The Higgs

It could give mathematical consistency to the -the

theory that describes the intera ctions of fundam en tal .

The search for the elusive particlewill require new accelerators

by MartinusJ. G. Veltman

he truly fundamental problems dard model, making it applicable to generally make themselves felt by Tof can always be ex­ ranges beyond the capabilities means of the exchange of a mediating plained in simple terms without of the current generation of parti­ ; the particle that mediates the the help of complicated equations or cle accelerators but that may soon be electromagnetic , for example, is mathematical arguments. At least this reached by future accelerators. More­ the , or of . The was once told to me by Victor F. over, the is thought to mediating particles of the gravitation­ Weisskopf, an eminent who generate the of all the funda­ al field,the weak field and the strong often engages in such explanations, mental particles; in a manner of speak­ field are respectively the and he may very well be right. It cer­ ing, particles "eat" the Higgs boson to (which has not yet been detected), tainly holds for a proposed but un­ gain weight. three weak vector , called the discovered particle called the Higgs The biggest drawback of the Higgs W+, W-and ZO particles, and eight boson and the so-called Higgs field as­ boson is that so far no evidence of . In a somewhat analogous way sociated with it. its existence has been found. Instead the Higgs boson is the mediating parti­ The Higgs boson, which is named a fair amount of indirect evidence al­ cle of the proposed Higgs field. after Peter W. Higgs of the University ready suggests that the elusive particle It is now assumed that there is a con­ of Edinburgh, is the chief missing in­ does not exist. Indeed, modern theo­ stant Higgs field throughout all space, gredient in what is now called the stan­ retical physics is constantly filling the that is, the of is dard model of elementary processes: vacuum with so many contraptions not empty but contains this constant the prevailing theory that describes the such as the Higgs boson that it is amaz­ field. The Higgs field is thought to gen­ basic constituents of and the ing a person can even see the on a erate by to particles. fundamental by which they in­ clear night! Although future accelera­ Depending on the coupling strength, a teract. According to the standard mod­ tors may well find direct evidence of particle in space has a certain potential el, all matter is made up of and the Higgs boson and show that the mo­ energy. By Einstein's famous equa­ , which interact with one anoth­ tivations for postulating its existence tion, E = mc2 (energy equals mass er through four forces: , elec­ are correct, I believe things will not be multiplied by the of the speed tromagnetism, the weak and the so simple. I must point out that this of light), the coupling energy is equiva­ strong force. The strong force, for in­ does not mean the entire standard lent to a mass. The stronger the cou­ stance, binds quarks together to make model is wrong. Rather, the standard pling, the greater the mass. and , and the residual model is probably only an approxima­ The way particles are thought to ac­ strong force binds protons and neu­ tion-albeit a good one-of reality. quire mass in their interactions with trons together into nuclei. The electro­ the Higgs field is somewhat analogous magnetic force binds nuclei and elec­ ven though the only legitimate rea­ to the way pieces of blotting paper ab­ trons, which are one kind of , E son for introducing the Higgs bos­ sorb ink. In such an analogy the pieces into , and the residual electro­ on is to make the standard model of paper represent individual parti­ magnetic force binds atoms into ­ mathematically consistent, much at­ cles and the ink represents energy, or cules. The weak force is responsible tention has been given to the conceptu­ mass. Just as pieces of paper of differ­ for certain kinds of nuclear decay. The ally easier proposal that the particle ing size and thickness soak up vary­ influence of the weak force and the generates the masses of all the funda­ ing amounts of ink, different particles strong force extends only over a short mental particles. I shall therefore be­ "soak up" varying amounts of energy, range, no larger than the radius of an gin with that topic. or mass. The observed mass of a parti­ ; gravity and electro­ Central to an understanding of how cle depends on the particle's "energy­ have an unlimited range the Higgs boson would generate mass absorbing" ability and on the strength and are therefore the most familiar of is the concept of a field.A field is sim­ of the Higgs field in space. the forces. ply a quantity, such as temperature, In spite of all that is known about defined at every point throughout hat are the characteristics of the the standard model, there are reasons some region of space and time, such as Wproposed Higgs field? In or­ to think it is incomplete. That is where the surface of a frying pan. In physics der to endow particles with mass, the the Higgs boson comes in. Specifical­ the term "field"is usually reserved for Higgs field, if it exists, would have to ly, it is held that the Higgs boson gives such entities as the gravitational field assume a uniform, nonzero value even mathematical consistency to the stan- and the electromagnetic field. Fields in the vacuum. Moreover, the Higgs

76

© 1986 , INC field would be a , which is what oversimplified way, the mass of The Higgs boson is called a scalar one of two kinds of field important in a person would change if he or she boson because it has a of O. Most describing the interactions of particles. turned around while standing in the other bosons associated with fields are A scalar field is a fieldin which each same place. In other words, the Higgs thought to be vector bosons: particles point has associated with it a single field is "spinless." that have a spin of l. The photon, magnitude, or number. The other im­ Because the Higgs field is spinless, and W+, W-and ZO particles, portant field is a vector field: a field the Higgs boson must also be spinless. for instance, are spin-1 bosons. where at each point a vector, or arrow, Spin, as applied to elementary parti­ Since vector bosons are typically as­ is drawn. A vector has both a mag­ cles, is a quantum-mechanical proper­ sociated with the fundamental forces nitude, which is represented by the ty roughly equivalent to the classical of and the Higgs boson is a sca­ length of the arrow, and a direction. spin of a rotating ball. Elementary par­ lar boson, the force by which particles The electromagnetic, weak and strong ticles can take on only integer (0, 1, 2 couple to the Higgs fieldmust be a fields are all vector fields.(The gravi­ and so on) and half-integer (1/2, 3/2 new force. It is introduced explicitly tational field is a special entity called a and so on) values of spin. Particles that and solely as a mechanism to improve tensor field.) have integral spin are called bosons the mathematical consistency of the The proposed Higgs field must be a and particles that have half-integral standard model. The Higgs force be­ scalar field, because if it were a vector spin are called . Bosons and haves mathematically in a similar field, the mass of a particle would in fermions have sharply differing prop­ manner to the recently publicized general depend on the particle's align­ erties, but I shall not delve into that "fifth force" reported by Ephraim ment with the field. Stated in a some- topic here. Fischbach of Purdue University. The

MAGNETIC MONOPOLES should exist if the Higgs boson ex­ monopoles could, however, be formed by sweeping ists. Classically, of course, magnetic monopoles are not found be­ lines under the Higgs "rug" (top). The bottom illustration shows a cause when a bar magnet is cut in half, two smaller bar magnets pair of monopoles. Although there have been scattered reports of are created-not isolated "north" and "south" poles. Magnetic finding monopoles, none of them has been substantiated to date.

77

© 1986 SCIENTIFIC AMERICAN, INC proposed Higgs force is, however, known, for example, why the Higgs as the weak vector bosons, the energy weaker and has a much shorter range field should couple more strongly to density of the Higgs field in the vacu­ than the "fifth force." some particles than it does to others. um would be 10 trillion times greater The Higgs force is not a universal Nor do investigators understand how than the density of matter in an atomic force, because it couples differently the mass of the Higgs boson itself nucleus. If the earth were compressed to different particles. Specifically, if a (which is not known) comes about, al­ to this density, its volume would be ap­ particle is observed to have mass, the though it is generally presumed to be proximately 500 cubic centimeters, or strength of the coupling to the Higgs dominantly through a self-interaction a bit more than the size of a soft-drink field is assumed to be whatever quan­ with the Higgs field. In this sense ig­ can. Needless to say, this is contrary to tity is necessary to generate precisely norance about the origin of particle experiment. that mass. Presumably the Higgs field masses is replaced by ignorance about The theorists' way out is really does not couple to the photon, since particle-Higgs couplings, and no real something. It is assumed that the experiment shows the photon is mass­ knowledge is gained. "true" vacuum (one without a Higgs less. But apparently it couples to the Moreover, the introduction of the field) is curved in a negative sense: it W+, W-and ZO particles, because Higgs boson creates a significant prob­ has a cosmological constant equal in they do have mass. It should perhaps lem with respect to the "holy" field of magnitude but opposite in sign to the be noted that particles could have a gravitation. The equivalence of mass one generated by the Higgs field. The mass of their own, in addition to what and energy implies that the graviton, introduction of the Higgs field then they are thought to acquire from the which couples to anything that carries flattens out space to make precisely Higgs field. Curiously, however, in mass, should couple to anything that the as we know it. This solu­ the standard model not a single parti­ carries energy, including the Higgs tion is, of course, not very satisfactory, cle could have a mass of its own with­ field. The coupling of the graviton and many ingenious attempts have out destroying the mathematical com­ to the Higgs field-ever present in all been made to solve the problem of the pleteness of the theory. space-would generate a huge "cosmo­ huge cosmological constant. None logical constant": it would curve the of the attempts has succeeded. If any­ rom a physical point of view little is universe into an object roughly the size thing, have grown wor.se be­ F gained by proposing that the Higgs of a football. If the Higgs boson is as­ cause theorists keep dumping more boson accounts for mass. It is not sumed to have roughly the same mass particles and fieldsinto the vacuum.

LEPTONS QUARKS

MASS AT REST ELECTRIC MASS AT REST ELECTRIC PARTICLE NAME SYMBOL PARTICLE NAME SYMBOL (MeV) (MeV) CHARGE

ELECTRON ve ABOUT 0 0 UP u 310 +% e- DOWN 0.511 -1 d 310 -'h

MUON NEUTRINO v/J. ABOUT 0 0 c 1,500 +% STRANGE 1-'- 106.6 -1 s 505 -'h

TAU NEUTRINO v, LESS THAN 164 0 TOPfTRUTH t 22,500; +% HYPOTHETICAL PARTICLE ,- 1,784 -1 BOTTOM/BEAUTY b ABOUT 5,000 -'h

STRENGTH AT 10-13 CENTIMETER IN MASS AT REST ELECTRIC FORCE RANGE CARRIER SPIN REMARKS COMPARISON WITH (GeV) CHARGE STRONG FORCE

GRAVITY INFINITE 10-38 GRAVITON 0 2 0 CONJECTURED

OBSERVED INFINITE 2 10- PHOTON 0 1 0 DIRECTLY

WEAK SECTOR OBSERVED BOSONS: W + 81 1 +1 DIRECTLY WEAK LESS THAN 10-16 10-13 OBSERVED W- 81 1 -1 CENTIMETER DIRECTLY OBSERVED ZO 93 1 0 DIRECTLY

LESS THAN 10-13 PERMANENTLY STRONG GLUONS 0 1 0 CENTIMETER 1 CONFINED

STANDARD MODEL of elementary- holds that one down . The particles interact with one another by means there are 12 fundamental constituents of matter (top) and four ba­ of the four forces. Each force in turn has a particle associated with sic forces (bottom). The constituents of matter are divided into two it (called a boson) that conveys the force. The Higgs force, if it groups of six: leptons and quarks. Leptons exist independently, exists, would be a fifth one, which would be mediated by the Higgs whereas an individual quark has never been isolated. Quarks are boson. The masses of the fundamental constituents are given in always part of larger particles such as protons and neutrons; a millions of electron (MeV) and the masses of the particles , for instance, is thought to be made of two up quarks and that convey the forces are given in billions of electron volts (GeV).

78

© 1986 SCIENTIFIC AMERICAN, INC Perhaps somehow the universe be­ natively, the walls could have disap­ The introduction of an extra Higgs came flatfrom the dynamics of the peared early in the history of the uni­ boson also creates difficultiesin a big-bang explosion, which is believed verse. This is rather typical: one starts model that is attracting considerable to have created the universe some 15 with an excellent argument, drags in a attention called the SU(5) grand uni­ to 20 billion years ago. Higgs field and then things go wrong. fied theory. The goal of unifiedtheo­ The theory as it stands, with one It certainly inspires little faith in the ries in general is to account for the Higgs field,does not explicitly contra­ mechanism altogether. four forces in terms of one fundamen- dict observation, even if one must ac­ cept the incredible disappearance of SCALAR FIELD the cosmological constant. Certain ex­ • • • • • • • • • • • • • • • tensions of the theory proposed over the past decade often involve the intro­ • • • • • • • • • • • • • • • duction of additional Higgs fields. Al­ • • • • • • • • • • • • • • • though the arguments for such exten­ sions are often compelling, the phe­ • ••• ••••••••••• • • nomena associated with these extra Higgs fields have either never been • •••••••••••••••• seen or contradict observed facts. • •• •••••••••••• •• To account in an elegant way for certain symmetries observed in the ••••••••••••••••••• strong interactions, for example, a sec­ ••••••••••••••••••• ond Higgs field was proposed by Hel­ en . Quinn of the Stanford Linear • ••••••••••••••• ••• Accelerator Center (SLAC) and Ro­ • •••••••••••••• •• berto Peccei of the Deutsches Elec­ tronen- (DESY, the elec­ • •••••••••••••• • • tron accelerator in Hamburg). The ensuing theory predicted a new and ••• ••••••••••• • • presumably very light particle called • • • • • • • • • • • • • • • the . So far, in spite of extensive searches, the ax has not been found. • • • • • • • • • • • • • • In addition the theory has dramatic • • • • • • • • • • cosmological consequences concern­ • • • • • ing a phenomenon known as "domain VECTOR FIELD walls." In general a domain wall marks where two regions of differing proper­ �//����," ties meet each other. Domain walls are, for instance, found in permanent / /�� ---�'-.. '.\ \ magnets, where one region of atoms //�<--"��'.,\\ ���iH��t whose spins are aligned in one direc­ /k-"��--''. \ttij f 1\\ tion meets another region of atoms I , \ \ t whose spins are aligned in a different \ ttl/lt \, / � k-"""--. --- ��'. f direction. / t t tll/!!t I//.v'�-'�' \ t t / / t is believed that certain Higgs fields / �k-" +- � ". / ! ! ! ! I would have given rise to domain I / -- walls in the early universe. When the I//���k"� � If?'?,.?'.?'.?'/,!! universe was young, the temperature ����.?? was extremely hot and no Higgs field .,/"/'/I is thought to have existed. At some 11///�IC"IC" i/ �-����./'/! time the universe would have cooled j I I I / / / I / � sufficiently to allow a background \I � --.,..-�,/'" � / / Higgs field to come into being. Unless t � �� �-----..-"?�// the cooling were completely uniform, illllill the Higgs field would quite likely have \ \ � �---, --��// exhibited different properties from dill/iiI one region in space to the next. To \\.������/./' what extent the clash of such regions t � would result in visible or even violent \ \. '>..��- ----�/ / phenomena depends on detailed prop­ 11 \\ \\ 1\ f f t �\���,.-Y/ /� erties of the Higgs fields, but one \ \ \ \ \ \. \. would expect some kind of clash in FIELDS are important in describing the interactions of particles with one another. A connection with the suggestive propos­ field is a quantity (such as temperature) defined at every point throughout some region of al of Quinn and Peccei. space and time (such as the surface of a frying pan). Two kinds of fields are scalar fields (top) and vector fields(bottom). A scalar field is a fieldin which every point has associat­ The question is why domain walls ed with it a single magnitude, or number, represented here by the area of the dots. A between such regions have not been vector field has both a magnitude, which is represented here by the length of an arrow, observed. It could mean that there is and a direction, which is represented by the orientation of the arrowhead in space. The no Higgs field, or that nature has been electromagnetic, weak and strong fields are examples of vector fields; the Higgs field,if it careful in its use of the field. Alter- exists, would be a scalar field. (The gravity field is a special entity called a tensor field.)

79

© 1986 SCIENTIFIC AMERICAN, INC tal force. A step toward achieving that are so heavy, they essentially need a isolated pole of a bar magnet. (Classi­ goal was reached over the past two de­ Higgs fieldof their own. In SU(5) the­ cally, of course, such objects are not cades with the introduction and verifi­ ory, therefore, the vacuum contains found, because when a bar magnet cation of the so-called electroweak two Higgs fields that couple with dif­ is cut in half, two smaller bar mag­ theory. The theory holds that the elec­ ferent strengths to different particles. nets are created rather than isolated tromagnetic force and the weak force The most important consequence "north" and "south" poles.) Propo­ are manifestations of the same under­ of the SU(5) theory is that quarks, nents of the SU(5) theory differ over lying force: the electroweak force. The through the new set of vector bosons, the internal composition of the mono­ electroweak theory was dramatically can change into leptons. As a result the pole and over how many monopoles confirmed in 198 3 at CERN, the Euro­ proton-that "immortal" conglomera­ should exist; it is generally agreed that pean laboratory for particle physics, tion of three quarks-could decay into the monopole should have an enor­ with the detection of the W+, W-and lighter particles such as a (a mous mass for an , ZO particles. type of lepton that can be thought of as perhaps from 10 16 to 10 17 times the The SU(5) a positively charged electron) and a mass of the proton. Although there seeks to bind the strong force and the particle called a . Given the exis­ have been scattered reports of find­ electroweak force into one common tence of two Higgs fields, the decay ing monopoles, none of the reports force; the designation SU(5) refers to rate can be computed. Experiments has been substantiated; nature seems the mathematical group of symmetries done in recent years have not, howev­ to dislike anything involving Higgs on which the theory is based. Accord­ er, found any such decay [see "The fields. The search for monopoles con­ ing to SU(5) theory, the strong, weak Search for ," by J. M. tinues [see "Superheavy Magnetic and electromagnetic forces, which be­ LoSecco, and Daniel Monopoles," by Richard A. Carrigan, have quite differently under ordinary Sinclair; SCIENTIFIC AMERICAN, June, Jr., and W. Peter Trower; SCIENTIFIC circumstances, become indistinguish­ 1985]. It would seem that there is AMERICAN, April, 1982]. able when particles interact with an something wrong with the SU(5) the­ A further smattering of evidence energy of approximately 10 15 billion ory or the Higgs field or both. I believe suggests that nature has been sparing electron volts (GeV). the main concepts of the SU(5) theory in its use of the Higgs fields-if they The unification of the strong force will survive over the long run. have been used at all. As it happens, in with the electroweak force requires the Moreover, if the SU(5) grand uni­ the electroweak theory the employ­ existence of an additional set of vector fied theory is correct and the Higgs ment of only the simplest type of bosons, whose masses are expected to field does exist, magnetic monopoles Higgs field to a relation between be several orders of magnitude great­ should have been created in the first the masses of the Wbosons and the ZO er than the masses of the weak vector 10 -35 second of the universe. An ex­ boson. The relation is expressed in bosons. Since the new vector bosons ample of a is an terms of a factor called the rho-param­ eter, which is essentially the ratio of the mass of the W bosons to the mass ELECTRON ELECTRON of the ZO boson. (There are correction factors that need not bother us here.) The expected value of the rho-parame­ ter is 1; experimentally it is found to be 1.0 3, with an estimated error of 5 per­ cent. If there is more than one Higgs field, the rho-parameter can take on virtually any value. Assuming that the agreement between theory and experi­ ment is not accidental, the implication is that only one Higgs field exists.

PROTON PROTON A t this point it becomes necessary I\. to question seriously whether the Higgs boson exists in nature. I men­ PHOTON PHOTON tioned above that the only legitimate reason for postulating the Higgs boson is to make the standard model mathe­ matically consistent. Historically the ELECTRON introduction of the Higgs boson to give such consistency had nothing to do with its introduction to account for ELECTRON ELECTRON ELECTRON ELECTRON mass. The introduction of the Higgs boson to account for mass came out of FEYNMAN DIAGRAMS are shorthand representations of a well-defined mathematical a "model building" line, in which the­ procedure for determining the probability that one particle will scatter off another. In ories were explicitly constructed to the top illustration an electron scatters off a proton by exchanging a photon, the carrier model nature as closely as possible. of the electromagnetic force. The particles can also scatter off each other by exchanging Workers in this line include Sidney A. two or more (not shown); such exchanges are statistically less likely, so that the Bludman of the University of Pennsyl­ one-photon exchange is a good approximation of reality. A photon can also scatter off an vania, who proposed the bulk of the electron. Two diagrams are necessary to approximate such an interaction (bottom). In this case it is hard to think of in terms of a force. Instead one must think in model containing Wbosons, and Shel­ terms of elementary processes: the photon can be absorbed or emitted by an electron. don Lee Glashow of Harvard Univer­ There is, however, no fundamental difference between electron-proton scattering and sity, who incorporated electromagnet­ electron·photon scattering; one can think of both types of event as elementary processes. ism into Bludman's model. Steven

80

© 1986 SCIENTIFIC AMERICAN, INC Weinberg of the University of Texas at W+ BOSON W+ BOSON Austin, using methods developed by Thomas W. B. Kibble of the Imperial � College of and in London, replaced the part of the mod­ el concerning particle masses with the for generating mass. The integration of quarks into the vec­ ELECTRON ELECTRON ELECTRON ELECTRON tor-boson theory was achieved by Ni­ cola Cabibbo and of the University of Rome, Y. Hara of the University of Tsukuba, Glashow W+ BOSON W+ BOSON and of the Ecole Nor­ male Superieure in Paris. W+ BOSON W+ BOSON All these papers were prod uced over a rather long period, from 1959 � ?- through 1970. In that same period many other suggested attempts at model building were also published, ELECTRON NEUTRINO but none of them, including the ones I have cited, drew any attention in the physics community. In fact, most of the authors did not believe their own work either, and they did not pursue ELECTRON ELECTRON the subject any further (with the ex­ WEAK , the carrier of the weak force, can scatter off an electron in a ception of Glashow and Iliopoulos). way somewhat analogous to the scattering of a photon off an electron (see bottom of The reason for the disbelief was obvi­ illustration on opposite page). The interaction at the top right, although mathematically ous: no one could compute anything. desirable, would require the existence of a doubly charged negative particle. No such The methods and mathematics known particle is known to exist. The problem is resolved by introducing a neutrally charged at the time led to nonsensical answers. particle, called the ZO boson (bottom right). The existence of the boson has been verified. There was no way to predict experi­ mental results. While I was considering the body of interactions." A noted exception was a theory is incomplete and the solutions available evidence in 1968, I decided Russian group, led by E. S. Fradkin of to certain problems are nonsense. that Yang-Mills theories (a general the University of Moscow, that made I must point out, however, that the class of theories of which the standard substantial contributions. electroweak theory can make power­ model is a specific example) were rele­ ful predictions even without the Higgs vant in understanding weak interac­ nterestingly enough, the model­ boson. The predictions concern the tions and that no progress could be I building line and the mathematical­ forces among elementary particles. made unless the mathematical diffi­ theory line proceeded simultaneously Those forces are investigated in high­ culties were resolved. I therefore start­ for many years with little overlap. I energy-physics laboratories by means ed to work on what I call the "mathe­ confess that up to 197 1 I knew nothing of scattering experiments. In such ex­ matical theory" line, in which little at­ about the introduction of the Higgs periments beams of high-energy parti­ tention is paid to the extent theory boson in the model-building line. For cles are directed at a "target" particle. corresponds to experimental observa­ that matter neither did 't Hooft. At one A beam of might, for in­ tions. One focuses instead on mathe­ point, in fact, I distinctly remember stance, be scattered off a proton. By matical content. In this line I was by no saying to him that I thought his work analyzing the scattering pattern of the means the first investigator. It was had something to do with the Gold­ incident particles, knowledge of the started by C. N. Yang and Robert stone theorem (a concept that came forces can be gleaned. L. Mills of the Brookhaven National out of the model-building line). Since The electroweak theory successful­ Laboratory. of the neither of us knew the theorem, we ly predicts the scattering pattern when California Institute of Technology, stared blankly at each other for a few electrons interact with protons. It also L. Faddeev of the University of Len­ minutes and then decided not to worry successfully predicts the interactions ingrad, Bryce S. DeWitt of the Univer­ about it. Once again progress arose of electrons with photons, with W sity of North Carolina and Stanley from "Don't know how," a phrase bosons and with particles called neu­ Mandelstam of the University of Cali­ coined by Weisskopf. trinos. The theory runs into trouble, fornia at Berkeley had already made Progress in the mathematical-theory however, when it tries to predict the in­ considerable inroads in this very diffi­ line would ultimately show that the teraction of W bosons with one anoth­ cult subject. electroweak theory becomes better­ er. In particular, the theory indicates I did not finish the work either. The behaved mathematically and has more that at sufficiently high the concluding publication was the 197 1 predictive power when the Higgs bos­ probability of scattering one W boson thesis of my former student Gerard 't on is incorporated into it. Specifically, off another W boson is greater than 1. Hooft, who was then at the Universi­ the Higgs boson makes the theory re­ Such a result is clearly nonsense. The ty of Utrecht. In that period few re­ normalizable: given a few parameters, statement is analogous to saying that searchers believed in the subject. More one can in principle calculate experi­ even if a dart thrower is aiming in the than once I was told politely or not so mentally observable quantities to any opposite direction from a target, he or politely that I was, in the words of Sid­ desired precision. A nonrenormaliz­ she will still score a bull's-eye. ney R. Coleman of Harvard Universi­ able theory, in contrast, has no predic­ It is here that the Higgs boson enters ty, "sweeping an odd corner of weak tive power beyond a certain limit: the as a savior. The Higgs boson couples

81

© 1986 SCIENTIFIC AMERICAN, INC In 1959, Kraft Foods became the first U.S. company to choose East Kilbride as an overseas location. Since then, the town has continued to attract more and more com pa n i es fro m the States. East Kilbride sits in the very heart of Scotlands Glen. Within a 50 mile radius there are over 200 companies forming not only a close-knit nucleus of suppliers, but a considerable market too. As well as being the ideal gateway to the expanding markets in the U.K., East Kilbride is also well positioned for companies wishing to exploit the vast European markets. Using East Kilbride as a tariff-free springboard, your company has another 600 million potential European customers. Our labour record is excellent, with 95% of facilities enjoying a strike-free period of five years. Because 80% of companies are union free, East Kilbrides position as a right to work town is further consolidated. The town has a proven track record in successfully catering for industrial investment and our range of financial incentives is among the best offered by any area in the U.K. If your company is considering an offshore project, contact Rick Packer on (617) 431 7474 at PRTM, 36 WashingtonStreet , Wellesley Hills, Massach usetts 02181. And join the other U.S. companies currently flying the flag in East Kilbride.

© 1986 SCIENTIFIC AMERICAN, INC Asa NewYork"R!lephone customeryou Advanced communications have our experience and technology need advanced support. to support you. We're leading the way to bring you the NewYorkli!lephone latest communications technology. But communications can only be as good offers you both. as the company that stands behind them. And no one else has the resources to keep your communications running as smoothly as New York Te lephone. Our service people have an average of 15 years experience each. They monitor the network 24 hours a day and use advanced com­ puter technology to respond instantly to your calls about service or billing. And our computer systems are among the world's largest. They enable us to process effi­ ciently the 21,000 service orders New Yorkers call in daily. This helps hold costs down for everyone. If you need advanced business communi­ cations, then you also need a company that can stand behind them. For innovative communications backed by the most experienced support team, call on New York Te lephone at 1800942-1212, ext. 25.

NeWYOrkWOrks on ��t �����::::::::::::::::::::::::::::::::::::�New York Telephone. @ NewYbrkTelephone ©NewYork Telephone 1986 A NYNEX Company

© 1986 SCIENTIFIC AMERICAN, INC with the W bosons in such a way that [see series 0/ illustrations beginning on volts (TeV). The necessary energies the probability of scattering falls with­ page 80 and ending below]. could be achieved at the proposed 20- in allowable bounds: a certain fixed TeY Superconducting Supercollider value between 0 and 1. In other words, Armed with the insight that the Higgs (ssc), which is currently under consid­ incorporating the Higgs boson in the I\.. boson is necessary to make the eration in the U.S. [see "The Super­ electroweak theory "subtracts off"the electroweak theory renormalizable, it conducting Supercollider," by J. Da­ bad behavior. A more thorough de­ is easy to see how the search for the vid Jackson, Maury Tigner and Stan­ scription of the way in which the Higgs elusive particle should proceed: weak ley Wojcicki; SCIENTIFIC AMERICAN, boson makes the electroweak theory vector bosons must be scattered off March]. If the pattern of the scattered renormalizable requires a special no­ one another at extremely high ener­ particles follows the predictions of the tation known as Feynman diagrams gies, at or above one trillion electron renormalized electroweak theory, then there must be a compensating force, for which the Higgs boson would be MUON NEUTRINO the obvious candidate. If the pattern does not follow the prediction, then the weak vector bosons would most likely be interacting through a strong force, and an entire new area of phys­ ics would be opened up. A difficultyin searching for the Higgs boson is that its mass is virtually unconstrained. As determined by ex­ periment, the mass must be greater than about 5 GeY. Theory presents no ELECTRON ELECTRON clue as to how heavy the Higgs boson could be, except· the particle would generate some of the same difficulties it has been designed to solve if its mass W· BOSON W· BOSON were 1 TeY, which is approximately 1,000 times the mass of the proton. At that point theory suggests the weak vector bosons could no longer be viewed as elementary particles; they could be composite structures made of smaller particles. The notion of a composite structure is, of course, nothing new in the . At the beginning of the ar­ ticle I mentioned five known layers W· BOSON of structure: , atoms, nuclei, W· BOSON W· BOSON (protons and neutrons) and quarks and leptons. In considering the Higgs boson as a composite structure it is only a small step to suppose such "fundamental" W· BOSON W· BOSON particles as quarks and leptons are W· BOSON really composite structures made from still smaller particles [see "The Struc­ ture of Quarks and Leptons," by Haim Harari; SCIENTIFIC AMERICAN, April, 198 3]. In a sense the notion of a sixth HIGGS BOSON layer of structure, one beyond quarks and leptons, brings me full circle. Tra­ ditionally the way to account for free parameters has been to go to a deeper layer of structure. The success of com­ W· BOSON posite models in predicting energy lev­ W· BOSON W· BOSON els of atoms and nuclei suggests that RENORMALIZED ELECTROWEAK THEORY requires the existence of the Higgs mass could also be predicted by going boson. A renormalized theory is one that, given a few parameters, can be applied to to a deeper layer of structure. The fact calculate experimentally observable quantities to any desired precision. A nonrenormal­ that in the standard model the Higgs izable theory, in contrast, has no predictive power beyond a certain limit: the theory is boson is responsible for all observed incomplete, and the solutions to certain problems are nonsense. Without the Higgs boson masses implies that, even if in the end the electroweak theory successfully accounts for the scattering of off electrons there is no such thing as a Higgs boson, (top). The theory runs into trouble, however, when it tries to predict the interaction of W there is at least a common source for bosons with one another (middle). Specifically, the theory indicates that. at energies above one trillion electron volts (TeV) the probability of scattering one W boson off all masses. Searching for the Higgs another W boson is greater than 1. Such a result is clearly nonsense. The theory is renor­ boson could ultimately be the same as malized by introducing the Higgs boson (bottom). Plausible predictions can be realized by searching for a deeper structure of ele­ effectively "subtracting" the set of illustrations at the bottom from the set in the middle. mentary particles.

84

© 1986 SCIENTIFIC AMERICAN, INC