetism were, or if o � one force could be made a residue of -' -1/2 COLORLESS a another, as the strong force was made a u. I I residue of the color force. Ironically, it may turn out that a simplificationof this +1/6 a en kind can be attained only by introducing z still more forces. o +1/6 a � o a: +1/6 a theory that "goes beyond" the stan­ I A o dard model need not contradict or -1/2 COLORLESS a invalidate it. The standard model may emerge as a very good approximation of the deeper theory. The standard model a COLORLESS 1 gives a remarkably successful descrip­ tion of all phenomena at distances no a COLORLESS 2 smaller than about 10-16 centimeter. A 3 deeper theory should therefore focus on a COLORLESS events at a sti1l smaller scale. If there are new constituents to be discovered, they PREON MODEL assigns three properties of quarks and leptons to three groups of hypotheti­ cal constituents called flavons, chromons and somons. A quark or a lepton is formed by choos­ must exist within suc h minuscule re­ ing one preon from each group. The flavons have the primary responsibility for determining gions of space. If there are new forces, electric charge, the chromons determine color and the somons determine generation number. their action must be effective only at a Ideally each kind of preon would carry just one property, but some adjustment is needed to dif­ distance of less than 10-16 centimeter, ferentiate the fractional electric charges of the quarks from the integral charges of the leptons. either because the force is inherently In the version of the model shown here the chromons carry electric charge as well as color. short-range (following the example of the weak force) or because it is subject to some form of confinement(as the col­ or force is). The search for a theory beyond the standard model was launched almost 10 ty Is years ago, and by now several directions have been explored. One promising di­ rection has led to the models known as grand unified theories, which incor­ porate the electromagnetic, color and

weak forces into one fundamental force. ------�------�--�--� S3 The essential idea is to put all the quarks and leptons that make up one generation into a si ngle family; new gauge bosons are then postulated to mediate interac­ tions between the colored quarks and the colorless leptons. The theories ac­ count for the regularities noted in the distribution of electric charge and ex­ plain the exact commensurability of the quark and lepton charges. On the other hand, they do nothing to reduce the number of fundamental constants, they shed no light on the triplication of the generations and they create certain new theoretical difficulties of their own. There have been several variations on the theme of grand unification.For ex­ ample, the concept of horizontal sym­ metry tackles the triplication problem by establishing a symmetry relation among the generations. The mathemati­ I, cally beautiful idea called supersymme­ (/) z try relates particles whose spin angu­ o lar momentum is a half-integer (such as 5 the quarks and leptons) to those with in­ U. teger spin (such as the gauge bosons). 12 The technicolor theory suggests that the

Higgs particle of the standard model is a S, composite object made up of new fun­ Cy CB damental entities; they would be bound CHROMONS

together by a new force analogous to the COMBINATIONS OF PREONS give rise to the 24 quarks and leptons of the three genera­ color force and called technicolor. Each tions. For example, the red s quark is made up of somon 52 (signif ying that the composite of these ideas answers some of the q ues- is a second-generation particle), in combination with the red chromon and the negative flavon.

© 1983 SCIENTIFIC AMERICAN, INC 61 tions that remain open in the standard quarks, the leptons, the photon, the glu­ worked before, repeatedly, in going model. Each idea also fails to answer ons and the weak bosons are the truly from the atom to the nucleus to the pro­ other questions, raises new difficulties fundamental particles of the ultimate ton to the quark. In another sense the and worsens existing ones, for example theory of nature. The alternative of sug­ idea of quark and lepton substructure is by further increasing the number of un­ gesting that the quarks and leptons are a most radical proposal. The electron related arbitrary constants. themselves composite is in one sense the has now been studied for almost a centu­ In all the above schemes for grand uni­ most conservative and the least origi­ ry, and its pointlike nature has been es­ fication it is explicitly assumed that the nal hypothesis. It is a strategy that has tablished very well indeed. In the case of the neutrino, which may tu rn out to be entirely massless, it is even more dif­ ELECTRIC ficult to imagine an internal structure. HYPERCOLOR COLOR CHARGE The assertion that these particles and the others like them are composites will clearly have to overcome formidable CIJ T +1/3 Z obstacles if it is to have any future. o I Offsetting the difficultiesof the under­ CIJ a: taking are its potential rewards. A fully v o successful composite model might re­ solve all the questions left unsettled in the standard model. Such a hypotheti­ cal theory would begin by introducing a new set of elementary particles, which I CIJ z V 0 shall refer to generically as prequarks. 0 I Ideally there would not be too many of CIJ a: them. Each quark and lepton in the stan­ i= dard model would be accounted for as a z T -1/3 « combination of prequarks, just as each hadron can be explained as a combina­ tion of quarks. The mass of a quark or a RISHON MODEL constructs all the quarks and leptons out of just two species of fundamen­ lepton would no longer be an arbitrary tal particles and their antiparticles. The rishons carry both hypercolor, a property associat­ constant of nature; instead it would be ed with the force that binds them to one another, and ordinary color, which they convey to determined by the masses of the constit­ the composite systems they form. One rishon is electrically charged and the other is neutral. uent prequarks and by the strengt h of the force that binds the prequarks to­

ELECTRIC gether. The exact ratios that relate the RISHON COMBINATION PARTI CLE COLOR CHARGE charge of a quark to that of a lepton would be explained in a similar way: both kinds of composite particles would TTT e COLORLESS +1 derive their charges from those of the same constituent prequarks. The entire pattern of quarks and leptons within a generation would presumably reflect TTV u +2/3 some simple rules for combining the prequarks. The existence of multiple generations TVV d +1/3 might also be explained in a natural way. The quarks and leptons in the high­ er generations might have an internal constitution similar to that of the corre­ VVV Ve COLORLESS 0 sponding particles of the first genera­ tion; the differences could be in the ener­ gy and the state of motion of the constit­ uents. Thus the sand b quarks would be VVV COLORLESS o excited states of the d quark, and the muon and the tau lepton would be excit­ ed states of the electron. Similar excited states are known in all other composite VVT d -1/3 systems, including atoms, nuclei and hadrons. For example, at least a dozen hadrons have been identifiedin exper­ iments as excited states of the proton; VTT -2/3 they and the proton itself are all thought to have essentially the same quark com­ position, namely uud.

TTT e COLORLESS -1 his imaginary, ideal prequark theory Taccomplishes everything one might ask of it except for unifying the funda­ COMBINATIONS OF RISHONS taken three at a time give a correct accounting of all the quarks and leptons (and antiquarks and antileptons) in any one generation. The pattern of elec­ mental forces. Even there some progress tric charges noted in the standard model, and the apparent relation between fractional charge is conceivable, since a new force would and color, emerge as natural consequences of the way the rishons combine. All the allowed very likely be introduced to bi nd the combinations of three rishons or of three antirishons are neutral with respect to hypercolor. prequarks together; the new force might

62 © 1983 SCIENTIFIC AMERICAN, INC lead to a new understanding of how the The color of the co mposite system is Weizmann Institute of Science in Reho­ known forces are related. Imagining determined by preons called chromons; vot. The model postulates just two spe­ . what a successful model might be like, there are four of them, one with the col­ cies of fundamental building blocks, however, is not at all the same thing as or red, one yellow, one blue and one called rishons. (Rishon is the Hebrew ad­ actually constructing a realistic and in­ colorless. The remaining family of pre­ ject�ve meaning first or primary.) One ternally consistent one. So far no one ons, which is assigned the role of defin­ rishon has an electric charge of + 1!3 has done it. ing electric charge, needs to have only and the other is electrically neutral. I What has been tacking is a satisfac­ two members in or der for every quark designate them respectively Tand V, for tory theory of prequark dynamics, a and lepton to be uniquely identified. Tohu Vavohu, Hebrew for "formless and theory that would describe how the pre­ These last preons have been given the void," the description of the initial state quarks move inside a quark or a lepton name fiavons, after flavor, the whimsi­ of the universe given in the first chapter and that would enable one to calculate cal term for whatever property it is that of Genesis. The co mplementary anti­ the mass and total energy of the system. distinguishes the u quark from the d rishons have charges of -1/3 and zero As I shall set forth bel ow, there are fun­ quark, the c from the s, the neutrino and are designated l' and V. damental obstacles to the formulation from the electron and so on. The model has one simple rule for of such a theory, although I would sub­ In the preon model the classification constructing a quark or a lepton: any mit that they are not insurmountable. In of a composite particle follows directly three rishons can be assembled to form the meantime, lacking any persuasive from its complement of preons. All lep­ a composite system, or any three an­ account of prequark motions, theorists tons, for example, are distinguished by a tirishons, but rishons and antirishons have nonetheless been exploring the colorless chromon, and all first-genera­ cannot be mixed in a single particle. combinatorial possibilities of the pre­ tion particles must obv iously have a The rule gives rise to 16 combinations, quark idea, that is, they have been exam­ first-generation somon. In the allocation which reproduce exactly the properties ining the ways quarks and leptons might of electric charge, however, a complica­ of the 16 quarks, antiquark�, leptons be built up as specific combinations of tion arises. If there are only two fiavons and antileptons in the firstgener ation. In finer constituents. and if they are the sole carriers of elec­ other words, every quark and lepton in In the past few years several dozen tric charge, not all the charge values ob­ the first generation corresponds to some composite models have been proposed; served in nature can be reprod uced. The allowed combination of rishons or anti­ they can be cl assified in perhaps four u quark and the neutrino, for example, rishons. (In this system of classification or five main groups. No single model must have the same charge (because each color is counted separately.) solves all pr oblems, answers all q ues­ they include the same fiavon),and so The pattern of quark and lepton tions and is widely accepted. It would be must the d qu ark and the electron. The charges is generated as foll ows. The unfair to describe only one scheme, but problem can be solved in any of several TTT combination, with rishon charges it is impractical to enumerate them all. I ways. In one scheme electric charge is of 1/3 + 1!3 + 1/3, has a total charge shall present a few of the central ideas. assigned to both the fiavons and the of +1 and therefore corresponds to the The firstexplicit model of quark and chromons, and the total charge of a positron; similarly, 1'1'1' has a total lepton substructure was proposed in composite particle is eq ual to the sum of charge of -1 and is identified with the 1974 by Jogesh C. Pati of the University the two values. Models of this kind can electron. The VVV and vVV combina­ of Maryland at College Park and Salam, be made to yield the correct charge tions are both electrically neutral and who have since returned to the topic sev­ states, but only by abandoning the prin­ represent the neutrino and the antineu­ eral times in collaboration with John ciple of having each kind of preon carry trino respectively. The remaining al­ Strathdee of the Int ernational Centre just one property. lowed combinations yield fractionaHy for Theoretical Physics. It was they who Another troublesome feature of the charged quarks. TTV, with a charge of introduced the term preq uark, which I preon model is the requirement that +213, is the u quark, and TVV, with a have adopted here as a generic name composites be formed only by drawing charge of + 1/3, is the J antiquark. The for hypothetical subconstituents of all one preon from each family. Why are analogous antirishon states VVT and kinds. The specific elementary particles there no particles made up of three J7TT correspond to the d qu ark and the of the model devised by Pati and Salam chromons, say, or of two somons and a iiantiq uark. I shall call preons, which is another term fiavon? The exotic properties of such The mode! also accounts successfully of their invention. particles would make them quite con­ for the color of the composite systems. The rationale for the preon model be­ spicuous. It seems likely that if they A T rishon can have any of the three gins with the observation that every existed, they would have been detected colors red, yellow and blue, whereas a V quark and lepton can be identifiedun­ by now. rishon has an anticolor. Combinations ambiguously by listing just three of its Many variations of the preon mo del such as TTT and VVV, which designate properties: electric charge, color and have been proposed by other physicists, leptons, can be made colorless since generation number. These properties, using the same basic idea but slightly they can include one rishon in each col­ then, suggest a straightforwar d way of different sets of preons. Notable among or or one in each anticolor. The other organizing a set of constituent particles. the variations are the models suggested combinations, which yield quarks, must Three families of preons are needed. by Hidezumi Terazawa, Yoichi Chi­ have a net color. For example, a TTV In one family the preons carry electric kashige and Keiichi Akama of the Uni­ state might have the rishon colors red, charge, in another they carry color and versity of Tokyo and by O. Wallace blue and antiblue; the antiblue would in the third they have some property Greenberg and Joseph Sucher of the cancel the blue, leaving the system with that determines generation number. A University of Maryland. a net color of red. In this way the given quark or lepton is assembled by connection between color and electric selecting exactly one preon from each erhaps the simplest model of quark charge, which was apparent but unex­ family. Pand lepton structure is the rishon plained in the standard model, is readily The preons that determine genera­ model, which I proposed in 1979. A sim­ understood. Because of the way electric tion number are called somons, from ilar idea was put forward at abou t charge and color are allotted to the the Greek soma, meaning body, because the same time by Michael A. Shupe of rishons, all composite systems with frac­ they have a dominant influenceon the the University of Il linois at Urbana­ tional charge turn out to be colored, and mass of the composite system. Since Champaign. The model has since been all systems with an integer charge can be there are three generations of quarks further developed and studi ed in great made colorless. and leptons, there must be three somons. detail by Nathan Seiberg and me at the Other regularities of the standard

63 © 1983 SCIENTIFIC AMERICAN, INC model also lose their ai r of mystery The simplest idea would be to describe cle could be formed by the add ition of when rishons are introduced. Consider the muon, for example, as having the pairs of prequarks and antiprequarks. the hydrogen atom, made up of a proton same prequark constituents as the elec­ All charges and other properties mu st and an elec;tron, or in terms of quarks tron, but in the muon the prequarks cancel in such a pair, and so again only and leptons two u quarks, a d quark and would have some higher-energy config­ the mass would be affected. an electron. The total rishon content of uration. It is an elegant idea but, regret­ These ideas are currently at the stage the quarks is four T's, one T,two V's and tably, it appears to be unworkable. The of unrestr.ained spec ulation. No one two V's . The electric charge of the T scheme implies differences in energy be­ knows what distinguishes the three gen­ cancels the charge of one T rishon, and­ tween the successive excited states that erations from one another, or why there the V's and V;s also cancel (they have no are much larger than the actual differ­ are three or whether there may be more. charge in any case), leaving the proton ences. The flaw is a fundamental one, No explanation can be given of the mass with a net charge equal to that of a TTT and there seems to be no remedy. differencebetween the generations. In system. The electron's rishon content is Other possible mechanisms for creat­ short, the triplication of the generations just the opposite: 'fT'f. 'rhus it is evident ing multiple generations have been con­ is still a major unsolved puzzle. why the proton and the electron have sidered. Several physicists have suggest­ A third kind of substructure model charges of equal magnitude and why ed that the higher-generation relatives deserves mention. It tries to relate the the hydrogen atom is neutral: the ulti­ of a given state might be created by add­ possibility of quark and lepton structure mate sources of the charge are pairs ing a Higgs particle, the "extra" particle to another fundamental problem: un­ of matched particles and antiparticles. associated with the weak bosons in the derstanding the relativistic quantum standard model. Because a Higgs par­ theory of gravitation. Ideas of this kind he rishon model and many other ticle has no electric charge or color or have been explored by John Ellis, Ma ry Tmodels that explain the pattern of even spin angular momentum, adding K. Gaillard, Luciano Maiani and Bruno the first generation have difficu lty ac­ one to a compos ite system would alter Zumino of CERN. One approach to counting for the second and third gener­ only the mass. Hence an electron might their ideas is to consider the distances at ations. It would seem that such models be converted into a muon by adding one which preq uarks interact: the experi­ lend themselves well to the scheme of Higgs particle or into a tau by adding mental limit is less than 10-16 centime­ forming each particle in the higher gen­ two or more Higgs particles. Seiberg ter, but the actual distance could be sev­ erations as an excited state of the corre­ and I have proposed another possible eral orders of magnitude smaller still. sponding particle in the first generation. mechanism: a higher-generation parti- At about 10 -34 centimeter the gravita­ tional force becomes strong eno ugh to have a significant effecton individual 10'4 particles. If the scale of the prequark interactions is. this small, gravitation 1013 cannot be neglected. Ellis, Gaillard, CONSTITUENTS· OF QUARKS Maiani and Zumino have outlined an 10'2 ambitious program that aims to unify all the forces, incl uding gravitation,

(jJ 10" in a scheme that treats not only the � quarks and leptons but also the gauge_ 0 > bosons as composite particles. Like oth­ 10'0 z er composite models, however, this one 0 a: has serious flaws. I- 0 109 W ...J Any prequark model, regardless of its '::'. CONSTITUENTS OF PROTONS >- 10' n details, must supply some mecha­ <.') a: nism for binding the prequarks together. w CONSTITUENTS OF NUCLEI z 10' There must be a powerful attractive w force between them. One strategy is to 0 f= postulate a new fundamental force of S!! 106 a: nature analogous in its workings to the w I- color force of the standard model. To 0 105 <{ emphasize the analogy the new force is a: <{ called the hypercolor force and the car­ I 104 0 rier fields are called. hypergluons. The preq uarks are assumed to have hyper­

10' color, but they combi.ne to form hy­ percolorless composite systems, just as quarks have ordinary color but com­ 102 bine to form colorless protons and neu­ trons. The hyper color force presuma­ bly also gives rise to the property of 10-6 10-' 10 -' 10 -9 10-10 10-11 10 -12 10-13 10-14 10-15 10-16 10 -17 10 -18 10-19 confinement, again in analogy to the SIZE OF SYSTEM (CENTIMETER) color force. Hence all hyper colored pre­ quarks would, be trapped inside compos­ SIZE AND ENERGY have a reciprocal relation · in the quantum theory, indicating that the ite particles, which would explain why constituents of composite quarks and leptons must have an exceediugly high kinetic energy. free prequarks are not seen in experi­ The size of an atom implies that its constituents can have energies ranging from a few elec­ ments. An idea of this kind was first pro­ tron volts to a feW' thousand. (An electron volt is the energy gained by an electron accelerated posed by 't Hooft, who studied some of through a potential difference of ,one volt.) In a nucleus the protons and neutrons move with an its mathematical 'implications but also energy of several · million electron volts, and in a proton or a neutron the quarks have energies of. several hundred million electron volts. Any constituents of quarks and leptons must be con­ expressed doubt that nature actually fined to a radius of less than 1 0-16 centimeter, and possibly much less. As a result the kinet­ follows such a path. ic energy of the hypothetical prequarks can be no less than a few hundred billion electron volts. The typical radius of hypercolor con-

64 © 1983 SCIENTIFIC AMERICAN, INC finement must be less than 10-16 cen­ QUARK ATOM NUCL EUS PROTON OR LEPTON timeter. Only when matter is probed 10' 5 'at distances smaller than this would it be possible to see the hypothetical pre­ 10'4 quarks and their hypercolors. At a range of 10 -14 or 10-15 centimeter hypercolor effectively disappears; the only objects 10'3 visible at this scale of resolution (the quarks and leptons) are neutral with re­ 10" spect to hypercolor. At a range of 10-13 centimeter ordinary color likewise fades 10" away, and the world seems to be made

up entirely of objects that lack both col­ 10'0 or and hypercolor: protons, neutrons, (jJ � electrons and so on. 0 109 I· The notion of hypercolor is well suit­ > Z ed to a variety/of prequark models, in­ 0 108 a: cluding the rishon model. In addition f-- 0 to their electric charge and color the W � 107 rishons are assumed to have hypercol­ � or and the antirishons to have antihy­ >- (!J 106 percolor. Only comb inations of three a: rishons or· three antirishons are allowed w z W because only those combinations are 105 neutral with respect to hypercolor. A mixed three-particle system, such as 104 TTf cannot exist because it·. would not be hypercolorless. The assignment of 103 hypercolors thereby explains . the rule for forming composite rishon systems. Similar rules apply in other hypercolor­ 10' based prequark models. If the aim of a prequark model is to 10' simplify the understanding of nature, postulating a new basic force does not seem very helpful. In the case of hyper­ color, however, there maY'be some com­ MISMATCH OF ENERGY AND MASS makes it difficult to . devise a theory ·of how pre­ quarks might move and interact. In an atom or a nudeus the kinetic energy of·the constituents pensation. Consider the neutrino: it has (€olor) is mucll less than the total mass of the system (gray). In a proton the two quantities neither electric charge ' nor color, only are of comparable magnitude. In a composite quark, however, the energy of the prequarks weak charge. According to the standard greatly exceeds the total mass. Indeed, compared with the kinetic energy, the mass is essential­ .model, two neutrinos can act on each ly zero. Somehow virtually all mass is canceled, a development that is unlikely to be accidental. other only through the short-range weak force. If neutrinos are composites of hy­ percolored prequarks, however, there or. It should be noted, however, that the preq uarks could be particles with could be an additional source of interac­ all these forces are long-range ones; the charges resembling both magnetic and tions between neutrinos. When two neu­ short-range molecular, strong and weak electric charges. If they are, the forces trinos are' far apart, there are practically forces will have lost their fundamen­ binding them may be of a new and inter­ no hypercolor forces between them, but tal status. esting origin. when they are at close range, the hyper­ For now hyper color remains a conjec­ colored prequarks inside one neutrino ture, and so does the notion of explain­ one of the ideas I have just de­ are able to "see" the inner hypercolors ing the weak force as a resid ue of the N scribed constitutes a theory of pre­ of the other one. Complicated short­ hypercolor force. It may yet turn out quark dynamics. Indeed, there is a seri­ range attractions and repulsions are the that the weak force is fundamental. A ous impediment to the formulation of result. The mechanism, of course, is ex­ careful measurement of the mass, life­ such a theory; it is the requirement that actly the same as the one that explains time and other properties of the weak the preq uarks be exceedingly small. The the molecular force as a residue of the bosons should provide important clues most stringent limit on their size is set electromagnetic force and the strong in this matter. indirectly by measurements of the mag­ force as a residue of the color force. Hypercolor is not the only candidate netic moment of the electron, which The conclusion may also be the same. for a prequark binding force. Another agree with the calculations of quantum Seiberg and I, and independently Green­ interesting possibility was suggested by electrodynamics to an accuracy of 10 berg and Sucher, were the first to suggest Pati, Salam and Strathdee. Instead of in­ significant digits. In the calculations it is that the short-range weak force may ac­ troducing a new hypercolor force, they assumed that the electron is pointlike; tually be a residual effect of the hyper­ borrowed an idea that has long been fa­ if it had any spatial extension or inter­ color force. According to this hypothe­ miliar, namely the magnetic force, and nal structure, the measured value would sis, the weak bosons W+, W-and zo adapted it to a new purpose. An ordi­ differfrom the calculated one. Evident­ must also be composite objects, presum­ nary magnet invariably has two poles, ly any such discrepancy can at most af­ ably made up of certain comb inations which can be thought of as opposite fect the 11 th digit of the result. It is this of the same preq uarks that compose the magnetic charges. For 50 years there constraint that implies the characteristic quarks and leptons. If this idea is con­ . have been theoretical reasons for su p­ distance scale of the electron's internal firmed, the list of fundamental forces posing there could also be isolated mag­ structure must be less than 10-16 cen­ will still have four entrjes: gravitation, netic charges, or monopoles. Pati, Sa­ timeter. Roughly speaking, that is the electromagnetism, color and hypercol- lam and St rathdee have argued that maxim um radius of an electron, and any

© 1983 SCIENTIFIC AMERICAN, INC 65 prequarks must stay within it. If they the composite system (if it is indeed With the proton and its quark constit­ strayed any wider, their presence would composite) is much smaller than the en­ uents the energy-mass relation b�gins to already have been detected. ergy of its constituents. get curious. From the effective radius of Why should the small size of the elec­ The oddity of the situation can be illu­ the proton the typical energy of its com­ tron inhibit speculation about its inter­ minated by considering the relations of ponent quarks can be calculated; it turns nal structure? The uncertainty principle mass and kinetic energy in other com­ out to be comparable to the mass of the establishes a reciprocal relation between posite systems. In an atom the kinetic proton itself, which is a little less than 1 the size of a composite system and the energy of a typical electron is smaller GeV. The energy that must be invested kinetic energy of any components mov­ than the mass of the atom by many to create an excited state of the quark ing inside it. The smaller the system, orders of magnitude. In hydrogen, for system is of the same order of magni­ the larger the kinetic energy of the con­ example, the ratio is ro ughly one part tude: the hadrons identified as excited stituents. It follows that the prequarks in 100 million. The energy needed to states of the proton exceed it in mass by must have enormous energy: more than change the orbit of the electron and from 30 to 100 percent. Nev ertheless, 100 GeV (100 billion electron volts), thereby pu t the atom into an excited the ratio of kinetic energy to total mass and possibly much more. (One electron state is likewise a negligible fraction of is still in the range that seems intuitively volt is the energy acquired by an elec­ the atomic mass. In a nucleus the kinetic reasonable. Suppose one knew only the tron when it is accelerated through a energy of the protons and neutrons is radius of the proton, and hence the typi­ potential differenceof one volt.) Because also small compared with the nuclear cal energy of whatever happens to be mass is fundamentally equivalent to en­ mass, but it is not completely negligible. inside it, and one were asked to guess the ergy, it can be measured in the same The motion of the particles gives them proton's mass. Since the energy of the system of units. The mass of the elec­ an energy equivalent to about 1 percent constituents is generally a few hundred tron, for example, is equivalent to .0005 of the system's mass. The energy needed million electron volts, one would surely GeV. There is a paradox here, which I to create an excited state is also about 1 guess that the total mass of the system is call the energy mismatch: the mass of percent of the mass. at least of the same order of magnitude and possibly greater. The guess would be correct. 'For the atom, the nucleus and the pro­ ton, then, the mass of the system is at least as large as the kinetic energy of the � constituents and in some cases is much larger. If quarks and leptons are com­ , , posite, however, the relation of energy , , to mass must be quite different. Since , the preq uarks have energies well above <' • 100 GeY, one would guess that they OBSERVER OBSERVER would form composites with masses of hundreds of GeV or more. Actually the known quarks and leptons have masses that are much smaller; in the case of the electron and the neutrinos the mass is smaller by at least six orders of magni­ tude. The whole is much less than the sum of its parts. The high energy of the prequarks is also what spoils the idea of viewing the higher generations of quarks and lep­ tons as excited states of the same set of prequarks that form the first-genera­ RIGHT-HANDED LEFT-HANDED tion particles. As in the other composite PARTICLE PARTICLE systems, the energy needed to change the orbits of the prequarks should be of the same order of magnitude as the ki­ netic energy of the constituents. One would therefore expect the successive generations to differ in mass by hun­ dreds of GeV, whereas the actual mass differences are as small as .1 GeY.

At this point one might well adopt the I\.. view that the energy mismatch can­ CHIRAL SYMMETRY offers a possible explanation of the "miraculous" cancellation of mass in quarks and leptons. Chirality, or handedness, describes the relation of a particle's spin not be accepted, indeed that it simply angular momentum to its direction of motion. Suppose an observer is overtaken by a faster­ demonstrates the elementary and struc­ moving electron (a). From the observer's point of view the electron obeys a right-hand rule: tureless nature of the quarks and lep­ When the fingers of the right hand curl in the same direction as the spin, the thumb gives the tons. Many physicists hold this view. direction of motion. If the observer speeds up, however, so that he overtakes the electron (b), The energy mismatch, however, contra­ the handedness of the 'particle changes. In the observer's frame of reference the electron is dicts no basic law of physics, and I now approaching instead of receding, but its spin direction has not changed; as a result its mo­ would argue that the circumstantial evi­ tion is described by a left-hand rule. Chirality, therefore, is not conserved. There is one kind of dence for quark and lepton composite­ particle to which this argument cannot be applied, namely a massless particle, which must al­ ness is sufficiently persuasive to warrant ways move with the speed of light. No observer can move faster than a massless particle, and so its handedness is an invariant property. If a theory of preqnarks had a chiral symmetry, in further investigation. which handedness mnst be conserved, the low mass of the qnarks and leptons might not be ac­ What is peculiar about the quark and cidental. They wonld have to be virtually massless for the chiral symmetry to be maintained. lepton masses is not merely that they are

66 © 1983 SCIENTIFIC AMERICAN, INC small but that they are virtually zero when measured on the energy scale defined by their constituents' energy. In other composite systems a small amount of mass is "lost" by being con­ verted into the binding energy of the sys­ tem. The total mass of a hydrogen atom, for example, is slightly less than that of an isolated proton and electron; the dif­ ference is equal to the binding energy. In a nucleus this "mass defect" can reach a SYMMETRY SPONTANEOUSLY few percent of the total mass. In a quark BROKEN SYMMETRY or a lepton, it seems, the entire mass of the system is canceled almost exactly. SPONTANEOUS SYMMETRY BREAKING is a mechanism that could spoil a prequark Such a "miraculous" cancellation is cer­ theory even if it has a chiral symmetry. Both of the physical systems shown here-a simple tainly not impossible, but it seems most trough and a trough with a bump in the bottom-can be described as symmetrical in the sense unlikely to happen by accident. Similar that exchanging left and right leaves the system unaltered. For the simple trough the system large cancellations are known elsewhere remains symmetrical when a ball is put in the trough; the ball comes to rest in the center, so that exchanging left and right still has no effect. In the trough with a bump, however, the ball in physics, and they have always been takes up a position on one side or the other, and the symmetry is inevitably broken. Similarly, found to resu lt from some symmetry a prequark theory that has a chiral symmetry might nonetheless give rise to composite systems principle or conservation law. If there is that do not observe the symmetry. Showing that a chiral symmetry can definitely remain un­ to be any hope of constructing a theory broken is currently the principal challenge in formulating a theory of how prequarks move. of prequark dynamics, it is essential to find such a symmetry in this case. There is a likely candidate: chiral symmetry, or chirality. The name is de­ that might conceivably account for the and leaves the photon massless. The the­ rived from the Greek word for hand, small mass of the quarks and leptons. ory that describes these gauge bosons is and the symmetry has to do with hand­ The argument runs as follows. If the symmetrical, and in it the four bosons edness, the property defined by a parti­ prequarks are massless particles, if they are essentially indistinguishable, but cle's spin and direction of motion. Like have a spin of 1!2 and if they interact because of the symmetry breaking the other symmetries of nature, chiral sym­ with one another only through the ex­ physical states actually observed are metry has a conservation law associated change of gauge bosons, any theory de­ quite different. Chiral symmetries are with it, which gives the clearest account scribing their motion is gu aranteed to notoriously susceptible to symmetry of what the symmetry means. The law have a chiral symmetry. If the massless breaking. Whether the chiral symmetry states that the total number of right­ prequarks then bind together to form of prequarks breaks or not when the handed particles and the total number composite spin- l!2 objects (namely the prequarks form composite objects can of left-handed ones can never change. quarks and leptons), the chiral symme­ be determined only with a detailed un­ In the ordinary world of protons, elec­ try might ensure that the composite par­ derstanding of the forces acting on the trons and similar particles handedness ticles also remain massless compared prequarks. For now that understanding or chirality clearly is not conserved. A with the huge energy of the preq uarks does not exist. In certain models it can violation of the conservation law can be inside them. Hence the small mass of the be shown that a chiral symmetry does demonstrated by a simple thought ex­ quarks and leptons is not an accident. exist but is definitely broken. No one has periment. Imagine that an observer is They must be essentially massless with yet succeeded in constructing a compos­ moving in a straight line when he is respect to the energy of their constitu­ ite model of quarks and leptons in which overtaken by an electron. As the elec­ ents if the chiral symmetry of the theo­ a chiral symmetry is known to remain tron recedes from him he notes that its ry is to be maintained. unbroken. Neither the preon model nor spin and direction of motion are related The crucial step in this argument is the rishon model succeeds in solving by a right-hand rule. Now suppose the the one extending the chiral symmetry the problem. The task is probably the observer speeds up, so that he is overtak­ from a world of massless prequarks to most difficult one facing those attempt­ ing the electron. In the observer's frame one made up of composite quarks and ing to demonstrate that quarks and lep­ of reference the electron seems to be leptons. It is essential that the symmetry tons are composite. approaching; in ot her words, it has re­ of the original physical system survive versed direction. Because its spin has in and be respected by the composite f a consistent pre quark theory can be not changed, however, it has become a states formed out of the massless con­ I worked out, it will still have to pass left-handed particle. stituents. It may seem self-evident that if the test of experiment. First, it is impor­ There is one kind of particle to which a theory is symmetrical in some sense, tant to establish in the laboratory wheth­ this thought experiment cannot be ap­ the physical systems described by the er or not quarks and leptons have any plied: a massless particle. Because a theory must exhibit that symmetry; ac­ internal structure at all. If they do, ex­ massless particle must always move tually, however, the spontaneous break­ periments might then begin to discrimi­ with the speed of light, no observer can ing of symmetries is commonplace. A nate among the various models. The ex­ ever go faster. As a result the handed­ familiar example is the roulette wheel. periments will have to penetrate the un­ ness of a massless particle is an invariant A physical theory of the roulette wheel known realm of distances smaller than property, independent of the observer's would show it is completely symmetri­ 10-16 centimeter and energies higher frame of reference. Furthermore, it can cal in the sense that each slot is equiva­ than 100 GeV. There are two basic ways be shown that none of the known forces lent to any other slot. The physical sys­ to explore this region: by doing experi­ of nature (those mediated by the pho­ tem formed by putting a ball in the ments with particles accelerated to very ton, the gluons and the weak bosons) can roulette wheel, however, is decidedly high energy and by making precise mea­ alter the handedness of a particle. Thus asymmetrical: the ball invariably comes surements of low-energy quantities that if the world were made up exclusively of to rest in just one slot. depend on the physics of events at very massless particles, the world could be In the standard model it is the spon­ small distances. said to have chiral symmetry. taneous breaking of a symmetry that Experiments of the first kind include Chiral symmetry is the root of an idea makes the three weak bosons massive the investigation of the weak bosons and

67 © 1983 SCIENTIFIC AMERICAN, INC the search for the Higgs particles of the rope and Japan are expected to yield these is the search for the decay of the standard model. When such particles detailed information about the weak proton, a particle that is knowp to have can be made in sufficient numbers, a bosons and will also continue the ongo­ an average lifetime of at least 1030 years. careful look at their properties should ing investigation of the quarks and lep­ Several experiments are now monitor­ reveal much about the physics of very tons themselves. ing large quantities of matter, incorpo­ small distances. New accelerators now Equally interesting are the high-preci­ rating substantially more than 1030 pro­ being planned or built in the U.S., Eu- sion, low-energy experiments. One of tons, in an attempt to detect the signals emitted when a proton disintegrates. None of the forces of the standard mod­ el can induce such an event, but none of the rules of the standard model abso­ lutely forbids it. Both the grand unified theories and the prequark models, on the other hand, include mechanisms that could convert a proton into other parti­ cles that would ultimately leave behind only leptons and photons. If the decay is detected, its rate and the pattern of de­ p cay products could o./fer an important glimpse beyond the standard model. There is similar interest in the hypo­ thetical process in which a muon emits a photon and is thereby converted into an electron. Again none of the forces of the standard model can bring about an event of this kind, but again too no fun­ damental law forbids it. Some of the composite models allow the transition and others do not, so that a search for the process might offer a means of choosing among the models. Experi­ ments done up to now put a limit of less than one in 10 billion on the probability that any given muon will decay in this way. Detection of such events and a de­ termination of their rate might illumi­ J: nate the mysterious distinction between the generations. A third class of precision experiments are those that continue to refine the "1.. measurement of the magnetic moment 1 of the electron and of the muon. Further improvements can be expected bot h in experimental accuracy and in the associ­ ated calculations of quantum electrody­ o! namics. If the results continue to agree with the predictions of the standard ______� model, the limit on the possible si ze of ___. ' } e any quark and lepton substructure will T RISHON STRUCTURE become remoter. If a discrepancy be­ �______T tween theory and experiment is detect­ ed, it will represent a strong hint that "G quarks and leptons are not elementary. It may well be a decade or two before the next level in the structure of matter comes clearly into view (if, again, there is another level). What is needed is a sound theoretical picture, one that is self-consistent, that agrees with all ex­ -�� :}l periments and that is simple enough to explain all the features of the standard model in terms of a few principles and a d{;-� }r· few fundamental particles and forces. � The correct picture, whether it is a grand unified theory or a composite model of DECAY OF THE PROTON is a conjectured event that might be interpreted as experimental the quarks and leptons, may already ex­ evidence for a grand unified theory or for a model of quark substructure. In one form of decay ist in some embryonic form. On the oth­ the proton would be observed to disintegrate into a positron (e)and a neutral pion (170). The er hand, it is also possible the correct event can be understood in terms of the proton's quark constituents: an interaction of the two theory will emerge only from some to­ u quarks converts one of them into a positron and the other into ad anti quark; the latter combines with the remaining d quark of the proton to form the neutral pion. Grand unified theories sug­ tally new idea. In the words of Niels gest that the interaction of the u quarks is mediated by a new force of nature. The rishon mod­ Bohr, it may be that our present ideas el provides an alternative explanation: the two u quarks merely exchange a T and a V rishon. "are not sufficiently crazy to be correct."

68 © 1983 SCIENTIFIC AMERICAN, INC