CONSTRUCTING

QUARKS

A SOCIOLOGICAL HISTORY
OF PARTICLE
PHYSICS

CONTENTS

PREFACE

Etched into the history of twentieth-century physics are cycles of atomism. First came atomic physics, then nuclear physics and finally elementary-particle physics. Each was thought of as a journey deeper into the fine structure of matter. In the beginning was the nuclear atom. The early years of this century saw a growing conviction amongst scientists that the chemical elements were made up of atoms, each of which comprised a small, positively charged core or nucleus surrounded by a diffuse cloud of negatively charged particles known as electrons. Atomic physics was the study of the outer layer of the atom, the electron cloud. Nuclear physics concentrated in turn upon the nucleus, which was itself regarded as composite: the atomic nucleus of each chemical element was supposed to be made up of a fixed number of positively charged particles called protons plus a number of electrically neutral neutrons. Protons, neutrons and electrons were the original ‘elementary particles’ — the building blocks from which physicists considered that all forms of matter were constructed. However, in the post-World War ii period, many other particles were discovered which appeared to be just as elementary as the proton, neutron and electron, and a new specialty devoted to their study grew up within physics. The new specialty was known either as elementary-particle physics, after its subject matter, or as high-energy physics (hep), after its primary experimental tool — the high-energy particle accelerator.

Atomic physics, nuclear physics and even the early years of elementary-particle physics have all been subject to historical scrutiny, but the story of the latest cycle of atomism has yet to be told. Not content with regarding protons, neutrons and the like as truly elementary particles, in the 1960s and 1970s high-energy physicists became increasingly confident that they had plumbed a new stratum of matter: quarks. Gross matter was composed of atoms; within the atom was the nucleus; within the nucleus were protons and neutrons; and, finally, within protons and neutrons (and all sorts of other particles) were quarks. The aim of this book is to document and analyse this latest step into the heart of the material world.

The analysis given here is somewhat unconventional in that its thrust is sociological. Rather than treat the quark view of matter as  {ix}  an abstract conceptual system, I seek to analyse its construction, elaboration and use in the context of the developing practice of the hep community. My explanation of why the reality of quarks came to be accepted relates to the dynamics of that practice, a dynamics which is at once social and conceptual. I try to avoid the circular idiom of naive realism whereby the product of a historical process, in this case the perceived reality of quarks, is held to determine the process itself. The view taken here is that the reality of quarks was the upshot of particle physicists’ practice, and not the reverse: hence the title of the book, Constructing Quarks.

The sociology of science is often taken to relate purely to the social relations between scientists, and hence to exclude esoteric technical and conceptual matters. That is not the case here. There is no escape from such topics because the emphasis is on practice and, in hep, practice is irredeemably esoteric. This, of course, creates a communication problem: arcane practices are best described in arcane language, otherwise known as scientific jargon. To ameliorate the problem, I have sought to explain each item of hep jargon whenever it first enters the text. I have also cited popular accounts of the developments at issue, for the reader who feels he would benefit from more background on particular cases. In this way I have tried to make the text accessible to anyone with a basic scientific education. It is perhaps appropriate to add that the main object of my account is not to explain technical matters per se but to explain how knowledge is developed and transformed in the course of scientific practice. My belief is that the processes of transformation are easier to grasp than the full ramifications of, say, a given theoretical structure at a particular time. My hope is to give the reader some feeling for what scientists do and how science develops, not to equip him or her as a particle physicist.

There remain, nevertheless, sections of the account which may prove difficult for outsiders to physics. I have in mind here especially the passages in Part ii of the account which deal with the formal development of ‘gauge theory’. Gauge theory provided the theoretical framework within which quark physics was eventually set, and the development of gauge theory was intrinsic to the establishment of the quark picture. It would therefore be inappropriate to omit these passages from a historical account. However, the key idea which I use in analysing the development of theories is that of modelling or analogy and, unfortunately in the present context, gauge theory was modelled upon a highly complex, mathematically-sophisticated theory known as quantum electrodynamics (qed). Qed was taken for granted by physicists during the period we will be considering, and it  {x}  is beyond the scope of this work to go at all deeply into its origins. Thus, in discussing the formal development of gauge theory, I have to refer to accepted properties of qed (and quantum field theory in general) which I can only partially explain. This is the origin of the communication gap which remains in the text. On the positive side, I should stress that the more difficult phases of the narrative are non-cumulative in effect. For example, the uses to which particle physicists put gauge theory, discussed in Part in of the account, are much more easily understood than the prior process of theory development, discussed in Part II. The conceptual intricacies of the early discussions of field theory and gauge theory need not, therefore, deter the reader from reading on.

It remains for me to acknowledge some of my many debts: intellectual, material and financial. Taking the latter first, the research on which this book is based has been supported by grants from the uk Social Science Research Council. Without their support, it would have been impossible. The active co-operation of the hep community was likewise crucial, and I would like to thank the many physicists who found the time for interview and correspondence. In the following pages I argue that research is a social activity, and I am happy to apply the same argument to my own work. The account of particle physics offered here is intended as a contribution to the ‘relativist-constructivist’ programme in the sociology of scientific knowledge, and I owe a considerable debt to all of those working in this tradition. I am particularly grateful to Harry Collins, Trevor Pinch, Dave Travis and John Law. The Science Studies Unit of the University of Edinburgh has been my base for this work; it has supported me in many ways and I am indebted to everyone there, especially Mike Barfoot, Barry Barnes, David Edge, Bill Harvey, Malcolm Nicolson and Steve Shapin. Thanks also to Peter Higgs and the other members of the Edinburgh hep group for much information and many useful discussions. Moyra Forrest prepared the Index, and her assistance with library materials has also been invaluable. The typing of Carole Tansley, Margaret Merchant and, especially, Jane Flaxington has been heroic. To Jane F. likewise my thanks for life-support while this book was being written.

PART I

INTRODUCTION,

THE PREHISTORY OF hep AND

ITS MATERIAL CONSTRAINTS

1
INTRODUCTION

The scientist. . . must appear to the systematic epistemologist as an unscrupulous opportunist.

Albert Einstein¹

The historian of modern science has to come to terms with the fact that the scientists have got there first. Very many accounts of the topics to be examined here have already been presented by particle physicists in the popular scientific press, as well as in the professional literature of high-energy physics (hep).² These accounts all have a similar form — they are contributions to a well-established genre of scientific writing — and present a vision of science which is in some ways the mirror image — or reverse — of that developed in the following pages. I want therefore to begin by sketching out the archetypal ‘scientist's account’ of the history of hep, in order both to indicate its shortcomings and to introduce the motivations behind my own approach.³ This sketch will involve the use of some technical terms which will only be explained in later chapters, but the detailed meanings of the terms are not important in the present context.

The scientist's account begins in the early 1960s. At that time, particle physicists recognised four fundamental forces of nature, known, in order of decreasing strength, as the strong, electromagnetic, weak and gravitational interactions. The strong force, responsible for the binding of neutrons and protons in nuclei, was of short range and was the dominant force in elementary-particle interactions. The electromagnetic force, around 10³ (i.e. 1000) times weaker than the strong force and acting at long range, was responsible for binding nuclei and electrons together in atoms, and also for macroscopic electromagnetic phenomena: light, radio waves and so on. The weak force, of short range and around 10⁵ (100,000) times weaker than the strong force, had, except in special circumstances, negligible effects. Those special circumstances pertained to certain radioactive decays of nuclei and elementary particles, and to processes of energy generation in stars. Finally the gravitational force was a long-range force like electromagnetism. It was responsible for macroscopic gravitational phenomena — apples falling from trees, the earth orbiting the sun — but it was also 10³⁸ times weaker than the  {3}  strong force, and its effects were considered to be completely negligible in the world of elementary particles.

Associated with this classification of forces was a classification of elementary particles. Particles which experienced the strong force were called hadrons. There were many hadrons, including the proton and neutron, the constituents of atomic nuclei. Particles which were immune to the strong force — the electron and a handful of other particles — were known as leptons. The picture began to change in 1964, with the proposal that the constituents had constituents: hadrons were to be seen as made up of more fundamental entities known as quarks. Although it left many questions unanswered, the quark model explained certain experimentally-observed regularities of the hadron mass spectrum and of hadronic decay processes. Moreover, in the late 1960s and early 1970s it was seen that quarks could explain the phenomenon known as scaling, which had recently been discovered in experiments on the interaction of leptons with hadrons. In the scientist's account quarks thus represented the fundamental entities of a new layer of matter. Initially, though, the existence of quarks was not regarded as firmly established, principally because experimental searches had failed to detect any particles having the distinctive properties postulated for them (i.e. their having fractional electric charges). Leptons were not subject to a parallel ontological transformation; unlike hadrons they continued to be regarded as truly elementary particles.

Early in the 1970s, new theories of the interactions of quarks and leptons began to be formulated. First came the realisation that the weak and electromagnetic interactions could be seen as manifestations of a single electroweak force within the context of a theoretical approach known as gauge theory. This unification, reminiscent of Maxwell's nineteenth-century unification of electricity and magnetism, carried with it the prediction of the existence of the weak neutral current, which was verified in 1973, and of charmed particles, which was verified in 1974. Meanwhile, it had been realised in 1973 that a particular gauge theory, known as quantum chromodynamics or qcd, was a possible theory of the strong interactions of quarks. It was found first to explain scaling, and later to explain observed deviations from scaling. It explained certain interesting properties of charmed and other particles, and various other hadronic phenomena. Therefore qcd became the accepted theory of the strong interactions. Quarks had still not been observed in isolation. But both electroweak theory and qcd assumed the validity of the quark picture, and thus the existence of quarks was established simultaneously with the establishment of the gauge-theory description of their interactions. In  {4}  the late 1970s, particle physicists were agreed that the world of elementary particles was one of quarks and leptons interacting according to the dictates of the twin gauge theories: electroweak theory and qcd. Finally it was noticed that since the unified electroweak theory and qcd were both gauge theories, they could, in their turn, be unified with one another. This last unification brought with it more fascinating predictions, which began to arouse the interests of experimenters in 1979. These predictions were not immediately verified, but many physicists were confident that they would be. Thus, not only was a new and fundamental layer of structure discovered, in the shape of quarks, but three forces previously thought to be quite different from one another — the strong, electromagnetic and weak interactions — stood revealed as but particular manifestations of a single force.

Apart from brevity, this sketch of the scientist's account of the history of quarks has the virtue that it names key developments. For example, it indicates that the quark idea was only one theoretical component in the developments we will discuss. The other component was gauge theory, which eventually provided the framework within which the interactions of quarks and leptons were understood. This is something to keep firmly in mind: it is impossible to understand the establishment of the quark picture without at the same time understanding the perceived virtues of gauge theory. The scientist's account also points to the role of new phenomena — scaling, neutral currents, charmed particles and the like — in supporting the quark-gauge theory view. The observation that the quark-gauge theory picture referred to new phenomena, quite different from those which supported the pre-quark view of the world, will also figure prominently in the following account. However, beyond specifying the key developments in hep, the scientist's account goes on, either explicitly or implicitly, to specify a relationship between them. I want now to discuss this relationship, in order to highlight where the present approach departs from that of the scientist.

In the scientist's account, experiment is seen as the supreme arbiter of theory. Experimental facts dictate which theories are to be accepted and which rejected. Experimental data on scaling, neutral currents and charmed particles, for example, dictated that the quark-gauge theory picture was to be preferred over alternative descriptions of the world. There are, though, two well-known and forceful philosophical objections to this view, each of which implies that experiment cannot oblige scientists to make a particular choice of theories.⁴ First, even if one were to accept that experiment produces unequivocal fact, it would remain the case that choice of a theory is  {5}  underdetermined by any finite set of data. It is always possible to invent an unlimited set of theories, each one capable of explaining a given set of facts. Of course, many of these theories may seem implausible, but to speak of plausibility is to point to a role for scientific judgment: the relative plausibility of competing theories cannot be seen as residing in data which are equally well explained by all of them. Such judgments are intrinsic to theory choice, and clearly entail something more than a straightforward comparison of predictions with data. Furthermore, whilst one could in principle imagine that a given theory might be in perfect agreement with all of the relevant facts, historically this seems never to be the case. There are always misfits between theoretical predictions and contemporary experimental data. Again judgments are inevitable: which theories merit elaboration in the face of apparent empirical falsification, and which do not?

The second objection to the scientist's version is that the idea that experiment produces unequivocal fact is deeply problematic. At the heart of the scientist's version is the image of experimental apparatus as a ‘closed’, perfectly well understood system. Just because the apparatus is closed in this sense, whatever data it produces must command universal assent; if everyone agrees upon how an experiment works and that it has been competently performed, there is no way in which its findings can be disputed. However, it appears that this is not an adequate image of actual experiments. They are better regarded as being performed upon ‘open’, imperfectly understood systems, and therefore experimental reports are fallible. This fallibility arises in two ways. First, scientists’ understanding of any experiment is dependent upon theories of how the apparatus performs, and if these theories change then so will the data produced. More far reaching than this, though, is the observation that experimental reports necessarily rest upon incomplete foundations. To give a relevant example, one can note that much of the effort which goes into the performance and interpretation of hep experiments is devoted to minimising ‘background’ — physical processes which are uninteresting in themselves, but which can mimic the phenomenon under investigation. Experimenters do their best, of course, to eliminate all possible sources of background, but it is a commonplace of experimental science that this process has to stop somewhere if results are ever to be presented. Again a judgment is required, that enough has been done by the experimenters to make it probable that background effects cannot explain the reported signal, and such judgments can always, in principle, be called into question. The determined critic can always concoct some possible, if improbable,  {6}  source of error which has not been ruled out by the experimenters.⁵

Missing from the scientist's account, then, is any apparent reference to the judgments entailed in the production of scientific knowledge -judgments relating to the acceptability of experimental data as facts about natural phenomena, and judgments relating to the plausibility of theories. But this lack is only apparent. The scientist's account avoids any explicit reference to judgments by retrospectively adjudicating upon their validity. By this I mean the following. Theoretical entities like quarks, and conceptualisations of natural phenomena like the weak neutral current, are in the first instance theoretical constructs: they appear as terms in theories elaborated by scientists. However, scientists typically make the realist identification of these constructs with the contents of nature, and then use this identification retrospectively to legitimate and make unproblematic existing scientific judgments. Thus, for example, the experiments which discovered the weak neutral current are now represented in the scientist's account as closed systems just because the neutral current is seen to be real. Conversely, other observation reports which were once taken to imply the non-existence of the neutral current are now represented as being erroneous: clearly, if one accepts the reality of the neutral current, this must be the case. Similarly, by interpreting quarks and so on as real entities, the choice of quark models and gauge theories is made to seem unproblematic: if quarks really are the fundamental building blocks of the world, why should anyone want to explore alternative theories?

Most scientists think of it as their purpose to explore the underlying structure of material reality, and it therefore seems quite reasonable for them to view their history in this way.⁶ But from the perspective of the historian the realist idiom is considerably less attractive. Its most serious shortcoming is that it is retrospective. One can only appeal to the reality of theoretical constructs to legitimate scientific judgments when one has already decided which constructs are real. And consensus over the reality of particular constructs is the outcome of a historical process. Thus, if one is interested in the nature of the process itself rather than in simply its conclusion, recourse to the reality of natural phenomena and theoretical entities is self-defeating.

How is one to escape from retrospection in analysing the history of science? To answer this question, it is useful to reformulate the objection to the scientist's account in terms of the location of agency in science. In the scientist's account, scientists do not appear as genuine agents. Scientists are represented rather as passive observers  {7}  of nature: the facts of natural reality are revealed through experiment; the experimenter's duty is simply to report what he sees; the theorist accepts such reports and supplies apparently unproblematic explanations of them. One gets little feeling that scientists actually do anything in their day-to-day practice. Inasmuch as agency appears anywhere in the scientist's account it is ascribed to natural phenomena which, by manifesting themselves through the medium of experiment, somehow direct the evolution of science. Seen in this light, there is something odd about the scientist's account. The attribution of agency to inanimate matter rather than to human actors is not a routinely acceptable notion. In this book, the view will be that agency belongs to actors not phenomena: scientists make their own history, they are not the passive mouthpieces of nature. This perspective has two advantages for the historian. First, while it may be the scientist's job to discover the structure of nature, it is certainly not the historian's. The historian deals in texts, which give him access not to natural reality but to the actions of scientists — scientific practice.⁷ The historian's methods are appropriate to the exploration of what scientists were doing at a given time, but will never lead him to a quark or a neutral current. And, by paying attention to texts as indicators of contemporary scientific practice, the historian can escape from the retrospective idiom of the scientist. He can, in this way, attempt to understand the process of scientific development, and the judgments entailed in it, in contemporary rather than retrospective terms — but only, of course, if he distances himself from the realist identification of theoretical constructs with the contents of nature.⁸

This is where the mirror symmetry arises between the scientist's account and that offered here. The scientist legitimates scientific judgments by reference to the state of nature; I attempt to understand them by reference to the cultural context in which they are made. I put scientific practice, which is accessible to the historian's methods, at the centre of my account, rather than the putative but inaccessible reality of theoretical constructs. My goal is to interpret the historical development of particle physics, including the pattern of scientific judgments entailed in it, in terms of the dynamics of research practice. To explain how I seek to accomplish this, I will sketch out here some of the salient features of the development of hep, and describe the framework I adopt for their analysis.⁹

The establishment of the quark-gauge theory view of elementary particles did not take place in a single leap. As we shall see, it was a product of the founding and growth of a whole constellation of experimental and theoretical research traditions structured around  {8}  the exploration and explanation of a circumscribed range of natural phenomena. Traditions within this constellation drew upon different aspects of the quark-gauge theory picture of elementary particles, and, as they grew during the late 1960s and 1970s, they eventually displaced traditions which drew upon alternative images of physical reality. Seen from this perspective, the problem of understanding the establishment of quarks and gauge theory in the practice of the hep community is equivalent to that of understanding the dynamics of research traditions. To see what is involved here, consider an idealised discovery process.

Suppose that a group of experimenters sets out to investigate some facet of a phenomenon whose existence is taken by the scientific community to be well established. Suppose, further, that when the experimenters analyse their data they find that their results do not conform to prior expectations. They are then faced with one of the problems of scientific judgment noted above, that of the potential fallibility of all experiments. Have they discovered something new about the world or is something amiss with their performance or interpretation of the experiment? From an examination of the details of the experiment alone, it is impossible to answer this question. However thorough the experimenters have been, the possibility of undetected error remains.¹⁰ Now suppose that a theorist enters the scene. He declares that the experimenters’ findings are not unexpected to him — they are the manifestation of some novel phenomenon which has a central position in his latest theory. This creates a new set of options for research practice. First, by identifying the unexpected findings with an attribute of nature rather than with the possible inadequacy of a particular experiment, it points the way forward for further experimental investigation. And secondly, since the new phenomenon is conceptualised within a theoretical framework, the field is open for theorists to elaborate further the original proposal.

One can imagine a variety of sequels to this episode, but it is sufficient to outline two extreme cases. Suppose that a second generation of experiments is performed, aimed at further exploration of the new phenomenon, and that they find no trace of it. In this case, one would expect that suspicion will again fall upon the performance of the so-called discovery experiment, and that the theorist's conjectures will once more be seen as pure theory with little or no empirical support. Conversely, suppose that the second-generation experiments do find traces which conform in some degree with expectations deriving from the new theory. In this case, one would expect scientific realism to begin to take over. The new phenomenon  {9}  would be seen as a real attribute of nature, the original experiment would be regarded as a genuine discovery, and the initial theoretical conjecture would be seen as a genuine basis for the explanation of what had been observed. Furthermore, one would expect further generations of experimentation and theorising to take place, elaborating the founding experimental and theoretical achievements into what I am calling research traditions.

This image of the founding and growth of research traditions is very schematic. It typifies, nevertheless, many of the historical developments which we will be examining, and I will therefore discuss it in some detail. In particular, I want to enquire into the conditions of growth of such traditions. I have so far spoken as though traditions are self-moving; as though succeeding generations of research come into being of their own volition. Clearly this image is inadequate as it stands: research traditions prosper only to the extent that scientists decide to work within them. What is lacking is a framework for understanding the dynamics of practice, the structuring of such decisions. I want, therefore, to present a simple model of this dynamics which will inform my historical account. The model can be encapsulated in the slogan ‘opportunism in context’.

To explain what context entails, let me continue with the example of two research traditions, one experimental the other theoretical, devoted to the exploration and explanation of some natural phenomenon. It is, I think, clear that each generation of practice within one tradition provides a context wherein the succeeding generation of practice in the other can find both its justification and subject matter. Consider the theoretical tradition: to justify his choice to work within it, a theorist has only to cite the existence of a body of experimental data in need of explanation. And fresh data, from succeeding generations of experiment, constitute the subject matter for further elaborations of theory. Conversely, for the experimenter, his decision to investigate the phenomenon in question rather than some other process is justified by its theoretical interest, as manifested by the existence of the theoretical tradition. And each generation of theorising serves to mark out fresh problem areas to be investigated by the next generation of experiment. Thus, through their reference to the same natural phenomenon, theoretical and experimental traditions constitute mutually reinforcing contexts. Without in any way committing oneself to the reality of the phenomenon, then, one can observe that through the medium of the phenomenon the two traditions maintain a symbiotic relationship.

This idea of the symbiosis of research practice, wherein the practice of each group of physicists constitutes both justification and subject  {10}  matter for that of the others, will be central to my analysis of the history of hep. I have explained it for the simple case of experimental and theoretical traditions structured around a particular phenomenon, because this is the archetype of many of the developments to be discussed. But it will also underlie my treatment of more complex situations — where, for example, many traditions interact with one another, or when the traditions at issue are purely theoretical ones. In itself, though, reference to context is insufficient to explain the cultural dynamics of research traditions. The question remains of why particular scientists contribute to particular traditions in particular ways. Here I find it very useful to refer to ‘opportunism’. The point is this. Each scientist has at his disposal a distinctive set of resources for constructive research. These may be material — the experimenter, say, may have access to a particular piece of apparatus — or they may be intangible — expertise in particular branches of experiment or theory acquired in the course of a professional career, for example.¹¹ The key to my analysis of the dynamics of research traditions will lie in the observation that these resources may be well or ill matched to particular contexts. Research strategies, therefore, are structured in terms of the relative opportunities presented by different contexts for the constructive exploitation of the resources available to individual scientists.

Opportunism in context is the theme which runs through my historical account. I seek to explain the dynamics of practice in terms of the contexts within which researchers find themselves, and the resources which they have available for the exploitation of those contexts. It is, of course, impossible to discuss the entire practice of the hep community at the micro-level of the individual, and when discussing routine developments within already established traditions I confine myself to an aggregated, macro-level analysis in terms of shared resources and contexts. As far as experimental traditions are concerned this creates no special problems. Resources for hep experiment are limited by virtue of their expense; major items of equipment are located at a few centralised laboratories. Those facilities constitute the shared resources of hep experimenters. The interest of theorists in particular phenomena likewise constitutes a shared context. If the facilities available are adequate to the investigation of questions of theoretical interest, one can readily understand that an experimental programme devoted to that phenomenon should flourish. Similarly, the data generated within experimental traditions constitute a shared context for theorists. But a problem arises when one comes to discuss the nature of shared theoretical resources: what is the theoretical equivalent of shared  {11}  experimental facilities? One might look here to the shared material resources of theorists — the computing facilities, for example, which have played an increasingly significant role in the history of modern theoretical (as well as experimental) physics. But this would be insufficient to explain why quarks and gauge theory triumphed at the expense of other theoretical orientations within hep. Instead I focus primarily upon the intangible resource of theoretical expertise. To explain how I use this concept let me briefly preview the main features of theory development which emerge from the historical account.

The most striking feature of the conceptual development of hep is that it proceeded through a process of modelling or analogy.¹² Two key analogies were crucial to the establishment of the quark-gauge theory picture. As far as quarks themselves were concerned, the trick was for theorists to learn to see hadrons as quark composites, just as they had already learned to see nuclei as composites of neutrons and protons, and to see atoms as composites of nuclei and electrons. As far as the gauge theories of quark and lepton interactions were concerned, these were explicitly modelled upon the already established theory of electromagnetic interactions known as quantum electrodynamics. The point to note here is that the analysis of composite systems was, and is, part of the training and research experience of all theoretical physicists. Similarly, in the period we will be considering, the methods and techniques of quantum electrodynamics were part of the common theoretical culture of hep. Thus expertise in the analysis of composite systems and, albeit to a lesser extent, quantum electrodynamics constituted a set of shared resources for particle physicists. And, as we shall see, the establishment of the quark and gauge-theory traditions of theoretical research depended crucially upon the analogical recycling of those resources into the analysis of various experimentally accessible phenomena.

In discussing the development of established traditions, then, my primary explanatory variables are the shared material resources of experimenters and the shared expertise of theorists. However, there remains the problem of accounting for the founding of new traditions and the first steps towards the establishment of new phenomena. Such episodes are not to be understood in terms of the gross distribution of shared material resources or expertise, but they pose no special problems because of that. I will try to show that these episodes are just as comprehensible as routine developments within established traditions, and are similarly to be understood. The only difference between my accounts of the development of traditions and of their founding is that to discuss the latter I move, perforce, from the macro-level of the group to the micro-level of the individual. I aim  {12}  to show that the founding of new traditions can be understood in terms of the particular resources and context of the individuals concerned, just as the elaboration of those traditions can be understood in terms of the shared resources and contexts of the groups involved.¹³

Having outlined the opportunism-in-context model, we can now return to the problem posed earlier of how scientific judgments pertaining to experimental fallibility and theoretical underdetermination can be related to the dynamics of practice. Consider first the fallibility of experiment. Whilst it is possible to argue that all experiments are in principle fallible, experimenters do not enter this as an explicit caveat when reporting their findings: they simply report that, say, a particular quantity has been measured to have a particular value (often within a stated margin of uncertainty). It is then up to their colleagues to decide whether or not to challenge them, and such decisions are related to decisions over future practice. If the theorist can find the resources for a constructive analysis of the data, one should not expect him to spend long periods of time in searching for ways to challenge the experiment. If the data, through the medium of theory, raise new problems for experiment to investigate, then neither will experimenters be disposed to probe deeply. In this way, the potential fallibility of experiments is rendered manageable.¹⁴ A parallel solution is available to the problem of the underdetermination of theory. While a multiplicity of different theoretical explanations may be conceivable for any set of data, not all of these will be attractive in terms of the dynamics of practice. Theorists may possess the appropriate expertise to articulate one or more in a constructive fashion, raising, say, new questions which experimenters can tackle; other theoretical proposals may be divorced from any significant pool of theoretical expertise and effectively meaningless; and yet others will lead to questions which experimenters cannot investigate with available techniques, and therefore fail to sustain a symbiosis between theory and experiment. A choice which is impossible to make on purely empirical grounds can thus be straightforward when construed in terms of the dynamics of practice.

The outline of the explanatory framework to be adopted here is now complete. The scientific judgments, which in the scientist's account are retrospectively legitimated by reference to the reality of theoretical entities and phenomena, will here be related to the dynamics of contemporary practice. That dynamics will be analysed as a manifestation of opportunism in context.¹⁵ However, before closing this discussion, I want to draw attention to an important  {13}  point which has been so far left implicit. I have stressed that the fallibility of experiment is rendered manageable through the symbiosis of experimental and theoretical research traditions, and this has a rather striking consequence. To say that all experiments are ‘open’ and fallible is to note that no experimental technique (or procedure or mode of interpretation) is ever completely unproblem-atic. Part of the assessment of any experimental technique is thus an assessment of whether it ‘works’ — of whether it contributes to the production of data which are significant within the framework of contemporary practice. And this implies the possibility, even the inevitability, of the ‘tuning’ of experimental techniques — their pragmatic adjustment and development according to their success in displaying phenomena of interest. If one takes a realist view of natural phenomena, then such tuning is both unproblematic and uninteresting, being simply a necessary skill of the experimenter, and the scientist's account correspondingly fails to pay any attention to it. But if one abstains from realism, tuning becomes much more interesting. Natural phenomena are then seen to serve a dual purpose. As theoretical constructs they serve to mediate the symbiosis of theoretical and experimental practice (and hence to make realist discourse retrospectively possible); and, at the same time, they sustain and legitimate the particular experimental practices inherent in their own production. To suspend my earlier strictures against the imputation of agency to inanimate objects for the sake of a symmetric formulation, one can speak of a symbiosis between natural phenomena and the techniques entailed in their production, wherein each confers legitimacy upon the other. Such a symbiosis is a far cry from the antagonistic idea of experiment as an independent and absolute arbiter of theory, and does, I think, call for more attention than it has so far received from historians and philosophers of science. Perhaps the best way to explore it is through detailed case-studies of individual experiments. Space permits the inclusion of only one such study here: the set-piece analysis of the discovery of the weak neutral current, in Section 6.5. But throughout the book I point to instances of technical tuning in less detailed analyses of individual experiments, and in the closing chapter I return to a discussion of its implications.¹⁶

To round off these introductory remarks, let me briefly review the major historical developments discussed in the following chapters. The story to be told is of the founding and growth of research traditions structured around the quark concept. The account accordingly focuses upon the period from 1964, when quarks were first  {14}  invented, to 1980, when quark-physics traditions had come to dominate research practice in hep.¹⁷ Within that period it is useful to distinguish between two constellations of symbiotic research traditions which I will refer to as the ‘old physics’ and the ‘new physics’. The old physics dominated practice in hep throughout the 1960s and was distinguished by a ‘common-sense’ approach to the subject matter of the field. By this I mean that experimenters concentrated their efforts upon the phenomena most commonly encountered in the laboratory, and theorists sought to explain the data so produced. Amongst the theories developed in this period were early formulations of the quark model, as well as theories related to the so-called ‘bootstrap’ conjecture which explicitly disavowed the existence of quarks. The old physics thus consisted of traditions of common-sense experiment, devoted to the investigation of the most conspicuous laboratory phenomena, which sustained and were sustained by both quark and non-quark traditions of theorising. It should be noted that gauge theory did not figure in any of the dominant theoretical traditions of the old physics. By the end of the 1970s the old physics had been almost entirely displaced by the new. Experimentally, the new physics was ‘theory-oriented’: experimenters had come to eschew the common-sense approach of investigating the most conspicuous phenomena, and research traditions focused instead upon certain very rare processes. Theoretically, the new physics was the physics of quarks and gauge theory. Once more, theoretical and experimental research traditions reinforced one another, since the rare phenomena on which experimenters focused their attention were just those for which gauge theorists could offer a constructive explanation.

Thus there were elements of continuity between the old and new physics: the quark concept, for example, was carried over from one to the other. But there were also discontinuities. The non-quark, bootstrap approach to theorising largely disappeared from sight, and the quark concept became embedded in the wider framework of gauge theory. And, more strikingly, experimental practice in hep was almost entirely restructured in order to explore the rare phenomena which were at the heart of the new physics. Thus the transformation between the old and new physics and the consequent establishment of the quark-gauge theory world-view involved much more besides conceptual innovation. It was intrinsic to the transformation that the particle physicists’ way oft interrogating the world through their experimental practice was transformed too. This is one of the most fascinating features of the history of hep and I will try to explain how and why it came about. One wonders whether other great conceptual  {15}  developments in the history of science — the establishment of quantum mechanics, for example — were associated with similar shifts in experimental practice. Unfortunately, much historical writing tends to reflect the scientist's retrospective realism, regarding experiment as unproblematic and therefore uninteresting, and it is hard to answer such questions at present.

The historical account, then, focuses upon the origins of the quark concept in the old physics and upon the establishment of the new physics of quarks and gauge theory, paying particular attention to the transformation between the old and the new. The structure of the narrative reflects these preoccupations. Part i, comprising this and the two following chapters, aims to delineate the context within which the history of quark physics was enacted. Chapter 2 gives some statistics on the size and composition of the hep community, discusses the general features of hep experiment, and outlines the post–1945 development of experimental facilities in hep. Chapter 3 sketches out the growth of the major traditions of hep theory and experiment between 1945 and 1964, the year in which quarks were invented. It thus sets the scene for the intervention of quarks into the old physics.

Part ii begins the story proper. It covers the period from 1964 to 1974, ten years which saw the old quark physics established and the embryonic new-physics traditions founded. Chapter 4 discusses the two earliest formulations of the quark model and the relationships of these with common-sense traditions of experiment. Chapter 5 discusses the founding of the first new-physics traditions: the experimental discovery in 1967 of a new phenomenon — scaling — and its explanation in terms of a third variant on the quark theme, the quark-parton model. Chapter 6 reviews the first impact of gauge theory upon the experimental scene. This came with the 1973 discovery of another new phenomenon, the weak neutral current, the existence of which had been predicted on the basis of unified electroweak gauge theory. Chapter 7 covers the development of a gauge theory of the strong interactions. This was quantum chromo-dynamics, which promised to underwrite the quark-parton model, and hence to make contact with experimental work on scaling phenomena. Chapter 8 concludes Part ii and has three objectives. First, it summarises the conceptual bases of electroweak gauge theory and qcd in preparation for Part in. Secondly, it provides an overview of the topics of active hep research interest in 1974, emphasising that gauge theory had had relatively little impact at this stage: the old physics — of both quark and non-quark varieties — still dominated experimental and theoretical hep. Thirdly, Chapter 8 discusses three  {16}  transitional biographies, seeking to analyse why theorists who grew up (professionally) in the old-physics era should have appeared at the forefront of the developments of Part iii.

Part in of the account deals with the establishment of the quark-gauge theory world-view in the period from 1974 to 1980. Its subject is the growth and diversification of the experimental and theoretical traditions of the new physics. Chapter 9 discusses a crucial episode in the history of the new physics: the discovery of the ‘new particles’ and their theoretical explanation in terms of ‘charm’. The discovery of the first of the new particles was announced in November 1974 and by mid-1976 the charm explanation had become generally accepted. This was ‘the lever that turned the world’ in terms of the transformation between the old and the new physics. Theoretically, the existence of quarks came to be regarded as unproblematically established (despite the continuing failure of experimenters to observe isolated quarks in the laboratory), a specific electroweak gauge theory was singled out for intensive investigation, and qcd was brought most forcibly to the attention of particle physicists. On the experimental plane, charmed particles became a prime target for investigation, and the new interest in gauge theory provided a context in which all of the traditions of new-physics experiment could flourish, eventually to the exclusion of all else. Chapter 10 reviews developments concerning electroweak theory in the latter half of the 1970s. More new particles were discovered, pointing to an expanded ontology of quarks and leptons; detailed experimentation on the weak neutral current culminated in consensus in favour of ‘the standard model’ — the simplest and prototypical electroweak theory. Chapter 11 reviews the theoretical development of qcd in symbiosis with a range of experimental traditions. Chapter 12 then examines the growth of the new physics from the perspective of experimental practice. It aims to show that by the late 1970s the phenomenal world of the new physics had been built into both the present and future of experimental hep; the world was, in effect, defined by experimenters to be one of quarks and leptons interacting as gauge theorists said they should. Quantitative data on the new-physics takeover of experimental programmes are presented. The transformation of experimental hardware in this takeover is discussed. And the predication of planning for future major facilities on the new-physics world-view is documented.

By the end of the 1970s, the new physics had established a stranglehold upon hep. Gauge theories of quarks and leptons dominated contemporary practice; the same theories constituted particle physicists’ visions of the future and, via the realist assumption,  {17}  their understanding of the past. In this sense, the story is complete with Chapter 12. But gauge theorists did not rest content with electroweak theory and qcd, and one further substantial chapter is included. Chapter 13 discusses the synthesis of electroweak theory with qcd in the so-called Grand Unified Theories or guts, and outlines the implications for experiment drawn from guts in the late 1970s. Here we shall see gauge theory permeating the cosmos in a symbiosis between hep theorists, cosmologists and astrophysicists, and we shall see experimenters disappearing down deep mines in search of unstable protons. Finally, Chapter 14 summarises the overall form of the narrative, and suggests that the history of hep should be seen as one of the social production of a culturally specific world.

NOTES AND REFERENCES

2
MEN AND MACHINES

This chapter sets the scene for the historical drama to follow. Section 1 discusses the demography of the hep community. Section 2 reviews the basic hardware of hep experiment and the distinctively different patterns of its use in the old and the new physics. Section 3 outlines the chronology of accelerator construction, relating this to the fluctuating fortunes of old and new physics traditions of experimental research.

2.1 The hep Community

Hep has always been Big Science. In comparison with many other branches of pure research its expense is enormous. In 1980, for example, the annual expenditure of cern, the major European hep laboratory, was nearly 600 million Swiss Francs, and governmental support for hep in the United States ran to $343 million.¹ This is a field in which only the rich can compete. The history of experimental hep has accordingly been dominated by the United States and Europe. Outside those areas, the only significant experimental programme has been that of the Soviet Union, which has, in general, lagged behind that of the West.² The story to be told here is thus largely one of developments on either side of the North Atlantic.³

Hep emerged as a recognisable scientific specialty shortly after the end of World War ii and, with Europe devastated, the usa quickly took the lead. However, the Europeans made determined attempts to overhaul the Americans, and by the early 1960s had achieved rough comparability in manpower. In 1962, for example, there were estimated to be 685 practising elementary-particle physicists in Europe and 850 in the usa.⁴ These research communities grew continuously during the 1960s before stabilising in the early 1970s as governments began to resist the physicists’ ever-increasing requests for funds.⁵ By this stage, Europe had achieved pre-eminence in manpower and in the late 1970s the 3,000 European particle physicists easily outnumbered their 1,650 American colleagues.⁶

Throughout this book, then, we will be dealing with a cast of thousands, concentrated in the economically advanced countries but with representatives sprinkled all over the world. This cast, predominantly  {21}  white and almost entirely male, can be subdivided in various ways. One important distinction is that between theorists and experimenters. Theory and experiment constitute distinct professional roles within hep. Each form of practice is highly technical, drawing upon quite different forms of expertise, and it is rare to find an individual who successfully engages in both.⁷ During the 1970s, there were around two experimenters for every theorist.⁸ A second axis of division relates to the subject matter of hep research. As mentioned in the preceding chapter, particle physicists recognise four fundamental forces of nature: the strong, electromagnetic, weak and gravitational interactions. Amongst these, the electromagnetic interaction has been regarded as well-understood since the 1950s, while the gravitational force is too weak to have a measurable effect upon elementary-particle phenomena. Hep research has therefore primarily aimed at investigation of the strong and weak interactions, and studies of these forces have constituted two relatively distinct fields of practice: different experimental and theoretical strategies were considered appropriate to each. This was especially true in the era of the old physics, when a sizeable majority of particle physicists concentrated their energies upon the strong rather than the weak interactions.⁹ In the context of the new physics the distinctions in practice between research into the strong and weak interactions remained significant but became blurred. Theoretically, a unified framework for the strong, weak and electromagnetic interactions was developed; and many new physics experiments produced data relevant to theoretical models of both the strong and weak interactions.

Finally, a comment upon the institutional locus of hep research is needed. Particle physics is a pure science, with no evident practical application for the knowledge it produces. Its institutional base lies, as one would expect, in the universities, and this is where most theorists live and work. However, the expense entailed in building and running experimental facilities has increased continuously during the history of hep, and there has been a corresponding tendency to divorce these resources from individual universities in favour of regional, national and international laboratories. Teams of experimenters, usually drawn from several universities, assemble at such laboratories to perform specific experiments, often dispersing again to their home institutions to analyse their data.¹⁰ The laboratories typically also have their own permanent staff of researchers comprising both an experimental group and a theory group.¹¹ What goes on within the laboratories is the subject of the next section.

2.2 hep Experiment: Basics

Although technologically extremely complex and sophisticated, experiments in hep are in principle rather simple. As indicated in Figure 2.1, one takes a beam of particles and fires it at a target. Interactions take place within the target — some of the beam particles are deflected or ‘scattered’; often additional particles are produced — and the particles that emerge are registered in detectors of various kinds.

Figure 2.1. Layout of an hep experiment.

Hardware

Beam, target and detectors are the three important components in an hep experiment, and we can discuss them in turn. Historically, a variety of methods have been used for producing particle beams, but in the post-war era the workhorse of hep has been the synchrotron.¹² A synchrotron consists of a continuous evacuated pipe in the form of a circular ring — a stretched-out doughnut — which is encased in a jacket of electromagnets. A bunch of stable particles — either protons or electrons — is injected into the ring at low energy, and the magnetic fields produced by the magnets are so arranged that the particles move in closed orbits around the ring. At a given point in each orbit the particles are given a radio-frequency ‘kick’ to increase their energy, and this kick is repeated until the particles within the machine attain the energy required. They are then extracted from their orbits and directed as a high-energy beam towards the experimental areas. One might imagine that beams of arbitrarily high energy could be produced by the administration of a sufficient number of kicks, but this is not the case. Every machine has an upper energy limit dictated  {23}  by its radius and the maximum strength of its electromagnets. As we shall see in Section 3, the trend in accelerator construction has been towards ever-higher maximum energies, attained by machines of ever-increasing size. The big machines of the 1950s had radii around 10 to 20 metres, and could be housed in a covered building; by the 1960s they had grown to around 100 metres, and were buried underground; by the 1970s radii had reached a kilometre; and Europe's projected big machine for the 1980s, lep, will have a radius of 4 kilometres.¹³

The stream of particles ejected from an accelerator is known as the primary beam. It can be used directly for experiment, or it can be used to generate secondary beams. In the latter case, the primary beam is directed upon a metal target where it creates a shower of different kinds of particles. Secondary beams of the desired species of particle are then singled out from the shower using appropriate combinations of electric and magnetic fields. In this way, beams of particles which are not amenable to direct acceleration — either because they are unstable and would disintegrate during the acceleration process, or because they are electrically neutral and hence immune to the electric and magnetic fields used in acceleration — are made available for experiment. The chosen beam, primary or secondary, is brought to bear upon the experimental target, and the interactions which take place within the target are interpreted as those between the beam particles and the target nuclei. Liquid hydrogen is often the target of choice, since this constitutes a dense aggregate of the simplest nuclei — single protons — and thus facilitates the interpretation of data. When studying rare processes, however, interaction rate rather than simplicity of interpretation may be a prime consideration. In this case a heavy metal target may be used, in order to present as many nucleons (neutrons and protons) to the incoming beam as possible.

In a typical beam-target interaction several elementary particles are produced (the number increases with beam energy) and emerge to pass through detectors. A common characteristic of hep detectors is that they are only sensitive to electrically charged particles, since in different ways they all register the disruption produced by such particles in their passage through matter. Electrically neutral particles can only be detected indirectly, either by somehow converting them to charged particles and detecting the latter or, inferentially, by consideration of the energy imbalance between the incoming beam and the outgoing charged particles. Many different kinds of detectors have been used in hep over the years. The details of these need not concern us here, but a few words on the general tactics of particle  {24}  detection may be useful. Detectors can be classified into two groups — visual and electronic — and we can discuss examples of each in turn. Since its invention in 1953, the pre-eminent visual hep detector has been the bubble chamber.¹⁴ A bubble chamber is a tank full of superheated liquid held under pressure. When the pressure is released, the liquid begins to boil. Bubbles form preferentially along the trajectories of any charged particles which have recently traversed the chamber. Thus lines of bubbles mark out particle tracks, which can be photographed and recorded for subsequent analysis. Figure 2.2 reproduces a bubble-chamber photograph, where the particle tracks stand out as continuous white lines (the large white blobs are reference marks on the walls of the chamber).

Figure 2.2. Bubble-chamber photograph.

In hep experiments the bubble chamber serves as both target and detector. The chamber is placed in the path of a particle beam and repeatedly expanded and repressurised. At each expansion, the tracks  {25}  within the chamber are photographed, yielding, in a typical experiment, many thousands of pictures of beam-target interactions or ‘events’. As noted above, the most popular filling for bubble chambers is liquid hydrogen, but when higher interaction rates are sought a heavier liquid (such as freon) may be substituted.

Bubble chambers, and other visual detectors, have two principal advantages for experimental hep. First, the visible tracks give direct access to elementary particles — if one forgets about philosophical niceties, one can imagine that one actually sees the particles themselves. And secondly, they generate a lot of data. A bubble chamber in a particle beam can record events much faster than they can be analysed. Historically, this was an important factor in the rapid post-war growth and diffusion of hep in universities around the world. It meant that university scientists with no accelerator at their home institution could visit an accelerator laboratory for a short time, collect a lot of data, and then return to base for months of profitable analysis. However, the productivity of visual detectors is a mixed blessing. They generate a lot of data because they are indiscriminate: they register everything that takes place within them, whether it is interesting or not. Much of the analysis of track data therefore consists of separating wheat from chaff: isolating phenomena of interest from uninteresting background.

Electronic detectors minimise the problem of separating wheat from chaff because they are discriminating. A discriminating detector is one which can be ‘triggered’ — programmed to decide whether to record what is taking place within it as interesting, or to discard the event as uninteresting. High-energy particles travel at almost the speed of light and traverse any detector array in a tiny fraction of a second. Thus the time-scale for triggering is of the order of nanoseconds (10^–9 seconds). The only way to process information so quickly is electronically, and the requirement of a discriminatory detector therefore translates into that of a detector whose output is an electrical signal. The first device to satisfy this criterion was the scintillation counter, which came into use in hep in the late 1940s and has since remained an important weapon in the hep experimenter's arsenal.¹⁵ Scintillators are materials which emit a flash of light when struck by a charged particle. In his pioneering work on radioactivity, Rutherford had counted alpha-particles (helium nuclei) by eye by observing flashes on a scintillating screen of zinc sulphide. But scintillators only became useful for the purposes of hep when they were conjoined with the newly developed photo-multiplier tube (pmt). Pmts register flashes of light and amplify them electronically. Their output is an electronic pulse which can be fed directly into fast  {26}  electronic logic circuits, and thus arrays of scintillation counters-scintillating materials monitored by pmts — nicely fulfil the conditions for discriminating detectors. Spark chambers took their place alongside scintillation counters in the late 1950s.¹⁶ While the latter transform an optical signal into an electrical pulse, the former generate electrical signals directly. Descendants of the pre-war Geiger-Muller counter, the basic element of spark chambers is a pair of wires (or metal plates) to which a high voltage is applied. Charged particles traversing the gaseous medium of the chamber precipitate sparking between the wires. This generates an electrical pulse which can be fed into amplification and logic circuits in much the same way as the output of scintillation counters. During the 1970s highly sophisticated descendants of the spark chamber — multi-wire proportional chambers, drift chambers and streamer chambers — played an increasingly important role in experimental hep.¹⁷ They offered high-precision measurements conjoined with refined triggering capability, and threatened to make the bubble chamber redundant. Figure 2.3 shows the output from an electronic detector of the early 1980s. The white dots represent the firing of individual counters, but the eye readily reconstructs them as continuous particle tracks.

Figure 2.3. Output from an electronic detector array.

One last component of hep hardware remains to be discussed: the particle collider. The particle accelerators so far mentioned are fixed-target machines — their beams are directed upon experimental targets at rest in the laboratory. Colliders have no such fixed targets.  {27}  They store counter-rotating beams of particles and clash them together. In colliders, the target is itself a beam of particles: two counter-rotating beams of particles are stored within a single ring or within two interlaced rings, and interactions take place at the predetermined points where the beams cross one another. The advantage which colliders enjoy over fixed-target machines is the following. In fixed-target experiments only a fraction of the beam energy — known as the centre-of-mass (cm) energy — is available for physically-interesting processes; the remaining energy is effectively locked up in the overall motion of the beam-plus-target system relative to the laboratory. In a collider this is not the case. Because the two beams collide head on, the beam-target system is stationary relative to the laboratory, and all of the beam energy is cm energy. Thus cm energy in colliders grows linearly with beam energy (it is just twice the energy of a single beam) while, according to the theory of special relativity, cm energy in fixed-target experiment grows only as the square-root of beam energies. Maximum beam energy is a major determinant of accelerator cost, and colliders therefore offer a very cost-effective route to high cm energies. As an experimental tool, however, colliders are not without certain disadvantages. In fixed-target experiments, one fires a tenuous beam at a dense target; in colliders one fires a tenuous beam at another tenuous beam, and the reaction rate is correspondingly reduced. Broadly speaking, therefore, the collection of comparable data requires considerably more time and effort at a collider than at a fixed-target machine. Furthermore colliders are limited to the investigation of interactions between stable, electrically charged particles — electrons, protons and their antiparticles — and offer a highly restricted range of experimental possibilities relative to fixed-target machines with their wide variety of secondary beams.¹⁸

Experiment

We can now turn from the hardware of hep experiment to its substance. What do hep experimenters seek to find out, and how do they assemble their resources to do so? A typical hep experiment measures ‘cross-sections’. Cross-sections are quantified in ‘barns’, unitsofarea(1 barn = 10^–24 cm²) which represent the effective area of interaction between beam and target particles. Cross-sections are best thought of as measures of the relative probabilities of different kinds of events: a high cross-section corresponds to a highly probable kind of event, a low cross-section to a rare one. Cross-section data constitute the empirical base of particle physics. For future reference, it will be useful here to introduce some technical distinctions between  {28}  different types of cross-section. The total cross-section (denoted ‘σ_tot’) for the interaction of two species of particles measures the overall probability that they will interact together in any way. In self-evident notation, it refers to the process AB ⟶ X where A and B are the beam and target particles, and X represents all conceivable products of their interaction. Total cross-sections can be regarded as sums of various partial cross-sections defined by specifying X. The most basic partial cross-sections are exclusive cross-sections, in which X is fully specified. Thus one might measure the exclusive cross-section for the process AB ⟶ AABBB, in which one A and two B particles are produced. Exclusive cross-sections can be further divided into elastic and inelastic cross-sections. Elastic cross-sections refer to processes in which no new particles are produced: AB ⟶ AB; inelastic cross-sections refer to processes in which new particles are produced: AB ⟶ AAAB, for example. Detailed measurements on inelastic processes in which many particles are produced are very difficult, and in this case experimenters often measure inclusive cross-sections. In such measurements X is only partially specified by, say, insisting that it contains at least one A particle: AB ⟶ AZ, where no attempt is made to identify the particle or particles comprising Z.

Cross-sections are functions of the cm energy at which they are measured and of the energies and momenta of the particles detected. And, in principle, one could imagine that hep experimenters would set out to measure all conceivable cross-sections. They would take beams of different types of particles at all available energies, fire them at a various targets, and make detailed measurements on every single particle which emerged. One could equally well imagine that this programme of comprehensive enquiry would take an indefinite length of time. It would also be highly inefficient, since an overwhelming proportion of the data would be irrelevant to contemporary theory and effectively meaningless. Hep experiment, like experiment in all branches of science, is therefore systematic: it seeks to measure cross-sections which the experimenters consider to be potentially meaningful. The important parameters which the hep experimenter has at his disposal in pursuit of meaningful data are the nature of the beam, the target and the detector array. Within technological limits, he can choose a beam of specified energy and intensity containing a specified species of particle; he can choose the target particles — different atomic nuclei or (in the case of colliders), electrons, positrons, protons and antiprotons — and, through choice of detectors, their configuration in space, and electronic logic circuits, he can attempt to register the production of predetermined species of particles emerging from the target at given angles and with given momenta. At  {29}  different periods in the history of particle physics, different patterns of choice of beams and detectors have dominated experimental practice. These patterns were characteristic of first the old and later the new physics, and I want now to review the gross differences between them (more details will follow in later chapters).

Accelerators capable of providing beams of ever-increasing energy were built in the post-war period, and each new machine opened up new areas for experiment. As one might expect, experimenters concentrated initially upon exploring the processes most commonly encountered in the laboratory — processes having large cross-sections. By definition, such processes are those mediated by the strong interactions, and beams of strongly interacting particles — hadrons — were accordingly favoured in old-physics experiments. Lep-tons experience only the electromagnetic and weak interactions, and their interaction cross-sections are one thousand or more times smaller than those of hadrons.¹⁹ Lepton-beam experiments therefore played only a minor role in the old physics. In the new physics, the roles were reversed. The earliest new-physics traditions of experiment were based on the use of lepton beams. Experiments with hadron beams did persist into the new physics, but now detectors were redesigned to emphasise rare, low cross-section processes quite different from those explored in the old physics. The old-physics experiments had established that most hadronic reactions were ‘soft’: most particles emerged from the interaction region with only a small momentum component transverse to the beam axis. It was as though beam particles typically struck the target nuclei a glancing blow, suffering only a slight deflection. Cross-sections were found to fall off exponentially fast with transverse momentum both for the scattering of beam particles and for the production of new particles. Old-physics experiments accordingly concentrated upon exploring the details of high cross-section soft-scattering processes. The new physics, in contrast, largely abandoned this pursuit, and focused instead upon very rare ‘hard-scattering’ phenomena in which particles emerged with high transverse momenta.

Experimenters sought to isolate such high-transverse-momentum particles through appropriate detector configurations, which are most readily described in connection with proton-proton collider research. In such machines, proton beams collide head-on. The centre-of-mass system is at rest in the laboratory and this makes it particularly easy to distinguish experimentally between hard and soft scattering. Soft scattering corresponds to small transverse momenta, and hence to the emergence of particles from the interaction region at small angles to the beam axis. To investigate soft scattering at  {30}  colliders, therefore, experimenters set up their detectors as close to the beam axis as possible — as represented by detector A in Figure 2.4. In contrast hard scattering corresponds to the emergence of fast particles at large angles to the beam axis. To investigate hard scattering, experimenters simply moved their detectors to a point at right-angles to the interaction region relative to the beam axis (and arranged only to count high-energy particles) as represented by detector B in Figure 2.4. In time, hard scattering became an important new physics tradition at fixed-target machines as well as at colliders, but at the former it is much more difficult to pick out the relevant events from the enormous soft-scattering background. Because the beam-target system is in motion in fixed-target experiments, all of the produced and scattered particles move in the general direction of the incoming beam. Simple changes in geometry are therefore insufficient to pick out hard-scattering events: more subtle arrangements of detectors, electronic logic and analysis are required which I will not discuss here.

Figure 2.4. Detector configurations in a proton-proton collider experiment: detector A registers low-transverse-momentum soft scatters; detector B registers high-transverse-momentum hard scatters.

From the experimental point of view, then, two key differences between the new physics and the old physics which preceded it were: an emphasis on the use of lepton rather than hadron beams; and, within hadron-beam physics, an emphasis on hard rather than soft scattering achieved through novel combinations of detectors. But these were differences within the experimental programmes  {31}  conducted at fixed-target accelerators and proton-proton colliders, while perhaps the most striking correlate of the transition to the new physics lay in the importance which became attached to experiment at a third class of machines: electron-positron colliders. Electrons and their antiparticles, positrons, are electrically-charged leptons. Their interaction cross-sections have the relatively small values characteristic of electromagnetic processes, and electron-positron experiment played at most a marginal role in the old physics. In contrast, as discussed below, in the latter half of the 1970s electron-positron colliders came to be seen as new physics laboratories par excellence.

2.3 Accelerator Chronology

We can turn now from the generalities of hep experiment to particulars. This section reviews the history of the construction of the big machines of hep, accelerators and colliders, and discusses how their use was intertwined with the old and new physics. Table 2.1 lists the major particle accelerators built or planned in the post-war era.²⁰

Table 2.1. Particle accelerators

Proton Accelerators

All of the machines listed in Table 2.1 as accelerating protons are proton synchrotrons (pss). The first major ps came into operation at the first of the national hep laboratories: the Brookhaven National Laboratory (bnl) on Long Island, usa. Bnl was primarily intended to serve the universities of the East Coast, and became a centre for hep experiment in 1952 with the inception of the Cosmotron.²¹ The Cosmotron produced a 3 GeV primary beam,²² and was the first accelerator to have sufficient energy to produce the so-called ‘strange’ particles in the laboratory. Strange particles had hitherto only been observed in experiments with cosmic rays (high-energy particles impinging on the earth from space). The Cosmotron beam was more intense than its naturally occurring equivalent, and amenable to human control as cosmic rays are not, and thus investigation of strange particles passed from the province of cosmic-ray physics to what one would now call hep proper. The transfer of attention from tenuous and uncontrollable cosmic rays to accelerator experiments, begun at Brookhaven, was essentially complete by the early 1960s, and cosmic-ray physics will not figure in the subsequent account.²³ Accelerator physics truly came into its own in 1954 with the completion of the 6 GeV Bevatron at Berkeley, California — the university laboratory where E.O.Lawrence had led the world in pre-war accelerator development.²⁴ The Bevatron was designed to have sufficient energy to be the first machine artificially to produce antiprotons (the antiparticles of the proton) and this it dutifully did. To physicists’ surprise it did much more besides. Beginning at Berkeley, more and more quite unexpected, unstable strongly interacting particles or ‘resonances’ were discovered.²⁵ Before the Bevatron, the known elementary particles could be counted on one's fingers — by the time the ‘population explosion’ of hadronic resonances had run its course there were hundreds. The population explosion had, by the early 1960s, transformed much of the hep landscape. From the experimenter's point of view, it revealed strong-interaction physics to be an extraordinarily rich field of enquiry, and confirmed the ps as the prime experimental tool. On the theoretical side, while it had been relatively easy to accept a handful of particles as truly fundamental, it was not easy to maintain such a position when the list got longer every day. The theorists’ response to this manifested a kind of social schizophrenia. One group espoused the so-called ‘S-matrix’ or ‘bootstrap’ programme, which asserted that there were no truly elementary particles. The other group asserted that there were elementary particles, but that these were not  {33}  the particles observed in experiment: they were the quarks, from which all hadrons were built. The rival positions were often referred to as nuclear democracy and aristocracy respectively — in the former all particles were equal, while in the latter quarks had a privileged ontological position — and together they dominated theoretical hep in the 1960s. Only in the 1970s, with the rise of the new physics, did the quark programme eclipse the bootstrap.

The Berkeley Bevatron was soon overtaken in energy by machines at several national and international laboratories. An international laboratory serving the Eastern bloc countries was set up at Dubna in the Soviet Union, where a 10 GeV ps began operation in 1957. In 1954 the nations of Western Europe set up a joint hep laboratory just outside Geneva, Switzerland, and in 1959 a 28 GeV ps came into operation there. The European venture was formally known as the European Organisation for Nuclear Research, but was more often referred to as cern (an acronym for Conseil Europeen pour la Recherche Nucleaire, the body which oversaw the establishment of cern in the early 1950s). In 1961 the usa regained a narrow lead in energy, with the first operation of a new machine at Brookhaven, the 31 GeV Alternating Gradient Synchrotron (ags).²⁶ In 1963, two national machines of intermediate energy appeared: in the usa, the 13 GeV Zero Gradient Synchrotron (zgs) came into operation at the Argonne National Laboratory, Illinois;²⁷ and in the UK experiment began at a 7 GeV ps called Nimrod, situated at the Rutherford Laboratory, not far from Oxford.²⁸

In the 1960s, with the advent of new accelerators, research in strong-interaction physics split into two rather distinct domains. At low energies, cross-sections were observed to be large and to fluctuate rapidly as a function of beam energy and momentum transfer. These fluctuations were ascribed to the production and decay of hadronic resonances. At higher energies cross-sections remained large in the forward direction, but manifested a smooth non-resonant behaviour. This was ascribed to soft-scattering processes which were routinely analysed in terms of ‘Regge’ models belonging to the S-matrix programme. Investigations of the properties of resonances at low energies and of soft-scattering phenomena at high energies comprised the two principal strands of the old physics of the 1960s.

Both the cern ps and the Brookhaven ags were built on the so-called ‘alternating-gradient’ principle and with their successful operation it became clear that there should be no special problems involved in the construction of proton accelerators of even higher energies.²⁹ In 1967 the 76 GeV ps at Serpukhov regained the high-energy record for the Soviet Union. This machine produced  {34}  data of considerable interest for the Regge tradition but, like the Dubna machine before it, did not have the overall impact one might have expected.³⁰ Usa plans conceived in the mid-1960s came to fruition in 1972 with the first operation of a 500 GeV ps at a new national laboratory just outside Chicago.³¹ This laboratory was first called the National Accelerator Laboratory, then restyled the Fermi National Accelerator Laboratory, or Fermilab for short. The European reply to the Fermilab machine was a 400 GeV accelerator called the Super Proton Synchrotron (sps) which delivered its first beam in 1976.³²

Both the Fermilab ps and the cern sps were conceived during the era of the old physics, and old-physics topics of resonance production and soft scattering constituted the bulk of their initial research programmes. During the late 1970s, however, the old physics was largely displaced at these accelerators by new-physics research. But, as discussed below, the main themes of the new physics — lepton beam and hard-scattering experiments, also the study of charmed particles — all emerged from other machines. In the context of the new physics, proton synchrotrons lost the obvious pre-eminence as a research tool which they had enjoyed in the days of the old physics. They remained unique, however, in their ability to provide a wide variety of secondary beams and thus to support a large and diversified research programme. In the late 1970s plans were in hand to extend the maximum energy of the Fermilab machine to 1 TeV (=1000 GeV) — the Tevatron project³³ — and the Soviet Union envisaged operating a 3 TeV ps at Serpukhov by the late 1980s.

Electron Accelerators

As electrically charged and stable particles, electrons can be accelerated in machines identical in principle to proton accelerators. However, electrons are much lighter than protons (0.5 MeV and 1 GeV in mass, respectively) and therefore lose energy much faster than protons when accelerated in circular orbits: to achieve a beam of a given energy it is much more efficient to accelerate protons rather than electrons. Historically, too, proton beams have appeared a more direct probe of elementary particle interactions — especially, in a common-sense way, of the strong interactions. Thus the electron machines listed in Table 2.1 have always lagged behind pss in energy and were for a long time seen as second best. There were several small electron accelerators constructed in the post-war era, but even with the mid-1960s arrival of the 6 GeV Cambridge Electron Accelerator in the usa, the 7 GeV Deutsches Elektronen-Synchrotron (desy) in Hamburg, W. Germany, the 5 GeV nina synchrotron at the  {35}  Daresbury Laboratory in the uk and a 6 GeV synchrotron at Yerevan in the ussr, such machines remained the poor relations of proton accelerators.³⁴ Of lower energy than their ps contemporaries, electron machines served to add new data on the old-physics phenomena already explored using proton beams, rather than to point to entirely new research topics. But, in the late 1960s, the first results from the new 22 GeV electron machine at the Stanford Linear Accelerator Center (slac) in California thrust electron-beam physics into the hep limelight. The slac machine, alone amongst the machines discussed here, was a linear accelerator (a ‘linac’) rather than a circular synchrotron. Electrons at slac were simply accelerated along a linear path, emerging from the end of the machine as a 22 GeV beam. Stanford was the home of a long tradition of electron linac construction dating back to pre-war years, and the 22 GeV slac machine was the biggest (two miles long), best, and most expensive (SI 14 million, construction; $25 million per annum, running costs) of them all.³⁵ In the first round of experiments at slac a remarkable new phenomenon — scaling — was discovered. Scaling, and its theoretical interpretation in terms of first the quark-parton model and later qcd, constituted the first strand of the new physics to emerge. The discovery of scaling and its impact upon experimental and theoretical practice in hep is the topic of Chapter 5, and here I want just to comment upon the marked absence from Table 2.1 of any post-slac electron accelerators.

The discovery of scaling guaranteed high-energy electron scattering a place in the forefront of hep interest. However, as mentioned above, to attain a given energy, proton accelerators are much more efficient and economical than electron accelerators. And amongst the various secondary beams which can be generated from the primary proton beam of a ps are beams of leptons: electrons, muons and neutrinos (for a discussion of muons and neutrinos, see Chapter 3). Thus the impact of the discovery of scaling at slac was to focus attention on lepton beam experiments at the high-energy proton synchrotrons. In particular, the early 1960s had seen the beginning of programmes of neutrino experiment at both Brookhaven and cern and, after its discovery at slac, scaling was soon observed to hold in neutrino scattering as well. Thus the mantle passed from slac not, as one might have expected, to a new generation of electron accelerators, but to the very high-energy neutrino beams available at Fermilab and the cern sps. Neutrino physics experiments aiming at the investigation of scaling were one way in which the new physics entered the experimental programmes of those machines. As it happened, neutrino experiments in the 1970s had a dual significance  {36}  for the new physics. Besides scaling, neutrino beams were also the principal probe of another new phenomenon: the weak neutral current. The neutral current was discovered in 1973, and was regarded as the first piece of empirical evidence in favour of unified electroweak gauge theory. It was initially observed in a neutrino experiment at the cern ps, but quickly became a prime research topic at Fermilab and the cern sps where higher beam energies made it possible to collect more extensive and detailed neutral current data. One identifying characteristic, then, of new-physics ps experiments was an emphasis upon lepton beams. The other principal characteristics were an increasing focus upon hard-scattering phenomena and charmed particles. The emergence of these topics is discussed below.

Colliders

Table 2.2 lists the major colliding beam machines of hep. The CM-energy advantage which colliders enjoy is clearly evident in comparison with Table 2.1. The cern isr proton-proton collider, for example, is fed by 28 GeV proton beams from the cern ps. After a slight increase in beam energy to 31 GeV, the isr realises CM energies of 62 GeV (= 2 × 31 GeV), while to attain such a CM energy in a fixed-target experiment would require a 2 TeV primary beam.

Table 2.2. Colliders

Electron-Positron Colliders

Most of the early colliders (not shown in Table 2.1) were very low energy electron-positron (or electron-electron) machines. Their primary physics interest lay in testing the successful theory of quantum electrodynamics (qed) in a new regime, but they were beset by technical problems and very much the toys of particular, idiosyncratic, experimenter/machine-builders. In the early 1960s a set of hadronic particles known as ‘vector mesons’ were discovered using conventional accelerators. These particles were found occasionally to decay into electron-positron (e⁺e^–) pairs, and it was quickly realised that they should be produced by a converse process in e⁺e^– collisions. It therefore appeared possible that beyond the investigation of qed, interesting hadronic physics could be done at e⁺e^– colliders. None the less, it was generally felt that above the masses of the vector mesons (1 GeV) experiment would reveal an uninspiring ‘desert’.

One of the first machines to put this feeling to the test was the adone collider which began operation at the cnen National Laboratory at Frascati, Italy in 1967. Adone was the fruit of earlier experience gained at Frascati in the construction of a smaller ring, AdA, and used as its source of electrons and positrons a low energy electron synchrotron already in operation at Frascati.³⁶ Adone proved an excellent tool for the investigation of the vector mesons, and in the early 1970s showed that in the energy range above these (1–3 GeV) the desert was far from infertile. Theorists had expected that the cross-section for the production of hadrons would fall quickly towards zero in this region, whereas experiments at adone revealed that it stood up rather well. But no striking new phenomena were found, and e⁺e^– physics remained of marginal significance in hep. In the same year as adone, the cea ‘Bypass’ e⁺e^– facility became operational at Cambridge, fed once more from an existing electron synchrotron. By 1972, cm energies at cea had been extended up to 7 GeV, more than twice those attainable at adone, but with very low luminosity. Luminosity is a technical measure of the density of the beams in the interaction region, and cea's low luminosity implied a very low interaction rate. This in turn implied large statistical uncertainties in data taken in a reasonable length of time, and although observations made at cea were rather suggestive, it was left to the spear ring at Stanford to mark the real arrival of e⁺e^– physics.

The moving force behind the construction of spear was Stanford physicist Burton Richter. Having advocated for many years the construction of an e⁺e^– collider to exploit the beam from the slac  {38}  linear accelerator, Richter finally saw his dreams take shape in a cut-price, 8 GeV CM-energy version (spear was funded from the slac operational budget) which began to do physics in 1972.³⁷ In 1974 a watershed in the development of the new physics came with the discovery of the first of the new particles — the J-psi — announced simultaneously by experimenters at spear and the Brookhaven ags. The ags proved to have insufficient energy for detailed investigation of the properties of the new particles, and amongst fixed-target machines the Fermilab ps and cern sps took over this role. Spear, however, was well matched to experimental requirements. Much of the work which contributed to the identification of the new particles as manifestations of ‘charm’ was done there, and at another electron-positron collider, doris, which began operation at desy in 1974. As indicated in Chapter 1, data on charmed particles were seen as crucial to the theories of the new physics — both electroweak gauge theory and qcd — and in the latter half of the 1970s, e⁺e^– interactions came to be seen as perhaps the single most revealing source of information in experimental physics. In the space of a couple of years, electron-positron colliders moved from the margins to the forefront of hep research.

In 1978, desy took over the lead in electron-positron physics with the commissioning of the 38 GeV CM-energy collider, petra. The equivalent us facility, pep at slac, was delayed by funding problems until 1980. Another us e⁺e^– machine — an intermediate energy collider, cesr at Cornell — came into operation in 1979. In Europe, consensus hardened that the major accelerator project for the 1980s should be a giant e⁺e^– machine, and the decision to build lep (the Large Electron-Positron collider) at cern was ratified by the Member States in 1981.³⁸ Lep was envisaged as a new-physics machine, a gauge theory laboratory. A whole variety of new physics phenomena could be explored with it, but it had one primary objective: to detect a set of particles known as ‘intermediate vector bosons’ (ivbs). The ivbs were the key elements of unified electroweak gauge theory, and were predicted to be so heavy that no existing machine had sufficient energy to produce them. A late and novel entry into the field of electron-positron machines was the proposed Stanford Linear Collider (slc). This machine was envisaged to take 50 GeV beams of electrons and positrons from the slac linac (upgraded in energy) and collide them just once before discarding them (in contrast to conventional colliders in which stored beams collide repeatedly). The motivation behind the apparently wasteful slc was twofold. First, it could be argued that for energies much beyond lep it would be cheaper to build and operate two linear  {39}  accelerators and fire them at one another, rather than to go to another generation of circular colliders. The six could thus be regarded as a prototype for the machines of the future. More importantly in the short term, it seemed that the six could be built quickly, offering us physicists a chance to detect the ivbs before lep began operating in Europe. Although not officially funded, by 1982 it appeared likely that the six would be the next major facility to be built in the usa.³⁹

Proton-Proton and Proton-Antiproton Colliders Electron-positron machines provided the major experimental sensations in hep in the 1970s, but from 1971 onwards the world's highest CM-energy machine was a proton-proton collider — the Intersecting Storage Rings (isr) at cern. The isr stores counter-rotating proton beams from the cern ps in two interlaced rings. At the intersections of the rings a total of 62 GeV cm energy is available. Early studies at the isr concentrated on old-physics topics—in particular, on measurements of soft, low-transverse-momentum processes relevant to the contemporary versions of Regge theory. However, for the reasons outlined in Section 2.2, experimenters found the isr an especially convenient machine at which to investigate high-momentum transfers, and in the first round of isr experiments significant steps were taken towards establishing traditions of hard-scattering research. These early isr experiments observed that while cross-sections were indeed small at high-momentum transfers they were considerably larger than expected from a straightforward extrapolation of soft-scattering data. The excess of high-transverse-momentum events was construed as evidence of hard collisions between the quark constituents of the interacting hadrons, and was interpreted in terms of the quark-parton model originally developed for the analysis of the slac electron scattering data. Traditions of hard-scattering experiment grew rapidly at the isr during the 1970s. Through their relation to the quark-parton model (and later to qcd) they represented the first incursion of the new physics into purely hadronic experiment, and they eventually came to dominate the isr programme. Despite technical difficulties in detecting high-transverse-momentum particles in fixed-target experiments (see Section 2.2) traditions of hard-scattering research also sprang up at Fermilab and the cern sps, where they contributed yet another element to the new physics takeover.

No more proton-proton colliders were constructed during the 1970s, but us plans for a major investment in the 1980s came to centre on an 800 GeV CM-energy pp collider. Called Isabelle, this was to be built at the Brookhaven National Laboratory. Construction began in  {40}  1978 and tunnelling for the ring was complete in 1981. Unfortunately, the design for Isabelle relied upon largely untried superconducting-magnet technology, and the development of working magnets encountered many problems. These caused delays and cost escalation, and by the early 1980s it was unclear whether Isabelle would ever be completed.⁴⁰ Construction of two proton-antiproton (pp) colliders also got under way in the 1970s. This followed the 1976 proposal that it might be possible to fill the Fermilab ps and the cern sps with counter-rotating beams of protons and anti-protons and thus to operate them in a colliding-beam mode.⁴¹ These pp colliders promised to reach the same CM-energy range envisaged for lep and Isabelle. They could not promise data of the same quantity and quality but, as conversions of existing machines, they could be brought into operation relatively quickly and inexpensively. Their aim was a simple one: the first sighting of the ivbs.

To summarise this section, the history of accelerator physics can be divided into three eras. In the first era, which extended roughly to the end of the 1960s, accelerators were both built and used for old-physics purposes. Hadron-beam experiments at pss of increasing energy set the pace. The second era spanned the 1970s. Most of the machines which came into operation then had been planned with the old physics in mind, but they were increasingly used for new-physics purposes. Ps programmes were reorganised around the investigation of rare phenomena, and colliders came to the fore. The third era lay in the future, with big machines like lep and the pp colliders explicitly conceived as new-physics factories. In the following chapters we can analyse how the transitions between the three eras came about.

NOTES AND REFERENCES

3
THE OLD PHYSICS! hep, 1945–64

This chapter traces out the broad features of the post-war development of hep.¹ It aims to delimit the principal preoccupations of the old physics in the early 1960s, the immediate pre-quark era. The old physics was characterised by its commonsense approach to elementary-particle phenomena. Experimenters explored high cross-section processes, and theorists constructed models of what they reported. By the early 1960s, old-physics hadron-beam experiments at the major pss had isolated two broad classes of phenomena. At low energies, cross-sections were ‘bumpy’ — they varied rapidly with beam energy and momentum transfer. At high energies, cross-sections were ‘soft’ — they varied smoothly with beam energy and decreased very rapidly with momentum transfer. The bumpy and soft cross-section regimes were ascribed different theoretical meanings. The low-energy bumps were interpreted in terms of the production and decay of unstable hadrons. As more and more bumps were isolated, so the list of hadrons grew. This was the ‘population explosion’ of elementary particles, discussed in Section 1. The following sections review various theoretical attempts to get to grips with the explosion. Section 2 outlines the way in which conservation laws were used to sharpen the distinction between the strong, weak and electromagnetic interactions and to classify the hadrons into families. This approach resulted in the Eightfold Way classification scheme, of which the quark concept was a direct descendant. Section 3 discusses how hep theorists attempted to extend the use of quantum field theory from the electromagnetic to the weak and strong interactions. This attempt bore fruit in the early 1970s with the elaboration of gauge theory. But in the 1950s and early 1960s the field-theory programme did not prosper. For the weak interaction, the field-theory approach was at least pragmatically successful, but for the strong interaction it failed miserably. Section 4 reviews the struggle to salvage something from the wreckage. What emerged was the ‘S-matrix’ approach to strong interaction physics. The S-matrix was founded in quantum field theory but achieved independence from it and was seen, in the ‘bootstrap’ formulation, as an explicitly anti-field-theory approach. In the late 1950s the principal referent of  {46}  S-matrix theorising was the growing list of hadrons. But in the early 1960s one strand of S-matrix development, ‘Regge theory’, came to dominate the analysis of the high-energy soft-scattering regime.

Thus, from the early 1960s onwards, the old physics had a two-pronged structure: at low energies, the emphasis was on bumps in cross-sections and their interpretation as unstable hadrons; at higher energies, the emphasis was on soft scattering, interpreted in terms of Regge theory. The low-energy work led directly to quarks, as we shall see in the next chapter. The Regge-oriented traditions of theory and experiment led nowhere — in the sense that they contributed little to the eventual emergence of the new physics of quarks and gauge theory. My account of the Regge traditions in Section 4 is correspondingly brief, and in the following chapters I will not discuss them in any detail. But it is important to bear their existence in mind. During the 1960s and into the 1970s, the Regge traditions constituted a major component of old-physics research.² They enshrined a world-view quite different from that of the new physics. And as long as they were actively supported by hep theorists and experimenters the new physics could not be said to be established. The Regge traditions constituted the resistance which quarks and gauge theories had to overcome.

3.1 The Population Explosion

Writing in 1951 on ‘The Multiplicity of Particles’, hep theorist Robert Marshak from the University of Rochester looked back upon a golden age of elementary particles:

In the year 1932, when James Chadwick discovered the neutron, physics had a sunlit moment during which nature seemed to take on a beautiful simplicity. It appeared that the physical universe could be explained in terms of just three elementary particles — the electron, the proton, and the neutron. All the multitude of substances of which the universe is composed could be reduced to these three basic building materials, variously combined in 92 kinds of atoms. An atom consisted of a tight nucleus, built of protons and neutrons, and a swarm of electrons revolving around the nucleus like planets around a sun.³ In December 1951, Marshak counted 15 elementary particles — the list was already beginning to look untidy. As the years went by, the list grew longer, and this section traces out the principal early developments.⁴

In the late 1940s, cosmic-ray experimenters decided that they were observing the production of two different types of particle where hitherto they had suspected the existence of only one. One particle,  {47}  the muon (μ), was recognised as a lepton — an electron-like particle immune to the strong interactions. Having a mass of 105 MeV, the muon was around 200 times heavier than the electron (e), but otherwise appeared identical to it. The second particle, the pi-meson or pion (π), displayed the large interaction cross-sections with nuclear matter characteristic of a strongly interacting particle or hadron. With a mass of around 140 MeV, the pion was much lighter than other hadrons (the proton, for example, had a mass of 940 MeV) and was identified as the carrier of the strong interactions predicted by the Japanese physicist Hideki Yukawa in 1935 (see Section 3 below).

In 1953 another lepton was discovered: the electrically neutral and massless neutrino (ν) (see also Section 3). From then on, the list of leptons — e, μ, ν — remained static for many years. The list of hadrons continued to grow. Between 1947 and 1954 a succession of hadrons were identified in cosmic-ray experiments and in accelerator experiments at the Brookhaven Cosmotron: the K-meson or kaon (K: 500 MeV in mass); the lambda (Λ: 1115 MeV); the sigma (Σ: 1190 MeV); and the cascade or xi (Ξ; 1320 MeV).⁵ All of these particles were unstable and decayed to lower mass particles. They were observed as tracks a few centimetres long in visual detectors, and their lifetimes before decay were accordingly deduced to be around 10^–8 to 10^–10 seconds.⁶ This was the time scale expected for processes mediated by the weak interaction, and observations on the decay of these particles constituted an important new source of information on the weak interaction in the early years of hep.

In 1952, a particle known as the delta (Δ: 1230 MeV) was observed at a low-energy accelerator, the Chicago cyclotron. The delta then appeared to be unique in the shortness of its lifetime. Unlike the quasi-stable particles discussed above, which produced experimentally measurable tracks, the delta existed only for an infinitesimal time, around 10^–23 seconds, between its production and decay, and was impossible to observe directly. Instead, its existence was inferred from a large bump in pion-nucleon cross-sections around the cm energy of 1230 MeV. Figure 3.1 shows a modern compilation of cross-sections for the interaction of negative pions with protons; the delta is the first and largest peak, situated at around 0.34 GeV/c beam momentum.⁷ The energy-dependence of cross-sections in the vicinity of the delta peak was typical of ‘resonance’ phenomena already well known in nuclear physics, and the delta was often referred to as a ‘resonance’ — marking physicists’ uncertainty as to whether such a short-lived entity should be regarded as a genuinely fundamental particle.⁸ Whatever its nature, the delta's lifetime of 10^–23 seconds was characteristic of strong-interaction processes, and thus it  {48}  followed that the decay as well as the production of the delta was mediated by the strong interaction.

Figure 3.1. Cross-sections (σ) as a function of pion beam momentum (pbeam) for negative pion-proton interactions. The upper curve, labelled σtot, shows the total cross-section, corresponding to the probability of any kind of interaction taking place. The lower curve, σel, shows the cross-section for elastic scattering, i.e. the relative probability that the pion will scatter off the proton without production of any additional particles.

As one might guess from the several peaks evident in Figure 3.1, the uniqueness of the delta was, like the particle itself, short-lived. In the early 1960s, more and more entries were added to the list of hadronic resonances, all of which were entities decaying on a time-scale of 10^–23 seconds. In 1961 four new resonances were found in experiments at the Brookhaven Cosmotron and the Berkeley Bevatron: the eta (η: 550 MeV), rho (ρ: 770 MeV), omega (ω: 780 MeV) and K-star (K^*: 890 MeV). In 1962, the Brookhaven ags added the phi (φ: 1020 MeV). It was at around this time that the population explosion really took off. Masses of cross-section data were emerging from the Bevatron, the ags, the cern ps and the other new machines of the 1960s, and ‘bump-hunting’ for resonance peaks became the central experimental preoccupation of the old physics in the low-energy regime. More and more resonances were found, and it would serve  {49}  little purpose to list them individually. A review article published in 1964 noted that ‘only five years ago it was possible to draw up a tidy list of 30 sub-atomic particles’, but that ‘since then another 60 or 70 sub-atomic objects have been discovered’,⁹ and this is sufficient to make the point.

One last group of particle discoveries needs to be mentioned here: that of antiparticles. Antiparticles are states having the same mass as the corresponding particles, but with opposite electric charge and other quantum numbers (see below). The first antiparticle to be discovered was the antielectron or positron (e⁺), a particle apparently identical to the electron (e^–) except in carrying a positive rather than a negative charge. Observed in 1932 by Carl Anderson in a cloud-chamber experiment, the positron came to be regarded as confirmation of Paul Dirac's quantum theory of electromagnetism. According to Dirac's theory, all particles were expected to have associated antiparticles, but many physicists remained sceptical until the antiproton (p), the antiparticle of the proton (p), was discovered at the Berkeley Bevatron in 1955.¹⁰ From that point on, it became a routine assumption that all particles had antiparticles. Many species of antiparticle were experimentally observed, swelling the list of hadrons even further.

3.2 Conservation Laws and Quantum Numbers:
From Spin to the Eightfold Way

As the experimenters generated increasing quantities of data on increasing numbers of particles, so theorists set out to create some order in what was being found. One strategy was to theorise in detail about the constitution of elementary particles and their interactions, as discussed in Sections 3 and 4 below. Here I will discuss a second strategy: the use of conservation laws.¹¹ Conservation laws embody the idea that some quantities are fixed come what may, and have an honoured place in the history of physics. Particle physicists followed a traditional path in using them to make sense of their subject matter. On the one hand, they applied already established laws as definitions, more clearly to establish what was new in the interactions of elementary particles; on the other, they constructed new, empirical, conservation laws in order to systematise experimental data and to characterise the fundamental interactions.

We can begin with the truly definitional conservation laws which were rooted in fundamental beliefs about space-time. These were the energy-momentum and angular momentum conservation laws. One important consequence of the former was that it implied constraints upon particle decays: particles could only decay into other particles  {50}  whose combined mass was less than or equal to the mass of the parent.¹² Conservation of energy implied, for example, that the delta (mass 1230 MeV) could decay into a proton plus a pion (combined mass 1080 MeV) but not into a lambda plus a kaon (combined mass 1615 MeV). By virtue of its definitional status, conservation of energy-momentum could also be used to extract information about the interactions of electrically neutral particles. Neutral particles leave no direct record in particle detectors, but experimenters routinely inferred their presence by insisting that energy-momentum was conserved in all interactions: any apparent energy-momentum imbalance had to be due to undetected neutrals. It was through such reasoning that neutral particles like the lambda were discovered. Through its denning status, conservation of angular momentum served similar purposes. It also served as foundation for a system of labelling elementary particles, and a discussion of this will serve to introduce the important concept of a ‘quantum number’.

Modern conceptions of the atom derive from the planetary model first developed by Niels Bohr in the early years of this century. According to Bohr's model, electrons orbit the nucleus as do the planets the sun. Associated with the orbital motion is angular momentum: the faster an electron or planet travels in an orbit of given radius, the more angular momentum it carries. The difference between the planetary and atomic systems is that the former is macroscopic and believed to be well described by the laws of Newtonian classical mechanics, while the latter is microscopic and believed to require a quantum-mechanical analysis. According to quantum mechanics, orbital angular momentum is not a continuous quantity free to assume arbitrary values. Instead, it is quantised; restricted to values which are integral multiples of a fundamental unit, denoted by ℏ.¹³ The number of these units associated with a given orbit is known as the orbital angular momentum quantum number, denoted by L: to say that the quantum number of an electron orbit is L is to say that the orbital angular momentum associated with it is Lℏ.

As the result of a combination of experimental and theoretical work in the late 1920s, physicists concluded that it made sense to ascribe angular momentum or spin to elementary particles themselves as well as to their orbital motion.¹⁴ It was as though particles rotated about an internal axis just as planets rotate about theirs. Like angular momentum, the spin of elementary particles was supposed to be quantised — this time in either integral or half-integral multiples of ℏ. Each species of particle was supposed to carry a fixed spin which could not be changed in any physical process, and thus spin was  {51}  recognised as an identifying characteristic of a given species. In the pre-Second-World-War era, spin values were assigned to the known particles — the electron, proton and neutron were all identified as spin ¹/₂ objects; the photon, the quantum of the electromagnetic interaction, was assigned spin 1. As more particles were discovered in post-war hep they were routinely assigned spins on the basis of experimental measurements of their production and decay. Deltas, for example, were identified as spin ³/₂; pions and kaons, spin 0; and rho, omega and phi particles spin 1. Together with the spin concept came another layer of jargon. Particles with half-integral spin, like the electron and proton, became generically known as fermions; particles with integral spin, such as the pion and rho, as bosons.¹⁵ All of the known leptons were fermions, but fermions and bosons were equally well represented amongst hadrons. Hadronic fermions were generically christened baryons, while hadronic bosons were named mesons.

One subtlety concerning spin remains to be discussed. Angular momentum, spin and orbital, is a vector quantity: it has both magnitude and direction. The spin angular momentum of a planet, for example, has a magnitude determined by how fast the planet rotates, and a direction determined by the orientation in space of the axis about which it rotates. Now, just as quantum mechanics requires the quantisation of the magnitude of angular momentum so, speaking loosely, it requires the quantisation of orientation. To be more precise, it requires that the component of the total angular momentum as measured relative to any axis fixed in space is itself quantised. This is best explained in concrete terms. Consider a spin 2 particle, and suppose that one sets out to measure how much of the spin is oriented along a chosen axis (conventionally referred to as the 3-axis). Clearly the answer must be between 2, for a parallel alignment of the spin with the chosen axis, and –2, for an antiparallel alignment. In classical mechanics, any answer in this range is conceivable, but in quantum mechanics only answers differing by integers are conceivable: +2, +1, 0, –1, –2. A particular measurement may result in any one of these values — for example +1 — and one would then say that the 3-component of the particle's spin was +1. Similarly, the 3-component of spin of a spin ¹/₂ particle can only take on the values +¹/₂ or –¹/₂; that of a spin ³/₂ particle +³/₂, +¹/₂, –¹/₂ or –³/₂, and so on. Such considerations are central to the experimental analysis of elementary particle interactions, but their particular relevance here will become evident below when we discuss ‘isospin’.

Three further conservation laws have also enjoyed definitional status in the analysis of elementary particle interactions. These are  {52}  the conservation of electric charge, the conservation of baryon number and the conservation of lepton number. The first of these states that electric charge can be neither created nor destroyed in any physical process: a Δ⁺ (charge +1), for example, can decay to a π⁰ (0) and a proton (+1), but not to a π⁺ (+1) and a proton (+1). Charge conservation is grounded in the theory of electrodynamics, while the conservation laws of baryon and lepton numbers represent analogical extensions of the charge concept to explain purely empirical regularities. All baryons are assigned baryon number 1, all antibaryons –1, and all other particles 0. Baryon number is supposed to be an additive, charge-like quantity — so that, say, the baryon number of a system of five protons is 5 — and is supposed to be absolutely conserved. This has the experimentally confirmed consequence that antibaryons can only be produced in conjunction with baryons (zero net change of baryon number), and that the lightest baryon, the proton, is absolutely stable (since all the lighter particles to which it could decay are mesons or leptons with baryon number zero). Likewise, the observed regularities of lepton production and decay are systematised by assigning an additive lepton number +1 to leptons, –1 to antileptons, and 0 to other particles, and insisting that total lepton number is conserved. (In the late 1970s the conservation of baryon and lepton number came under theoretical challenge: we will discuss this in Chapter 13).

Restricted Conservation Laws

The conservation laws so far discussed were well established in pre-war physics, and were regarded by particle physicists as having unlimited and universal scope. We can now turn to a second class of laws, those which were believed to apply to some interactions and not to others. Let us begin with parity conservation. Parity is a concept with no classical analogue. It has meaning only within the framework of quantum mechanics, and is best thought of here as a book-keeping device.¹⁶ The parity quantum number can take on only two values, +1 (positive parity) or –1 (negative parity), and can be associated with both individual particles and assemblages of particles. Every type of particle has its own intrinsic parity — all pions have negative parity, all protons positive, and so on. Parity is a multiplicative rather than an additive quantum number, so that, say, a system of two stationary pions has positive parity (–1 × –1 = +1). Relative orbital angular momentum is also significant in assigning parities to multiparticle states: each unit of orbital angular momentum contributes a factor of –1 to the overall parity. Thus, a system of two pions orbiting one another with one unit of angular momentum has  {53}  negative parity (–1 = –1 × –1 × –1). The parity and spin quantum numbers together form the basis for more jargon. Physical quantities having spin 0, positive parity — denoted 0⁺ — are known as scalar quantities; 0^– quantities are pseudoscalars; 1⁺, axial vectors; and 1^–, vectors. This nomenclature is used in many circumstances: for example, it is applied to particles themselves — pions and kaons are referred to as pseudoscalar mesons; rhos, omegas, phis and photons as vectors — and to the weak currents (see Section 3 below).

For many years, it was thought that parity conservation was absolute since it followed from rather basic considerations concerning the mirror-symmetry of physical processes. The world of hep was therefore shaken in 1956 by the discovery that in certain processes parity-conservation was violated. Nuclear transitions and particle decays were observed in which the parity of the product state was not the same as that of the parent. These transitions and decays were all mediated by the weak interactions, and it became part of the conventional wisdom of hep that, while the strong and electromagnetic interactions did conserve parity, the weak interaction did not. Thus the weak interaction was distinguished from the other forces not only by its characteristically weak effects but also by its irreverent attitude to a hitherto well-established conservation law. Parity was a ‘good’ quantum number for strong and electromagnetic processes but it was meaningless in the characterisation of processes mediated by the weak interaction.

A similar comment applies to two other quantum numbers invented by hep theorists, strangeness and isospin. In the early 1950s, kaons and lambdas were known as ‘strange’ particles. Their strangeness lay in the fact that although they were copiously produced in particle interactions with typical strong-interaction cross-sections, they decayed (relatively) slowly, having lifetimes typical of weak decay processes. In 1952, us theorist Abraham Pais proposed his ‘associated production’ hypothesis.¹⁷ According to this, kaons and lambdas interacted strongly only in pairs: a kaon and a lambda could be produced in association with one another via the strong interaction, but in isolation they could only decay via the weak interaction. This idea was refined by the American theorist Murray Gell-Mann, and independently by the Japanese theorist Kazuhiko Nishijima, who proposed that the strange particles carried a new additive quantum number called, appropriately enough, strangeness.¹⁸ Kaons would carry strangeness +1, lambdas –1, and other particles, such as the pion and proton, strangeness zero. Strangeness was supposed to be exactly conserved by the strong interaction, and therefore every time a lambda particle, say, was produced it had to be accompanied  {54}  by a kaon. Like parity, strangeness was not supposed to be conserved by the weak interactions, and thus kaons and lambdas could decay to nonstrange particles with the observed weak-interaction lifetimes.¹⁹ As the population explosion got under way, associated production was observed to obtain for many hadrons, and appropriate values of strangeness were assigned to these: –1 for the sigma baryons, –2 for the xis, and so on.

Strangeness could be thought of as a conserved charge, like electric charge, baryon number and lepton number. Isospin, on the other hand was, as the name suggests, a vector quantity like spin. The isospin concept was an extension of the pre-war ‘charge-independence’ hypothesis,²⁰ and asserted that hadrons having similar masses, the same spin, parity and strangeness, but different electric charges, were identical as far as the strong interactions were concerned. Thus, for example, in their strong interactions the neutron and proton appeared to be indistinguishable, as did the three charge states of the pion, π⁺, π⁰ and π^– (the superscripts indicate electric charge). This was formalised by assigning each group of particles an isospin quantum number (I) analogous to the usual spin quantum number. Thus the neutron and proton, now collectively known as the nucleon, were assigned isospin ¹/₂; the pion, in all its charge states, isospin 1; and so on. Because isospin was supposed to be a vector quantity, its 3-component (I₃) was supposed also to be quantised, and different I₃ values were taken to distinguish between different members of each isospin family or multiplex. For the isospin ¹/₂ nucleon, possible I₃ values were +¹/₂, identified with the proton, and –¹/₂, identified with the neutron. Similarly for the isospin 1 pion, an I₃ value of +1 corresponded to the π⁺, of 0 to the π⁰, and of –1 to the π^–. As more and more particles were discovered they were routinely assigned to isospin multiplets — (K⁺, K⁰), (K⁰, K^–), (Δ⁺⁺, Δ⁺, Δ⁰⁺, Δ^–), (Σ⁺, Σ⁰, Σ^–), and so on. Particles with no partners, like the neutral A, were assigned to one-member groups or ‘singlets’.

Isospin, like parity and strangeness, was supposed to be exactly conserved by the strong interaction. But to explain the small observed mass differences within isospin multiplets (1 MeV between the proton and the neutron, for example) it was assumed that, unlike parity and strangeness, isospin conservation was violated by the electromagnetic as well as the weak interaction. The small observed violations of isospin conservation — the mass differences or splittings between members of a given multiplet — were ascribed to both weak and electromagnetic effects. These represented a minor perturbation in relation to the dominant strong interaction, and isospin conservation  {55}  thus remained a powerful tool in the analysis of strong-interaction processes.

SU(3): The Eightfold Way

Strangeness and isospin constituted new and empirically useful analytic tools with which to make sense of the properties of the many new particles discovered in the 1950s. Isospin, moreover, brought economy as well as order by grouping different particles into multiplets. As far as the strong interactions were concerned theorists had effectively fewer particles to deal with, since they had only to consider the overall properties of multiplets rather than the individual members of each. In the latter half of the 1950s many theorists attempted to build upon this success, looking for ways to achieve even greater economy by grouping particles into larger families. Their efforts culminated in 1961 with the ‘Eightfold Way’ or su(3) classification of hadrons. The content of the Eightfold Way scheme is perhaps most readily explained in terms of quarks, but this would be to invert the historical sequence. Here I will sketch out the process which led to the establishment of su(3); further clarification can await Chapter 4 wherein quarks themselves appear.

To explain what the Eightfold Way scheme entailed, it is useful to discuss isospin conservation in more formal terms. In theoretical physics there is a direct connection between conserved quantities and ‘symmetries’ of the underlying interaction. Thus the strong interaction, which conserves isospin, is said to possess an isospin symmetry. This corresponds to the fact that the choice of axis against which to measure the 3-component of isospin is arbitrary. A change of axis would entail different definitions of physical particles — if one reversed the direction of the 3-axis, for example, the π⁺ would have I₃ = –1 instead of +1 — but this would be irrelevant as far as the strong interaction is concerned: the strong interaction is said to be ‘invariant’ under transformations of I₃. In mathematical terms, such changes of axes are known as ‘symmetry operations’, and form the basis of a branch of mathematics called ‘group theory’. Different symmetries correspond to different symmetry groups, and the group associated with the arbitrariness of the orientation of the isospin axis is conventionally denoted as ‘su(2)’.²¹ Associated with each mathematical group is a set of ‘representations’ describing the families of objects which transform into one another under the relevant symmetry operation. The representations of su(2) can accommodate any integral number of objects, and each isospin multiplet can be identified with an appropriately sized representation of the group.

By making the connection with group theory, physicists translated  {56}  the search for a classification wider than isospin into the search for a more comprehensive group structure — a higher symmetry of the strong interactions with representations suitable to accommodate particles of different isospin and strangeness. Many groups were tried and found wanting, and I will discuss only the one which was finally accepted. First proposed in 1961 by Murray Gell-Mann and the Israeli theorist Yuval Ne'eman, this was the group which mathematicians denote ‘su(3)’ and which Gell-Mann, in a reference to Buddhist philosophy, christened the Eightfold Way.²² It is interesting to note that, in their original papers, neither Gell-Mann nor Ne'eman was aiming simply at the classification of hadrons. Both were also attempting to set up a detailed quantum field theory of the strong interaction. Indeed, as discussed further in Chapter 6, both formulated their proposals on the basis of gauge theory — the particular variant of quantum field theory destined to constitute the conceptual framework of the new physics.²³ However, the early 1960s saw the rapid development of a radical alternative to the field theory approach to strong-interaction physics (see Section 4 below) and field theory itself quickly went out of fashion.²⁴ Thus, very soon after its invention, su(3) was divorced from its roots in gauge theory and left to stand or fall on its merits as a classification system.

Those merits were the following. According to su(3), particles having the same spin and parity but different isospin and strangeness can be grouped into large families or multiplets. These families contain fixed numbers of particles — 1, 3, 6, 8, 10, 27, etc. — which are determined by the representation structure of su(3), and which fall into characteristic patterns when plotted against strangeness and the third component of isospin. Figure 3.2 shows the su(3) multiplet assignments for the lower mass mesons, and Figure 3.3 shows the lower mass baryon families. One point of confusion may possibly arise here. As indicated in Figure 3.3, the lower mass baryons can be assigned to 8 and 10 member families-an ‘octet’ and a ‘decuplet’ — corresponding to the 8 and 10 member representations of su(3). But the mesons are shown in Figure 3.2 as belonging to two 9 member families — ‘nonets’ — and from the list just quoted it is evident that there is no 9 member representation of su(3). The existence of meson nonets is explained by the quantum-mechanical concept of ‘mixing’. Mixing comes about because one member of each su(3) meson octet has zero isospin and strangeness — the same quantum numbers as the su(3) singlet. Since su(3) is not an exact symmetry (see below) the singlet and octet mesons can mix: the physically observed isospin and strangeness zero mesons are not pure su(3) octets or singlets, but are  {57}  instead mixtures of both. Thus, for mesons, octets and singlets lose their separate identities and are better represented as nonets.

Figure 3.2. su(3) classification of low-mass mesons: (a) spin 0 nonet; (b) spin 1 nonet. The hypercharge quantum number (Y) is given by the sum of the baryon and strangeness quantum numbers, and is the relevant group-theoretical variable.

Agreement that the su(3) multiplet structure was to be found in nature was only reached after several years’ debate within the hep community. One key problem was that early experiments indicated that the lambda and sigma baryons had opposite parity.²⁵ This made the su(3) assignment of the sigma and lambda to the same family (Figure 3.3(a)) impossible, and favoured alternative classificatory schemes. Only in 1963 did experimenters at the cern ps report that the lambda and sigma had the same parity, making the su(3) assignment tenable.²⁶ A further obstacle to the acceptance of the Eightfold Way classification was that the mass differences within su(3) multiplets were of comparable size to the particle masses. This

Figure 3.3. su(3) classification of low-mass baryons: (a) spin 1/2 octet; (b) spin 3/2 decuplet.

was especially true of the lowest mass meson nonet, where the splitting between the pion and kaon masses was of the order of 360 MeV, around three times greater than the mass of the pion itself. Unlike the small splittings within isospin multiplets, such large mass differences could not be explained away as electromagnetic or weak perturbations: they were presumably intrinsic to the strong interaction. su(3) was not thus an exact symmetry of the strong interaction like isospin; it was an approximate or ‘broken’ symmetry.

In order to deal with the novel problem of a broken symmetry, Gell-Mann and the Japanese theorist Susumu Okubo followed the strategy of assuming a simple but plausible form for the su(3)-breaking component of the strong interaction, which they used to derive  {59}  mass relations between members of su(3) multiplets.²⁷ The Gell-Mann-Okubo mass formula fitted the su(3) assignments for the nucleon octet and spin 1 meson nonet extremely well, and the spin 0 meson nonet at least fairly well. For the spin ³/₂ baryon decuplet shown in Figure 3.3(b), the formula reduced to an equal-spacing rule: the mass-differences between Δ and Σ*, Σ* and Ξ*, and Ξ* and Ω^– were all predicted to be equal. In 1961 only the Δ had been experimentally observed. At an international conference held at cern in 1962 the first evidence for the existence of the Σ* and Ξ* was reported, with masses confirming the equal-spacing rule. Gell-Mann took this as an opportunity to make a prediction of the mass and properties of the hitherto unseen Ω^–.²⁸ The equal-spacing rule gave a mass of 1685 MeV for the Ω^–, and its assignment to the su(3) decuplet required it to carry three units of strangeness. This combination implied that it could not decay via the strong interactions, instead decaying only weakly and with a very long lifetime. Such a massive yet long-lived particle offered a highly distinctive signature for experiment, and attempts to observe the required events soon got under way. First to the post was a group of experimenters working at the Brookhaven ags who, in February 1964, reported the discovery of a particle of mass 1686±12 MeV with just the right decay properties.²⁹ The discovery of the Ω^– was only the most visible and straightforward manifestation of the predictive and explanatory successes of the su(3) scheme, and from 1964 onwards there was little argument within the hep community against the conclusion that su(3) was the appropriate classification system for hadrons. 1964 was also the year in which quarks were born, transforming the su(3) approach and, for the time being, thrusting its gauge-theory origin into yet deeper obscurity. We will take up this thread of the story again in Chapter 4. First some more background on prior developments in theoretical hep is needed.

3.3 Quantum Field Theory

The use of conservation laws, symmetry principles and group theory brought some order into the proliferation of particles. su(3), for example, not only provided a classification scheme for hadrons but also predicted relations between cross-sections for the interaction of particles from different multiplets. But this was a broad approach and gave no clue to the detailed dynamics of the interactions which gave rise to those cross-sections. In pursuit of a detailed dynamical scheme, hep theorists again picked up a set of tools inherited from their pre-war forebears and attempted to adapt them to contemporary needs.

Quantum Electrodynamics

Theoretical hep's inheritance from the pre-war era was quantum field theory.³⁰ Quantum field theory is just what its name implies — the quantum-mechanical version of classical field theory. When the tools of quantum mechanics had been assembled in workable form in the 1920s, one of their first applications was to the field theory of electromagnetism developed by Maxwell. The quantised theory of the interactions of charged particles — quantum electrodynamics, or qed, as it became known — was successful in explaining an enormous range of topics in atomic physics, and this success contributed to the general acceptance of quantum mechanics itself. Even so, pre-war qed suffered from a theoretical disease which was only cured in the late 1940s. The cure transformed qed into the most powerful and accurate dynamical theory ever constructed, and was the single most influential theoretical achievement in the formative post-war years of hep. The disease and its cure cast their shadow over all that followed and bear examination in some detail. We can begin with a general outline of calculational procedures in qed. This will provide essential background to the discussion of qed's disease, and will also serve to typify the traditional approach to the construction of field theories of the weak and strong interactions. For reasons which will quickly become evident, this traditional approach is often known as ‘perturbative’ or ‘Lagrangian’ field theory.

The standard way in which to formulate a quantum field theory is to construct a mathematical quantity known as the Lagrangian of that theory. In highly schematic notation, the Lagrangian for qed can be written as:³¹

L(x) = ψ(x) D ψ(x) + m ψ(x) ψ(x) + (DA(x))² + eA(x) ψ(x) ψ(x).

Here L(x) is the so-called Lagrangian density at space-time point x, with ψ(x) and ψ(x) representing the electron and positron fields at point x, and A(x) being the electromagnetic field. D is a ‘differential operator’, so that Dψ and DA represent field gradients in space-time. e and m represent the charge and mass of the electron respectively. As in classical electrodynamics, all of the properties of systems of charged particles are supposed to be derivable from the qed Lagrangian. I will not go into the mathematics of such derivations, but I will try to outline some of the salient features. The simplest way to do this is diagrammatically. Each term in the qed Lagrangian can be represented by a diagram, understood as a shorthand notation for a well-defined mathematical expression. The first term ψDψ generates  {61}  the diagram of Figure 3.4(a). This is known as the electron ‘propagator’, and represents an electron (or positron) travelling freely through space in the direction indicated by the arrow. If only the first term were included in the Lagrangian then the mathematical expression associated with Figure 3.4(a) would be appropriate to a zero-mass electron. When the second term, mψψ, is included, the diagram is unchanged but the associated expression becomes that appropriate to an electron with mass m. Like the first term, the third term, (DA)², generates a diagram corresponding to a particle travelling freely through space. In this case the particle is the photon, the quantum of the electromagnetic field, as shown in Figure 3.4(b). Note that there is no mA² term in the Lagrangian analogous to the mψψ term for the electron. This indicates that the photon is being represented as a zero-mass particle. The absence of a mass-term for the photon arises from the fact that electromagnetism is a long-range force which acts over macroscopic distances. According to the Uncertainty Principle the range over which forces act is limited by the mass of the particle responsible for them, and only zero-mass particles can give rise to forces appreciable over macroscopic distances.³²

If only the first three terms are included in the Lagrangian, qed is an exactly soluble theory. The dynamics of any collection of electrons, positrons and photons can be exactly described — whatever particles are present simply propagate freely through space. Unfortunately, this ‘free-field’ solution is trivial. It is precisely the interactions of particles which hep theorists seek to analyse, and these are not described by the first three terms of the qed Lagrangian. Enter the fourth term, eAψψ. Unlike the first three terms which are ‘bilinear’, containing only two fields, the fourth term is ‘trilinear’: it contains two electron fields and a photon field. It represents the fundamental interaction or coupling between electrons and photons, as indicated in Figure 3.4(c). Figure 3.4(c) represents the electron-photon vertex, and is associated with a mathematical expression essentially given by the magnitude of the electron charge, e.

Figure 3.4. Basic diagrams in qed: (a) electron propagating through space; (b) photon propagating through space; (c) electron-photon vertex.

When diagrams of the type shown in Figure 3.4(c) are taken into consideration, qed becomes a physically interesting theory capable of describing interacting particles. Thus, for example, when the full Lagrangian is used, electron-electron scattering can be represented by Figure 3.5(a). Here two electrons (e^–) travel in from the left as indicated by the arrows; they interact and scatter off one another as a photon (γ) carrying energy and momentum passes between them; and then move off to the right. A well-defined mathematical expression can be associated with Figure 3.5(a) and is found to reproduce quite well the measured cross-sections for electron-electron scattering. However, in qed there is no reason why Figure 3.5(a) should lead to exact predictions for the interactions of charged particles. In principle, processes of much greater complexity could intervene in the scattering process. For example, the exchanged photon could convert to an electron-positron pair which would subsequently recombine, as in Figure 3.5(b), or one of the incoming electrons might emit a photon and reabsorb it on the way out, as in Figure 3.5(c). And, in general, the exchange of arbitrarily large numbers of photons, electrons and positrons can contribute to electromagnetic interactions.

Figure 3.5. Electron-electron scattering in qed: (a) one-photon exchange; (b) and (c) more complex exchanges.

The inclusion of the interaction term in the qed Lagrangian makes the theory physically-interesting. But it also makes the theory extremely complex mathematically, since very complicated multiparticle exchanges have to be taken into account in the analysis of physical systems. Indeed, no exact solutions to the qed equations are known, nor have such solutions ever been shown rigorously to exist. There is, however, one consolation for the qed theorist. I noted above that the overall magnitude of the expression corresponding to the  {63}  electron-photon vertex (Figure 3.4(c)) is given by e, the charge of the electron. The overall magnitude of Figure 3.5(a) is then given by e² — there are two electron-photon vertices, one for the emission of the photon the other for its absorption. The magnitude of the expressions for Figures 3.5(b) and (c), on the other hand, is e⁴, since there are two photons and four vertices. Similarly, whenever three photons appear the magnitude of the appropriate expression is e⁶ and, in general, for n photons the magnitude is e²ⁿ. For every photon line added to a diagram, the magnitude of the associated expression changes by a factor of e². For purposes of practical computation this is extremely important, e² is a small number (roughly 1/137), which means that qed diagrams can be arranged in order of decreasing size — a so-called ‘perturbation expansion’ — making possible the computation of sensible and systematic approximations to the unknown exact predictions of qed. In qed, the dominant contribution — the ‘first-order’ approximation — to electron-electron scattering is given just by the one-photon exchange diagram, Figure 3.5(a). The theorist can calculate this, and feel confident that diagrams involving more photons will contribute terms which are at least 137 times smaller and less important. The diagrams involving more photons correspond to small corrections or ‘perturbations’ relative to the first-order term. For greater precision, the theorist can calculate the second-order approximation corresponding to diagrams involving two photons, such as those of Figures 3.5(b) and (c), and still feel confident that the terms which he is omitting are at least 137 times smaller than those which he is including. The even more determined theorist can go to the third-order approximation by calculating and summing the three-photon diagrams, and so on. In this way more and more precise approximations to the exact but unknown predictions of qed can be systematically developed by evaluating successive terms in the perturbation expansion.

One problem with the perturbative approach to qed remains to be discussed, the theoretical disease mentioned above, but before we come to that it may be useful to clarify some basic features of the quantum field theory approach. One general feature which is implicit in the diagrammatic analysis but which should be made explicit is that in quantum field theory all forces are mediated by particle exchange: action-at-a-distance plays no part in quantum field theory. In qed the force-transmitting particle is the photon; the analogous particles for the weak and strong interactions will be discussed below. It is equally important to stress that the exchanged particles in the diagrams are not observable: the diagrams of Figure 3.5 should not be thought of as resembling, say, bubble-chamber pictures. In a bubble  {64}  chamber, it would be possible to photograph the tracks of the incoming and outgoing electrons, but the exchanged particles — the photons and electron-positron pairs-would leave no record. To explain why this is so, it is necessary to make a distinction between ‘real’ and ‘virtual’ particles. According to the theory of special relativity, there is a fixed relation between a particle's energy (E), momentum (p) and mass (m): E² = p² + m².³³ All observable particles, like the incoming and outgoing electrons in Figure 3.5, obey this relation and are said to be ‘real’. If one applies the law of energy-momentum conservation to, say, Figure 3.5(a), one finds that the photon is not real: E² – p² is not zero for this photon, as it should be for a real zero-mass particle. A similar calculation for the intermediate electron and positron of Figure 3.5(b) shows that they are not real either: their energies and momenta do not conform to the relation E² – p² = m². Such particles with unphysical values of energy and momentum are said to be ‘virtual’ or ‘off mass-shell’ particles. In classical physics they could not exist at all — the concept of a virtual particle is classically meaningless. In quantum physics, in consequence of the Uncertainty Principle, virtual particles can exist, but only for an infinitesimal and experimentally undetectable length of time. In fact, the lifetime of a virtual particle is inversely dependent upon how far its mass diverges from its physical value. Only when the energy and momentum of a particle conform to relation E² – p² = m² can the particle persist indefinitely through time — as one expects real particles to do.

Renormalisation

We now come to the disease of qed and its eventual cure. From the perspective of calculation there are two important differences between diagrams (b) and (c) and diagram (a) of Figure 3.5. On the one hand, diagrams (b) and (c) contain two photons and are thus a factor of 137 times smaller than diagram (a) (for the sake of brevity, I shall speak of diagrams as equivalent to the associated mathematical expressions from now on). On the other hand, diagrams (b) and (c) contain ‘closed loops’ of particles — the e⁺e^– loop of diagram (b) and the e^–e^–γ loop of diagram (c) — which create great computational difficulties. This is because although the total flow of energy-momentum through any loop is given by the law of energy-momentum conservation, the way in which the energy-momentum is shared between the particles of the loop is not so determined. For example, whatever energy-momentum is carried by the virtual photons of diagram (b) can be divided in an infinite number of ways between the virtual electron and positron which make up the intermediate loop.  {65}  Calculation of diagram (b) requires that one take this into account by summing over the infinite range of momenta of, say, the virtual positron. Now, in principle there is no problem in performing these sums as mathematical integrals over the infinite range of loop momenta. But when one performs them they ‘diverge’ — the integrals are formally infinite. Diagrams with closed loops — (b) and (c) of Figure 3.5, and the vastly more complicated diagrams which appear at higher orders of approximation in qed — are all infinite.³⁴ But these diagrams are supposed to correspond to experimentally measurable quantities, like the cross-section for electron-electron scattering, which are manifestly not infinite but finite. Thus much was recognised by pre-war theoretical physicists as the underlying disease of qed. The infinities caused no great practical problems — for most applications physicists could content themselves with the first-order approximation to qed (Figure 3.5(a), which contains no closed loops) and forget the rest — but, even so, they were taken by many to indicate a defect in the conceptual fabric.³⁵ As hep theorist Steven Weinberg wrote: ‘Throughout the 1930s, the accepted wisdom was that quantum field theory was in fact no good, that it might be useful here and there as a stopgap, but that something radically new would have to be added in order for it to make sense’.³⁶ Possible revisions included hypothesising a granular structure of space-time or abandoning field theory altogether, but these went by the board in the late 1940s.

In June 1947 a four day conference on the foundations of quantum mechanics was held at Shelter Island, New York. The centre of attention was a precision measurement of the hydrogen atom spectrum made by Willis Lamb and R.C.Retherford. Using microwave techniques developed during the war, Lamb and Retherford found that the energies of the first two excited states of hydrogen, predicted to be equal by the first-order qed calculation, differed by about 0.4 parts per million. The measurement of the ‘Lamb shift’, indisputably a second-order effect if qed were to make sense, brought matters to a head and resulted in the triumph of the ‘renormalisation’ programme. This programme ultimately accomplished the following. If one computes an electromagnetic process — such as the electron-electron scattering shown in Figure 3.5 — to an arbitrarily high order of approximation, including an indefinite number of closed loops, one finds that only a small number of distinct types of infinities occur. These can be understood as infinite contributions to the electron mass, charge and so on. If one puts up with this and, at the end of the calculation, sets the apparently infinite mass and charge of the electron equal to their measured values, one arrives at perfectly  {66}  sensible results. This ‘renormalisation’ of the theory by absorption of infinities into physical constants appeared intuitively suspect. But it immediately gave a quantitative explanation of the Lamb shift and subsequently went from strength to strength. In renormalised qed, calculations of electromagnetic processes could be pushed to arbitrarily high orders of approximation and always seemed to come out right. As Weinberg remarked in 1977:

For instance, right now the experimental value of the magnetic moment of the electron is larger than the Dirac value by 1.15965241 parts per thousand, whereas theory gives this anomalous magnetic moment as 1.15965234 parts per thousand, with uncertainties of about 0.00000020 and 0.00000031 parts per thousand, respectively. The precision of agreement between theory and experiment here can only be called spectacular.³⁷

The renormalisation idea had been suggested before the war by Weisskopf and Kramers, and was carried through in the late 1940s by Sin-Itiro Tomonaga and his colleagues in Japan, and by Julian Schwinger and Richard Feynman in the usa. In 1949 the British theorist Freeman Dyson completed the proof of the renormalisability of qed to all orders of approximation and showed the equivalence of the different approaches of Tomonaga, Schwinger and Feynman; these three later shared the 1965 Nobel Prize for Physics for their work. The most intuitively transparent renormalisation procedure was that developed by Feynman. His approach utilised diagrams like those in Figures 3.4 and 3.5, which subsequently became known as 'Feynman diagrams’. He derived a set of rules for associating a mathematical expression with each diagram, and these became known as ‘Feynman rules’. The divergent integrals became ‘Feynman integrals’.³⁸ The diagrammatic approach characterised much of the subsequent development of quantum field theory — as Schwinger recalled in 1980: ‘Like today's silicon chip, Feynman diagrams brought calculation to the masses’.³⁹

The success of the renormalisation programme transformed the quantised version of that most venerable of field theories, Maxwell's electromagnetism, into a theoretical instrument capable of describing the electromagnetic interactions of charged particles to an apparently arbitrary degree of accuracy. Not surprisingly, therefore, in the early 1950s almost all hep theorists attempted to build upon this success and to reach a fundamental understanding of the remaining forces — the weak and strong interactions — in terms of quantised theories of appropriate fields. Soon, however, this enterprise was looking even sicker than pre-war qed. To quote Weinberg again: For a few years after 1949, enthusiasm for quantum field theory  {67}  was at a high level. Many theorists expected that it would soon lead to an understanding of all microscopic phenomena, not only the dynamics of photons, electrons and positrons. However, it was not long before there was another collapse in confidence — shares in quantum field theory tumbled on the physics bourse, and there began a second depression, which was to last for almost twenty years.⁴⁰ The depression lasted until 1971, when there was an explosion of interest in one particular class of quantum field theories — gauge theories. We can pick up this thread of the story in Chapter 6 below. For the moment, the question is why did the depression begin? The quantum field theory approaches to the weak interaction and to the strong interaction failed for different reasons. Let us examine them each in turn.

The Weak Interaction

Beta decay, the emission of electrons and positrons from unstable nuclei, was one of the principal themes of radioactivity research in the early decades of the twentieth century. It was an especially puzzling phenomenon in that electrons were emitted over a range of energies; their energy spectrum was continuous, rather than discrete as expected for transitions occurring in a quantised system.⁴¹ Amongst the fathers of quantum mechanics, Bohr, Heisenberg and Pauli each proposed radical explanations for this observation — Bohr, that energy was not exactly conserved; Heisenberg, that space-time was not continuous — but it was Pauli's proposal that won the day. In 1930, Pauli suggested that in beta-decay two particles rather than one were emitted: the electron was accompanied by an electrically neutral massless lepton which carried off energy undetected. Because the latter particle, the neutrino, went unseen, a truly quantised total energy spectrum appeared experimentally as a continuous spectrum of electron energies. In 1934, Enrico Fermi formalised Pauli's suggestion by constructing a quantum field theory of the force responsible for beta-decay, the weak interaction.⁴² Fermi modelled his theory as closely as possible upon the existing theory of qed. Figure 3.6 will help to explain how he did this.

Figure 3.6(a) shows a possible mechanism for the weak decay of the neutron, directly modelled upon qed. The neutron converts into a proton by emitting a particle, labelled W, which is the weak-interaction analogue of the photon. The W particle is a prototypical intermediate vector boson, of the type already mentioned in connection with the weak interactions in Chapter 2.3 (recall that particles which have spin 1, like the photon and the hypothetical W, are

Figure 3.6. Neutron beta-decay.

generically known as vector particles). Because the neutron and proton differ in electric charge by one unit, the W itself must carry a charge (unlike the photon which is electrically neutral). The emitted W-particle then disintegrates into an electron-antineutrino (e-ν) pair, in the same way as a photon can convert into an electron-positron pair. However, Figure 3.6(a) does not correspond exactly to the weak-interaction theory enunciated by Fermi. The photon has zero mass which, according to the Uncertainty Principle, corresponds to a force of infinite range (as necessary to represent the macroscopic effects of electromagnetism). The weak force was known to be of short range, even on the typical length-scale of nuclear physics (10^–13 cm). According to the Uncertainty Principle again, short-range forces correspond to the exchange of massive particles, and Fermi effectively assigned the W infinite mass by contracting the weak interactions to a point in space, as shown in Figure 3.6(b). The interaction shown there was known as a current-current interaction, since it was analogous to two electric currents (here, n-p and e-ν) interacting directly without exchanging a photon. In the following years, a great deal of evidence was amassed in favour of Fermi's theory, but one key element was lacking — evidence for the existence of the neutrino itself.⁴³ This was forthcoming in 1953, when events induced by the neutrino flux from a nuclear reactor were reported by us experimenters F.Reines and C.L. Cowan.⁴⁴

In 1956, hep theorists T.D.Lee and C.N.Yang proposed, in response to the so-called ‘τ–θ’ problem concerning the weak decays of kaons, that parity conservation might be violated by the weak interaction. This proposal was quickly confirmed in several nuclear physics and hep experiments, and Lee and Yang shared the 1957 Nobel Prize for Physics for their part in this development.⁴⁵ The discovery of parity nonconservation required detailed amendments  {69}  to weak interaction theory, but the general form of Fermi's current-current interaction emerged unscathed in the ‘V minus A’ (V–A) theory of the weak-interactions published in 1958 by Feynman and Gell-Mann, and independently by two other us theorists, R. Marshak and E. Sudarshan.⁴⁶ Following the discovery of parity nonconservation, it was argued that the weak interaction respected a less restricted conservation law known as cp invariance. Although parity was no longer supposed to be a good quantum number of the weak interaction, the combined operation of charge-conjugation (c: replacing particles by antiparticles) and space reflection (p: inverting spatial coordinates) was still supposed to yield a good quantum number, cp. However, in 1964 further experiments on kaon decays pointed to the conclusion that the weak interactions did not even conserve cp.⁴⁷ Theorists accommodated to this observation as they had to parity-violation, and once more the overall current-current picture of the weak interaction emerged unscathed.⁴⁸

Throughout the 1950s and 1960s, then, the current-current quantum field theory was, in various guises, successful in organising a wide range of weak-interaction data. It suffered, though, from two major theoretical shortcomings. The first was that it was non-renor-malisable. As in the case of qed, the diagram of Figure 3.6(b) represents not the entire content of the Fermi theory but only the first approximation to its solution. Higher-order approximations correspond to more complex diagrams in which closed loops and numerically infinite integrals appear. When they came to compute these higher-order diagrams, theorists concluded that current-current theories involved ever more types of infinity at succeeding levels of the perturbation expansion. This plethora of infinities could not be conjured away by redefining a few parameters (as was done in qed) and higher-order calculations therefore appeared meaningless. In this respect the current-current weak-interaction theory was sicker than qed had ever been, and this was the first roadblock encountered by the attempts to model the weak interactions on electromagnetism.

One response to the sickness of the Fermi theory was the same as that taken by many theorists to the pre-war sickness of qed: to use the well-defined first-order diagram for calculation of weak-interaction processes, and to disregard higher-order corrections. But here, too, clouds loomed on the horizon. According to the Feynman rules for two currents interacting at a point in space, weak cross-sections were expected to increase in direct proportion to beam energies. This was nice for experimenters, since it promised easier detection of weak processes as higher-energy beams became available. On the other hand, it was obvious that at sufficiently high energy, weak cross-sections  {70}  must violate the ‘unitarity limit’. Unitarity was simply a statement of the conservation of probabilities in hep terms. As such it was strongly held, and violation of unitarity, even at energies only attainable with some future machine, was regarded as pointing to a failing of the first-order diagram.

One way in which to avert, or at least postpone, the ‘unitarity catastrophe’ was to work with theories of the type shown in Figure 3.6(a). In these, the weak interaction was mediated by a charged W-particle of finite mass, an intermediate vector boson, with the result that cross-sections were predicted to be better behaved at high energies. Theoretically, this line of thought was one strand leading eventually to the unified electroweak gauge theories discussed in Chapter 6. Experimentally, W-particle theories inspired a redirection of weak-interaction physics. In the 1940s and 1950s, experimental investigations had focused upon weak decay processes — the systematics of pion, kaon, lambda, sigma decay, and so on. In the 1960s experiments began which instead hoped to produce W-particles in high-energy scattering experiments using either neutrino or hadron beams. None of these experiments bore the expected fruit of the W (until, perhaps, 1983). But, as discussed in later chapters, they quite unintentionally laid the experimental basis of the new physics in ps experiments.

The Strong Interaction

The quantum field theory of the weak interaction, despite its manifest theoretical shortcomings, offered a coherent organising principle for weak-interaction research in the early decades of hep. This could not be said of the attempts which were made at a field theory of the strong interactions. While the failings of the Fermi theory were problems of principle, those of strong-interaction field theories were immediate and pressing.

The prototypical quantum field theory of the strong interaction was that proposed by Yukawa in 1935.⁴⁹ Like Fermi's theory of the weak interaction, Yukawa's was explicitly modelled upon qed. Following the reasoning discussed above, Yukawa argued that since the strong interaction was a short-range force, it must be carried by a non-zero-mass particle. Typical nuclear dimensions were of the order of 10^–13 cm, and Yukawa suggested that this would correspond to the existence of a particle having a mass of around 100 MeV. The properties of a suitable particle — the 140 MeV pion — were established in cosmic-ray and accelerator experiments in the late 1940s, and for a while the situation seemed rather straightforward. Theorists found no difficulty in writing down renormalisable field theories of  {71}  the strong interaction in which, for instance, nucleons interact with one another via the exchange of pions, as shown in Figure 3.7(a). Neither, as more particles were discovered, did they find it difficult to arrange for the conservation of isospin and strangeness: Figure 3.7(b) shows the associated production of kaons and lambdas in the interaction of pions and protons.

Figure 3.7. Strong interactions in Yukawa theory.

But despite their renormalisability and their respect for conservation laws, quantum field theories of the strong interaction were quickly perceived to be useless. The problem lay in a breakdown of the perturbation expansion. In qed, the contributions of complicated diagrams were suppressed by the appearance of factors of e². e² was a small number (1/137) and complex multi-loop diagrams made a similarly small contribution to the perturbation expansion. The strong-interaction analogue of e was the strong-interaction coupling constant (g) which fixed the strength of the hadron-hadron vertices (such as the meson-meson and meson-nucleon vertices of Figure 3.7). And the experimentally determined value of g² was around 15. Thus successively more complicated diagrams in strong-interaction field theories grew by a factor of 15, rather than diminishing by a factor of 137 as in qed.

In field theories of the strong interaction, then, it made little sense to rely upon a first-order term which was followed by an infinite series of ‘perturbations’ of increasingly greater magnitude. This was the conclusion of the hep theorists who attempted to develop field theories of the strong interaction. They drew the moral that in order to make any kind of predictions in such theories, it was necessary first to sum the entire perturbation series in its infinite complexity. Unfortunately, they had no idea how to do this, and the field-theory  {72}  approach to the strong interaction therefore appeared doomed to failure.⁵⁰ As Weinberg later wrote: ‘It was not that there was any difficulty in thinking of renormalisable quantum field theories that might account for the strong interactions — it was just that having thought of such a theory, there was no way to use it to derive reliable quantitative predictions, and to test if it were true’.⁵¹

Thus, by the mid-1950s shares had tumbled in the field-theory approach to the weak and strong interactions. The problems besetting theorists were far greater in respect of the strong interaction, in terms of both the range of data to be explained and of immediate calculational impotence. In the following section we can see how they accommodated themselves to this uncomfortable situation.

3.4 The S-Matrix

The central problem with field theories of the strong interaction lay in their description of hadronic processes as a perturbation series of Feynman diagrams. Theorists did not know how to sum this series. However, they reasoned, the individual terms of the series have no necessary physical significance: one cannot directly observe nucleons, say, exchanging pions as they scatter in an hep experiment. All that one can observe is that, in the course of an experiment, an initial collection of particles of specified quantum numbers and momenta is transformed into a different final state. All that can be known, therefore, is enshrined in the set of transition probabilities that from given initial states one will arrive at given final states. Thus, in the 1950s one reaction against the failure of field theory in strong-interaction physics was to turn away from intractable Feynman diagrams towards the transition probabilities themselves — perhaps at this level of analysis some sense could be made of the strong interaction.

For historical reasons, the entire array of probabilities covering transitions between all conceivable initial and final states was known as the Scattering- or S-matrix.⁵² The basic framework of the S-matrix approach to hep was laid down in the immediate post-war period, largely in response to the problem of infinities then plaguing qed. With the advent of renormalisation little further attention was paid to the S-matrix — until, that is, the problems of strong-interaction theory began to be acutely felt. From the mid-1950s onwards, an increasing number of theorists turned their attention to the S-matrix. Since they had no other theoretical tools available they inevitably — but ironically, in view of some later developments — used quantum field theory and diagrammatic techniques to explore the general properties of the S-matrix. As us hep theorist Geoffrey Chew wrote  {73}  in 1966: ‘All results at this stage [1958]. . . were either motivated by, or derived from, field theory’.⁵³ Between 1956 and 1959, the work of Chew, Gell-Mann and others, established a theoretical result of primary significance: the S-matrix could be regarded as an ‘analytic’ function of the relevant variables.⁵⁴ The concept of an analytic function was one which was already well explored in the branch of mathematics concerned with functions of ‘complex’ variables.⁵⁵ This branch of mathematics therefore provided a pool of conceptual resources with which theorists could elaborate models of the S-matrix in its own right as an analytic function. Thus it became possible to proceed with S-matrix theory as an autonomous research programme, independently of its origins in quantum field theory. In the early 1960s, many hep theorists took this opportunity to abandon the traditional field-theory approach to particle interactions. Some theorists persisted with diagrammatic, perturbative field-theory techniques, but now used them heuristically in sophisticated investigations of the analytic properties of the S-matrix.⁵⁶ Alternatively, and more adventurously, some theorists pronounced field theory dead — at least in respect of the strong interactions. The leader and spokesman of this group was Chew. From his base at the University of California at Berkeley Chew expounded the explicitly anti-field-theory ‘bootstrap’ philosophy.⁵⁷

The essence of the bootstrap was this. Consideration of the analytic structure of the S-matrix led to an infinite set of coupled non-linear differential equations. No one knew how to solve this set of equations exactly — it would have amounted to a solution of strong-interaction physics — but Chew proposed that it did have a solution; that the solution was unique; and that, through the requirement of self-consistency, it determined all of the properties of all of the hadrons. If this were the case, the general properties of the S-matrix determined everything about hadrons, and reference to field theory was, at best, a waste of time. Chew described his approach as ‘democratic’ — since all of the hadrons, stable and unstable, were supposed to pull themselves up by their bootstraps as a self-consistent solution to the S-matrix equations — in contrast to the ‘aristocratic’ qft approach, wherein each particle was assigned its own quantum field. The bootstrap was a statement of faith on Chew's part. Since the infinite set of equations could not be solved, it was hard to evaluate his assertions. Nevertheless, ways were found of implementing an approximate bootstrap programme. By truncating the infinite set of equations, for example, it was possible to calculate self-consistently the properties of rho mesons using as input only the properties of pions,⁵⁸ and to derive an su(3) hadronic symmetry using as input  {74}  only isospin.⁵⁹ Such approximate implementations of the bootstrap programme made it a viable alternative to the symmetry group approach to resonance physics in the early 1960s (until, that is, the advent of detailed quark-model analyses).

One final aspect of the S-matrix/bootstrap approach to strong-interaction physics remains to be discussed: Regge theory. The point of departure for Regge theory lay in work done in the late 1950s by the Italian theorist Tullio Regge. Working on formal problems connected with non-relativistic potential scattering, Regge pointed out the utility of examining analytic structure in terms of complex energy and angular momentum variables, rather than in terms of energy and momentum transfer.⁶⁰ Regge's work was seized upon by Chew and his collaborators and translated into relativistic, S-matrix language appropriate to the subject matter of hep.⁶¹ They argued that at high energies and small momentum transfers, the behaviour of the S-matrix could be understood in terms of the properties of a small number of ‘Regge poles’ — quasi-particles whose spin depended upon their energy. Whenever the energy of a Regge pole was such that its spin assumed a physical (integral or half-integral) value, it was supposed to manifest itself as an observable hadron. And, indeed, it was found experimentally that mesons and baryons appeared to lie upon ‘Regge trajectories’ with a linear relation between masses and spins, as shown in Figure 3.8.⁶²

Thus the Regge picture led to a novel classification of hadrons according to the trajectory on which they lay. More importantly, though, Regge theorists argued that their analysis was applicable to the high-energy soft-scattering regime which lay above the resonance region. In quantum-mechanical terms, scattering cross-sections were essentially squares of quantities known as scattering amplitudes (A). In the Regge picture, high-energy amplitudes had the form

A(s, t) ~ Γ(s/s₀)^α(t)

where s was the square of the centre-of-mass energy, t the square of momentum transfer, α(t) the spin of the appropriate Regge trajectory, and Γ and s₀ scale factors. Amplitudes of this form led immediately to two key predictions. First, high-energy cross-sections should depend smoothly upon s (for example, at zero momentum transfer, A(s) ~ s^α(0)); secondly, cross-sections should be soft, falling-off exponentially fast with t, that is A(t) ~ e^{α't ln(s/s₀)}, where a linear form, α(t) = α(0) + α't, has been assumed, to match the observed linear Regge trajectories. These two features were found to be characteristic of high-energy hadronic scattering. Figure 3.1 above shows the dependence upon beam momentum of the total and elastic

Figure 3.8. Various Regge trajectories for (a) mesons, and (b) baryons. Note the linear relation between spin (J) and mass-squared (M2).

cross-sections for pion-proton scattering. The bumpy resonance region extends up to beam momenta of around 2 GeV; beyond that cross-sections show the smooth variation predicted by Regge. Figure 3.9 shows the momentum-transfer dependence of high-energy pion-proton elastic cross-sections.⁶³ These decrease linearly with t when plotted on a logarithmic scale, corresponding again to the exponential fall-off expected in Regge theory.

Figure 3.9. High-energy elastic cross-sections (dσ/dt) for π+p and π-p scattering as a function of the square of momentum transfer (t). The curves are labelled by the pion beam momenta at which they were measured.

Experiment at the major accelerator laboratories generated enormous quantities of high-energy soft-scattering data during the 1960s. Regge theory offered a well matched set of analytical resources. Together, soft-scattering experiment and Regge theory constituted the high-energy wing of the old physics.⁶⁴ Regge theory led in the late 1960s to the ‘duality’ conjecture and to the ‘Veneziano’ or ‘dual resonance model’ of hadrons.⁶⁵ But these developments were at most  {77}  tangential to the development of the new physics. To explore them here would lead us too far afield. Instead we must return to the low-energy branch of the old physics, where we can examine the origins of the quark concept.

NOTES AND REFERENCES

PART II

CONSTRUCTING QUARKS AND

FOUNDING THE NEW PHYSICS:

hep, 1964–74

4
THE QUARK MODEL

In the 1960s the old physics split into two branches. The high-energy branch focused upon soft scattering, analysed in terms of Regge models, while at low energies resonance physics was the order of the day. In the early 1960s, group theory provided the most popular framework for resonance analysis but in the mid-1960s quark models took over this role. We can examine here how and why they did so.

4.1 The Genesis of Quarks

In early 1964, Caltech theorist Murray Gell-Mann published an article entitled ‘A Schematic Model of Baryons and Mesons’.¹ In it, he began by remarking that, ‘If we assume that the strong interactions of baryons and mesons are correctly described in terms of the broken “eightfold way”, we are tempted to look for some fundamental explanation of the situation’, and he went on to propose that hadrons should be seen as composite particles, built up from more fundamental entities which themselves manifested an su(3) symmetry. He indicated two possible choices for the building blocks. The first made use of four elementary entities, each carrying an electric charge of either 0 or 1 (in units of the charge of the electron). By taking appropriate combinations of these objects the observed su(3) multiplet structure of hadrons could be reproduced. However, there was an awkward asymmetry in this choice of entities — one particle acting as a ‘basic baryon’, and thus standing somewhat apart from the other three. As Gell-Mann remarked: ‘A simpler and more elegant scheme can be constructed if we allow non-integral values for the charges’.² The simpler and more elegant scheme was the quark model — proposed independently at around the same time by George Zweig, a Caltech graduate who was then visiting cern as a postdoctoral fellow.³ (Gell-Mann abstracted the name ‘quark’ from James Joyce's Finnegan's Wake; Zweig called his constituents ‘aces’ — as usual, Gell-Mann won.)

We shall see in the following two sections that Gell-Mann and Zweig formulated the quark concept in quite different ways, each of which was subsequently elaborated into a distinctive tradition of experimental practice. But before going into the differences between  {85}  the two schemes, it will be useful to review their common features and to relate these to the common background from which they derived. Gell-Mann and Zweig agreed not only that hadrons should have constituents but also upon what the basic attributes of those constituents should be. Quarks were supposed to have spin ¹/₂ and baryon number ¹/₃. As far as isospin and strangeness were concerned there were supposed to be three distinct species of quark: the ‘up’ (u) and ‘down’ (d) quarks made up an isospin ¹/₂ doublet of zero strangeness, and the ‘strange’ (s) quark an isospin 0 singlet of unit strangeness. Apart from the ¹/₃-integral baryon number, the oddest thing about quarks was their electrical charges: +²/₃ for the u quark, and –¹/₃ for the d and s quarks. From quark-antiquark pairs (qq) mesons could be constructed, and three quarks (qqq) would make a baryon. Thus, for example, the (ud) combination would have charge +1, strangeness 0 and baryon number 0 and could be identified with the spin 0 π⁺ (if the quark spins were antiparallel) or the spin 1 ρ⁺ (if the quark spins were parallel); similarly a spin ¹/₂ (uud) combination, having charge +1, strangeness 0 and baryon number 1 could be identified with the proton; (udd) with the neutron; (uds) with the lambda; and so on.

That Gell-Mann and Zweig should have chosen to suggest that hadrons were composites of the same fundamental entities was no coincidence, as one can see from an examination of the historical background to their proposals. The idea of reducing the number of elementary particles by explaining some of them as composite was by no means new. As early as 1949, C.N.Yang and Enrico Fermi had written a paper entitled ‘Are Mesons Elementary Particles?’, in which they speculated that the pion was a nucleon-antinucleon composite.⁴ When the strange particles began to be discovered, the Fermi-Yang approach was appropriately extended by several authors — most notably by the Japanese physicist S.Sakata in 1956.⁵ The fundamental entities of the Sakata model were the proton and neutron (as in the Fermi-Yang model) and the lambda, required to provide the additional element of strangeness. In the late 1950s, colleagues of Sakata at the University of Nagoya formulated his model in group-theory terms⁶ and, as Yuval Ne'eman later recalled, ‘throughout 1961–64, the Sakata model. . . was indeed the most serious competition to my own’.⁷ The competition was finally resolved in favour of the Eightfold Way by the 1964 discovery of the Ω^–: according to Gell-Mann and Ne'eman the Ω^– was the missing member of the spin ³/₂ baryon decuplet, while according to Sakata it contained at least three lambda particles — a most implausible hypothesis.  {86} 

The idea of composite hadronic systems was, then, quite familiar to hep theorists when quarks arrived. Furthermore, the group-theory approach to hadronic symmetries positively invited such a viewpoint. As we noted earlier, according to su(3) hadrons were expected to fall into multiplets containing 1, 3, 6, 8, 10, 27, etc., members, characteristic of the representations of su(3). Amongst these representations, the triplet, containing 3 members, was known as the ‘fundamental representation’ of su(3) (Figure 4.1) because all other representations could be derived from it by appropriate mathematical manipulations. Thus, even working in the pure su(3) tradition, theorists almost inevitably found themselves performing mathematical operations on the fundamental representation of the group. From there it was but a small step to the identification of the fundamental triplet representation of su(3) with a triplet of fundamental entities: the quarks.

Figure 4.1. Quarks as the fundamental representation of su(3).

These two features — awareness of the possibility of composite models, and operations on fundamental representations — were conspicuously present in both Gell-Mann and Zweig's development of the quark concept⁸ (as they were in the work of several other theorists working on symmetries of the strong interaction).⁹ Beyond that, however, Gell-Mann and Zweig's formulations of the quark model had only one thing in common: they were open to the same empirical objection — a free quark had never been seen. Routinely associated in physicists’ minds with the idea of compositeness was the idea that the primitive constituents should be experimentally detectable — the constituents of the atom, electrons and nuclei, could be routinely  {87}  exhibited in the laboratory, as could the nucieonic constituents of nuclei. The properties attributed to quarks were quite distinctive and yet no such objects had ever been observed. The inventors of quarks, and the theorists who followed them, exhibited a certain squeamishness on this point. Gell-Mann, for instance, concluded his first quark paper thus:

It is fun to speculate about the way quarks would behave if they were physical particles of finite mass (instead of purely mathematical entities as they would be in the limit of infinite mass). Since charge and baryon number are exactly conserved, one of the quarks (presumably u^2/3 or d^–1/3) would be absolutely stable . . . Ordinary matter near the earth's surface would be contaminated by stable quarks as a result of high energy cosmic ray events throughout the earth's history, but the contamination is estimated to be so small that it would never have been detected. A search for stable quarks of charge –¹/₃ or +²/₃ and/or stable diquarks of charge –²/₃ or +¹/₃ or +⁴/₃ at the highest energy accelerators would help to reassure us of the non-existence of real quarks.¹⁰

This quotation, with its reference to reassurance about the non-existence of real quarks, neatly exemplifies the ambiguity felt about the status of quarks. Gell-Mann was particularly prone to suspicions concerning their status. Others were less so — amongst them, the hardy experimenter. From the experimental point of view, quarks had one key attribute: fractional electric charge. The belief had come down from the days of Robert Millikan that all matter carried charges in integral multiples of the charge on the electron. Now this belief had been challenged, and experimenters were not slow to respond. According to their differing expertise, experimenters followed up one of three general strategies. One was that advocated by Gell-Mann: to look for particles of fractional charge in accelerator experiments. All of the detectors used in such experiments react to electrically charged particles, and it appeared straightforward to detect quarks should they exist. The second strategy, deployed by cosmic-ray physicists, was to use similar techniques to look for quarks in the cosmic ray flux. The third option was to use updated versions of the ‘oil-drop’ apparatus — with which Millikan had established the primacy of the electronic charge half a century earlier — to look for fractional charges in the terrestrial environment. Experiments in each category got under way in 1964. If any of them had reported success the story of quarks would have been much simpler. As it was, no evidence for quarks was reported from the first wave of experimental searches. And indeed, although experimenters  {88}  continued to look for quarks throughout the 1960s, the 1970s, and into the 1980s, an acknowledged quark was never found.¹¹

The lack of direct evidence for quarks did much to undermine the credibility of the quark model in its early years. Against this had to be set the growing success of variants of the model in explaining a wide range of hadronic phenomena. There were two principal variants of the model, which can be traced back respectively to Gell-Mann and Zweig. As Zweig put it at the time, Gell-Mann's ‘primary motivation’ for introducing quarks ‘differs from ours in many respects’.¹² Since Gell-Mann, inventor of strangeness and founder of the Eightfold Way, was a dominant figure in many developments of this period, it might seem reasonable to look at his style of work first. On the other hand, Zweig's approach, which I will call the constituent quark model (cqm), presents a much more readily comprehensible picture, so I will start there.

4.2 The Constituent Quark Model

George Zweig was born Moscow in 1937 but completed his higher education in the usa.¹³ In 1959 he was awarded a bSc degree in mathematics by the University of Michigan, and then began postgraduate work at Caltech. There he worked for three years on an unproductive hep experiment at the Berkeley Bevatron, before deciding in late 1962 to write a theoretical thesis under the supervision of Richard Feynman. Zweig began his theoretical work by looking at meson decay systematics. Following a circuitous route through the Sakata model (which he had already studied) and review articles on su(3) symmetry, he arrived at the realisation noted above: the multiplet structure of the observed hadrons could be recovered if all hadrons were composites of two or three quarks carrying the appropriate quantum numbers. From there, Zweig proceeded in a simple and direct fashion. As one would expect for a neophyte to theoretical physics, he treated quarks as physical constituents of hadrons and thus, as discussed below, derived all of the predictions of su(3) plus more besides.¹⁴ In 1963 he was awarded a one-year fellowship to cern, where he wrote up his findings, concluding: ‘In view of the extremely crude manner in which we have approached the problem, the results we have obtained seem somewhat miraculous’.¹⁵ Apparently the elders of the hep community agreed with Zweig both as to the crudity of his approach and as to the miraculous nature of his results. He later recalled:

The reaction of the theoretical physics community to the ace [quark] model was generally not benign. Getting the cern report published in the form that I wanted was so difficult that I  {89}  finally gave up trying. When the physics department of a leading university was considering an appointment for me, their senior theorist, one of the most respected spokesmen for all of theoretical physics, blocked the appointment at a faculty meeting by passionately arguing that the ace model was the work of a ‘charlatan’.¹⁶

In retrospect, it would be easy to dismiss the antagonism to Zweig's work as misguided, but it is important not to do this if one wants to understand the subsequent development of the cqm. We saw in the previous chapter that, in the early 1960s, there were two principal frameworks for theorising about the strong interaction: quantum field theory and the S-matrix. The cqm was distinguished by being unacceptable to protagonists of both. Consider quantum field theory first. In order to explain why free quarks were not experimentally observed, the obvious strategy was to assume that they were very massive (so that the accelerators of the day had insufficient energy to produce them). In the mid-1960s, this implied that quarks had masses of at least a few GeV. However, in combination with one another, quarks were supposed to make up much lighter hadrons — the 140 MeV pion being the extreme example. Theorists did not find it totally inconceivable that light particles should have heavy constituents. The idea that the mass of bound states should be less than the total mass of the constituents was familiar from nuclear physics, where the mass difference was known as the ‘binding energy’ of the nucleus. Unfortunately, the binding energy of quarks in hadrons was necessarily of the same order as the masses of quarks themselves — in contrast to the situation in nuclear physics, where binding energies were small fractions of nuclear masses. This implied very strong binding of the quarks, and strong binding, like strong coupling, was something which field theorists did not know how to calculate. Their techniques had been developed for weakly bound systems like atoms, where perturbative methods could be used. As discussed in the previous chapter, such methods failed for strong couplings, and thus the cqm left traditional field theorists cold. Of course, traditional field theory was in decline in the mid-1960s. The favoured approach was the S-matrix, and here opposition to quarks was even more clear-cut. At the heart of the S-matrix programme, especially in the bootstrap formulation, was the belief that there were no fundamental entities. The suggestion that all hadrons were built from three quarks was anathema to such thinking. As Zweig later commented, ‘the idea that hadrons, citizens of a nuclear democracy, were made of elementary particles with fractional quantum numbers did seem a bit rich.’¹⁷  {90} 

The cqm was hemmed in on all sides: experimentally, there was no sign of a free quark; theoretically, the model was disreputable in the extreme. These problems, and the quark modellers’ response to them, were summed up by the Dutch theorist J.J.J.Kokkedee in his 1969 book on the cqm:

Of course, the whole quark idea is ill-founded. So far quarks have escaped detection. This fact could simply mean that they are extremely massive and therefore difficult to produce, but it could also be an indication that quarks cannot exist as individual particles but, like phonons inside a crystal, can have meaning only inside the hadrons. In either case, nevertheless, the dynamical system of such quarks binding together to give the observed hadrons that has the properties demanded by the applications, is very difficult to understand in terms of conventional concepts. The quark model should, therefore, at least for the moment, not be taken for more than what it is, namely, the tentative and simplistic expression of an as yet obscure dynamics underlying the hadronic world. As such, however, the model is of great heuristic value.¹⁸

Enough has been said above about why the cqm was ill-founded; we can now examine the other side of the coin — its great heuristic value.

Phenomenology

Particle physicists make an imprecise distinction between doing ‘theory’ and doing ‘phenomenology’. The former refers to such activities as the abstract elaboration of respectable theories (like quantum field theory or the analytic S-matrix); the latter to the application of less dignified models to the analysis of data and as a guide to further experiment. As theory, the cqm was a disaster; as phenomenology it was a great success. The great merit of the cqm as a phenomenological tool was that it brought resonance physics down to earth. Instead of manipulating the abstract structures of group theory, physicists could now work in terms of physical constituents. And instead of looking to the often unfamiliar realm of pure mathematics for inspiration, physicists could draw upon their own shared expertise in the analysis of composite systems. While it was unclear to many physicists what to do next in elaborating su(3) as an abstract symmetry of hadrons, all physicists, by virtue of their training in composite systems, were well equipped to elaborate the cqm.

To put some flesh on these remarks, we can begin with three examples drawn from Zweig's 1964 work.¹⁹ The first concerns the Eightfold Way classification of hadrons. The representations of su(3)  {91}  could accommodate a wide variety of hadron multiplets with 1, 3, 6, 8, 10, 27, etc., members. However, in 1964 it appeared that all of the hadrons were members of singlets, octets or decupiets — there were no evident candidates for the triplet, sextet or 27-plets of su(3). From the group-theoretic point of view, this was an empirical fact of no evident significance. The cqm, in contrast, promised at least the beginnings of an explanation. If one insisted that all mesons were built from a single quark-antiquark (qq) pair, and that all baryons were three quark (qqq) composites then, according to accepted rules for combining quantum numbers, one arrived at only singlets and octets of mesons (which could mix as nonets) and singlets, octets and decupiets of baryons.²⁰ Thus the apparent absence of certain possible hadron multiplets could be translated into an attribute of quarks: they combined only in qq and qqq configurations. This did not constitute a complete solution to the problem of the missing multiplets, but it did transform the problem into a form which physicists had the resources to tackle, as we shall see in Chapter 7 in the discussion of ‘colour’.

As a second example of the translation of a group-theory fact into a physical attribute of quarks, we can consider the mass splittings within su(3) multiplets. We noted in Chapter 3.2 that Gell-Mann and Okubo explained the splittings in terms of the group-theory properties of the su(3)-breaking component of the strong interaction. Zweig recovered the Gell-Mann-Okubo mass formula by assuming that the s quark was heavier than the u and d quarks. This rendered the calculation of su(3) mass splittings easily manageable, and became a standard assumption in the subsequent development of the cqm.

The third example to be discussed here concerns Zweig's analysis of hadron couplings and decay rates. This is best illustrated through consideration of what later became known as the ‘Zweig rule’. In 1963 Brookhaven experimenters reported that the phi-meson decayed predominantly to a kaon-antikaon pair, rather than to a rho-meson plus a pion as expected from the usual systematics of hadron decays.²¹ Okubo explained this in abstract group-theory terms, but admitted that his approach was quite ad hoc: ‘Unfortunately’, he wrote, ‘the present author could not justify this “ansatz” on a more satisfactory mathematical ground.’²² Zweig, in contrast, visualised phi-decay as shown in Figure 4.2. The phi-meson was believed to be a non-strange particle, but Zweig argued that it had ‘hidden-strangeness’: that it was composed of an s quark and an anti-s quark — an ss pair — whose net strangeness cancelled out. He further argued that these constituent quarks persisted through the decay process, which entailed the materialisation of either a uu or dd pair  {92}  and hence led automatically to mesons containing strange quarks — kaons rather than non-strange rhos and pions.²³ This argument over the decay systematics of hidden-strangeness particles was recycled in the mid-1970s to hidden-charm particles with great effect, as we shall see in Chapter 9.

Figure 4.2. The decay φ ⟶ K+K– according to Zweig.

SU(6)

The advantage of reformulating the group-theoretical properties of hadrons in terms of quarks became increasingly evident as theorists began to load quarks with additional physical properties. One of the properties with which both Gell-Mann and Zweig had endowed quarks was spin. Quarks were assigned spin ¹/₂, so that (forgetting about orbital angular momentum for the moment) qq composites would have total spin 0 or 1 and qqq composites ¹/₂ or ³/₂. These results followed from the quantum-mechanical addition law for angular momenta, and reproduced the spins of the observed low-mass mesons and baryons (tabulated in Figures 3.2 and 3.3). In lectures given in August 1964 Zweig took this line of reasoning further. He suggested that the relative alignment of quark spins within hadrons was largely irrelevant to their binding: that for mesons whether the spins added to 0 or 1 was relatively unimportant, and similarly for baryons.²⁴ This amounted to the assertion of an additional if approximate symmetry of hadrons relating to their spins, and the combination of this new symmetry with the old su(3) was that of the group su(6).²⁵

Two important consequences could be drawn from the assertion of an approximate su(6) symmetry. First, the representation structure of su(6) offered a higher classification system for hadrons. For example, the qqq representations of su(6) were multiplets containing 20, 56 and 70 particles, and the 56, in particular, was just the right size to embrace the low-lying octet and decuplet baryons.²⁶ Secondly, as discussed below, simple assumptions about the electromagnetic and strong interactions of quarks led, in the su(6) scheme, to predictions  {93}  of hadronic properties in reasonable agreement with experiment. These were clear advances over the pure Eightfold Way approach which, for example, offered no explanation as to why the low-lying baryons should all have similar masses and either spin ¹/₂ or ³/₂. But it is important to note that at this stage the cqm had not entirely outstripped abstract group theory. There was a second and independent route to su(6) which avoided reference to quarks, and which predated the latter by a couple of weeks. The pioneers of the alternative route were Turkish theorist F.Gursey, Italian theorist L. Radicati and us theorist A. Pais, all working in the theory group at Brookhaven National Laboratory.²⁷ The three men shared a common background of work in group theory, and arrived at su(6) not via quarks but via an analogical extension of a group-theory approach to nuclear physics. In 1936 Eugene Wigner had proposed that nuclei manifested an approximate su(4) symmetry, corresponding to a combination of the su(2) isospin independence of nuclear forces with a similar independence from the relative spin orientation of nucleons within nuclei.²⁸ Gursey, Radicati and Pais proposed that hadrons should manifest a parallel symmetry, except that it should be su(6) rather than su(4) so as to accommodate the approximate su(3) independence of the strong interaction. Thus they arrived at su(6) via an abstract argument without any explicit reference to quarks.

In mid-1964 the pure group-theory approach to su(6) was more appealing to many theorists than the cqm, which was open to all of the theoretical objections discussed above. However, to the theoretical purist, there was one immediate objection to su(6) as a formal symmetry of hadrons: it was not in accord with the theory of special relativity; in technical terms it was not ‘Lorentz invariant’. In essence this was because the existing su(6) schemes made a distinction between spin and orbital angular momenta, and such a distinction was regarded as legitimate only in non-relativistic situations. Theorists therefore set out to repair this defect. As the Italian quark theorist (and quark searcher) Giacomo Morpurgo later noted: ‘The whole end of 1964 and the winter of 1965 were spent by many people trying to construct theories simultaneously invariant under the su(6) and the Lorentz group and realizing, finally, that this was impossible.’²⁹ This realisation derived from three sources. First, theorists proposed larger symmetry groups in which su(6) could be embedded in a relativistically invariant fashion, but these led to predictions in manifest disagreement with experimental data. Secondly, mathematical inconsistencies were found in the formulation of these higher symmetries. And thirdly, general and mathematically rigorous  {94}  ‘nonexistence’ theorems were proved, showing that no physically interesting marriage of the Lorentz group with internal symmetries of the Eightfold Way type was possible.³⁰

The failure of the search for a relativistic extension of su(6) marked the demise of the cqm's only theoretically respectable rival, and from early 1965 onwards the cqm held the field of resonance phenomenology alone. Morpurgo summarised this phase of development succinctly:

[T]hese efforts [towards a relativistic version of su(6)] were not entirely useless; indeed, as a sort of reaction they led to considering the brutal possibility of a nonrelativistic description of the internal dynamics of hadrons. The underlying line of reasoning was: It is not so tragic that it is impossible to have a theory which is simultaneously su(6) and Lorentz invariant; indeed we know from the start that su(6) is not an exact symmetry. Therefore all that is required is to have an approximate su(6) symmetry where the spin-dependent forces are small with respect to the spin-independent ones. This can easily be achieved in a nonrelativistic dynamics, where no problem arises in this respect. So why not explore the possibility that quarks are heavy (if they exist they should be heavy since they have not been seen), very strongly bound (the binding cancelling the largest fraction of their rest mass), and still, when bound, having nonrelativistic relative motion?³¹

Morpurgo himself showed that nonrelativistic motion was quite conceivable for heavy quarks bound in a deep but flat-bottomed potential well,³² and in the latter half of the 1960s a growing number of hep theorists indicated their willingness to join him in exploring the phenomenological possibilities of such a model. Similar images of composite systems were already familiar to physicists from their training in nuclear (and atomic) physics, and the order of the day was proclaimed by Morpurgo: ‘proceed as you would do in nuclear physics’.³³ Different theorists followed this suggestion in different ways, and a discussion of two of the major lines of development — hadron spectroscopy and hadronic couplings — will serve to illustrate this.³⁴

Hadron Spectroscopy

Spectroscopy is a venerable term in physics, relating to the study of the energy levels of composite systems. It originated in atomic physics before being taken over into nuclear physics. In elementary particle physics, the straightforward cqm conjecture was that the hadrons themselves constituted the spectrum of energy levels of composite  {95}  quark systems. One of the first and most influential theorists to take this idea seriously was Richard Dalitz. Dalitz was born in Australia in 1925 but completed his education in Britain, gaining a PhD in physics at Cambridge in 1950. He then held a variety of research positions before becoming Royal Society Research Professor at Oxford in 1963. Dalitz’ thesis work was in nuclear physics, but during the late 1950s and early 1960s he moved into hep, specialising in analyses of the strange hadronic resonances and of ‘hypernuclei’ — nuclei in which one of the usual nucleons had been replaced by a strange particle. He was thus an expert in both resonance physics and the analysis of composite systems, and in 1965 he set about elaborating the cqm accordingly.³⁵

Dalitz's strategy, later elaborated by many authors, was straightforward and taken over directly from nuclear physics. It went as follows. The first problem was to explain the successes of existing su(6) schemes in terms of quark dynamics. This was simple. Dalitz assumed that the dominant force binding quarks together was independent both of their spins and of the su(3) quantum numbers of the resulting hadronic bound state. In this way he could explain the overall su(6) symmetry of hadrons in just the same way as nuclear physicists explained the overall su(4) symmetry of nuclear states. Dalitz then had to confront the observation that su(6) was a broken rather than an exact hadronic symmetry: different hadrons assigned to the same su(6) multiplets had different masses, not the same masses as expected for an exact symmetry. Here again, Dalitz followed the traditional route of nuclear physics. He assumed that, although the dominant quark binding forces were su(6) invariant, there existed a hierarchy of lesser, perturbing, forces which acted upon quarks to break the su(6) symmetry and to produce the observed mass-splittings within su(6) multiplets. In this category he included forces depending upon the su(3) quantum numbers of the hadron in question, and ‘spin-spin’ and ‘spin-orbit’ forces acting between pairs of quarks. Such forces were already familiar from nuclear physics, and the spin-spin forces, for example, served to create mass differences between hadrons depending on whether the spins of their constituent quarks lined up parallel or antiparallel to one another.

Such assumptions served to account for mass splittings within su(6) multiplets. Dalitz then proceeded to consider the overall splittings between su(6) multiplets. To generate these some further assumption was required. Once again nuclear physics provided a clue. The total spin of a nucleus is regarded as made up of the combined spins of its constituents plus their orbital angular momentum.  {96}  The lowest mass nuclear state is typically that in which the orbital angular momentum is zero; higher energy states correspond to orbital (and vibrational) excitation of the constituents. Dalitz argued that the same was true of hadrons. The lowest mass su(6) multiplets corresponded to quark systems with zero orbital angular momentum; higher mass multiplets corresponded to systems with 1, 2, 3, etc., units of orbital angular momentum. This agreed with the observation that the lowest mass su(6) multiplets of mesons and baryons had spins consonant with the composition of quark spins alone, while higher mass resonances typically had larger spins which could only be accounted for by combining the spin of the quarks with one or more units of orbital angular momentum. Thus Dalitz suggested that there should exist a sequence of increasingly massive su(6) hadron multiplets, associated with increasing values of the orbital angular momentum of the constituent quarks.

Qualitatively, it was clear that the nuclear-physics inspired approach could make sense of the overall features of the hadron spectrum. To go further, Dalitz and many other theorists became quantitative, constructing mathematical models in which the strengths of the various su(6)-breaking and -splitting interactions were free parameters to be determined from experiment. They thus arrived, in effect, at highly complex mass formulae supposed to describe the entire hadronic spectrum. The phenomenologist's art was then to fit these formulae to contemporary data by appropriate adjustment of parameters (not an empty exercise, since there were far more resonances than parameters). Figure 4.3, taken from J.J.J.Kokkedee's 1967 cern lectures on the cqm,³⁶ schematises how this was done, and may serve both to clarify the above discussion and to illustrate some of the phenomenological complexity of cqm spectroscopy.

The first thing to note about Figure 4.3 is that it is entirely typical of the spectroscopic diagrams drawn in nuclear and atomic physics. The horizontal bars represent energy levels — in this case hadron masses — and the higher the bar, the greater the energy or mass. The bar on the left is labelled [70, L = 1], indicating that the hadrons in question are being assigned to a 70-dimensional representation of su(6) in which the quarks have one unit of relative orbital angular momentum (L). The Vs at the bottom of the diagram indicate the various forces included in the calculation. V and V' are su(6)-symmetric forces and, at this level of analysis, all of the hadrons within the su(6) multiplet have the same mass, as indicated by the single horizontal bar. As one moves towards the right of the diagram various su(6)-breaking forces are added into the calculation. V_σ

represents spin-spin forces and V_F su(3)-dependent forces, which together split the su(6) multiplet into four su(3) multiplets: two octets, a decuplet and a singlet. The superscripts on the su(3) assignments of these levels indicate the total quark spin ('4’ denotes total spin ³/₂, ‘2’ total spin ¹/₂). Finally, V_so and V_nc represent spin-orbit type forces, which induce further mass splittings through interaction of quark spins with their orbital motion. These separate the levels according to their total angular momentum (J) as shown on the right of the diagram. At this point the level structure has become sufficiently finely divided for assignment of candidate resonances to them, as indicated. Note that splittings within su(3) multiplets have not been included here, so that baryons of different masses within the same su(3) multiplet can appear at the same level, the N(1678), Σ(1770), Λ(1830), and Ξ(1930) for example. Were such su(3) splittings to be included, the diagram would be even more complicated.

During the latter half of the 1960s, the cqm analysis of hadron mass spectra grew into a complicated and sophisticated phenomeno-logical tradition. Fits to the known resonances were never exact, but it proved possible to reproduce the overall sequence of levels in the spectra of mesons and baryons: most resonances had the appropriate quantum numbers and masses to be assigned to the expected SU(6) multiplet structure. There were few obvious misfits.³⁷ Neither was there any competing theoretical scheme capable of offering a comparably fine-grained alternative to the cqm. Thus, as Kokkedee summarised his 1967 lectures:

We may conclude that the simplest quark model — qq and qqq configurations for mesons and baryons with the possibility of rotational and eventually vibrational excitation — can reproduce qualitatively the gross features of the presently established resonance spectra of the hadrons. To be able to generate an su(3) multiplet spectrum that agrees remarkably well with the observations is a challenging achievement.³⁸

As the years went by, hep experimenters explored the resonance spectrum in increasing detail, cqm modellers made increasingly sophisticated fits to the data, and the situation remained the same: with few exceptions, the resonances could be accommodated by the patterns expected in the cqm. Table 4.1 shows the accepted classification for the known baryons of masses up to around 2 GeV, as of 1981.³⁹

Hadronic Couplings

Besides classifying hadrons and explaining their mass spectrum, cqm

Table 4.1. Δssignments of the lower-mass baryons to su(6) multiplets.

enthusiasts set about analysing hadronic production and decay mechanisms. Again, theorists drew their inspiration directly from the standard treatments of composite systems in atomic and nuclear physics. Again the procedure was one of loading the properties of hadrons onto their constituent quarks. As a protypical example, consider Becchi and Morpurgo's 1965 analysis of the electromagnetic decay of the positively-charged delta resonance: Δ⁺ ⟶ pγ.⁴⁰ Just as in nuclear and atomic physics, Becchi and Morpurgo assumed that the photon was emitted not from the delta as a whole, but rather from a single quark within it, as indicated in Figure 4.4. In general, since the photon has spin 1, this could take place in one of two ways. Either the spin of the emitting quark could ‘flip’ from +¹/₂ to –¹/₂ (technically, a magnetic dipole or M₁ transition) or the relative orbital angular momentum of the three-quark system could change by one unit (an electric quadrupole, E₂, transition). However, Becchi and Morpurgo argued, both the delta and proton belonged to an su(6) multiplet in which the quarks had zero orbital angular momentum; therefore the latter possibility was ruled out. The electromagnetic decay of the delta had to proceed through a spin-flip M₁ transition: E₂ transitions  {100}  were forbidden by a ‘selection rule’ of the cqm. Experimentally, M₁ and E₂ transitions corresponded to different angular distributions for the emitted photons, and it was indeed found that the E₂ transition rate in delta decay was less than four per cent of the M₁ transition rate.

Figure 4.4. The electromagnetic decay Δ+ ⟶ pγ in the cqm.

This agreement between theory and data was one of the first successes of the application of the cqm to hadronic couplings,⁴¹ and encouraged theorists to press onwards. Other selection rules were found relating to the electromagnetic production and decay of higher spin resonances, which were again supported by the data.⁴² Finally, towards the end of the 1960s, theorists went beyond the search for selection rules, and mounted full-scale numerical calculations of electromagnetic resonance couplings using all of the details of resonance structure derived from fits to the hadron spectrum.⁴³ Here agreement with the data was not so impressive as the four-per-cent accuracy, of Becchi and Morpurgo's selection rule, but the predictions in general matched the overall trend of the data, explaining why some resonances were observed to be strongly coupled to photons and others not.⁴⁴ Like the fits to hadron spectra, such coupling calculations were counted as a success of the cqm, but it is again relevant to note that this was in the absence of any significant competition from rival theories.

Cqm modellers did not, of course, confine their attention to the electromagnetic interactions of hadrons. Models were also constructed of strong (and weak)⁴⁵ hadronic couplings. Here the analysis followed the same path as that of electromagnetic processes, with the obvious replacement of, say, pions for photons. This was somewhat paradoxical. The pion, although treated as an elementary particle in such calculations, was itself supposed to be a quark-antiquark composite. But quark modellers learned to live with such paradoxes. Early calculations focused upon the production and decays of the ³⁺/₂ baryon decuplet and the spin 1 mesons, but were soon extended to the properties of higher spin resonances as well.⁴⁶ Like hadron spectroscopy,  {101}  the cqm phenomenology of hadronic couplings also developed into a thriving and qualitatively successful tradition.⁴⁷

The Symbiosis of Theory and Experiment

Thus far we have been looking at the cqm from the theorists’ perspective, viewing it as an explanatory resource for the interpretation of data. But it is important to recognise that the traffic between experiment and theory was not one way: just as the theorists’ practice was structured by the products of experimental research, so the experimenters’ practice was structured by the products of the theorists’ research. Through the medium of the cqm theorists and experimenters maintained a mutually supportive symbiotic relationship.

The roots of this symbiosis lay in the pre-cqm era. During the 1950s theory was largely parasitic upon experiment — experimenters reported the existence of new hadrons, and theorists did their best to explain them — but with the advent of the Eightfold Way the balance became more even. Experimenters began to take as well as to give. The clearest example of this centred on Gell-Mann's 1962 prediction of the existence of the Ω^–. Drawing upon the resonance data already provided by experimenters, Gell-Mann predicted the mass and decay characteristics of this unobserved particle, and thus pointed to a new topic for experimental practice. We saw in Chapter 3.2 that the experimenters took Gell-Mann's hint, invested a great deal of effort in the search, and in 1964 repaid him in kind with the particle itself. The existence of the Ω^– then formed an integral part of the next generation of Eightfold Way theorising which included the formulation of the quark concept.

With the advent of quarks and the cqm, the symbiosis between theory and experiment entered a new and more intimate phase. In essence this was because experimenters had begun to move on from the ‘classic’ hadrons — the lowest mass meson and baryon su(6) multiplets — to the exploration of resonances of higher masses and spins. In this second generation of resonance experiments, ‘bump-hunting’ became a much more difficult and technical business than it had been in the first. Classic resonances like the delta could be associated with large and conspicuous peaks in experimental cross-sections (see Figure 3.1). But there were only a few such peaks and to find more resonances experimenters had to examine fine details of individual ‘decay channels’.⁴⁸ In consequence, resonance identifications became less confident than they had been in the early days of the population explosion. George Zweig recalled that, even in 1963, ‘Particle classification was difficult because many [resonance]  {102}  peaks . . . were spurious’, and that, of the 26 meson resonances then listed in an authoritative compilation, 19 subsequently disappeared.⁴⁹ Similarly, in his 1967 lectures on the cqm, Kokkedee prefaced his fits to the resonance spectrum with the comment: ‘Because of the unstable experimental situation many detailed statements of the model are probably not guaranteed against the passage of time’.⁵⁰ The instability of the resonance data persisted through the 1960s and 1970s, as indicated in Table 4.2 taken from the 1982 edition of the Review of Particle Properties — the standard hep catalogue of elementary particles.⁵¹ Table 4.2(a) lists the mesons which had been reported from one or more high-quality experiments up to 1982. On the entries marked by an arrow, the reviewers comment: ‘We do not regard these as established resonances’. Similarly, the entries in the baryon table (4.2(b)) are graded according to current status of the experimental evidence on a scale from four-star, ‘good, clear, and unmistakable’, to one-star, ‘weak’. A couple of entries are marked ‘Dead’, indicating that they were once believed to exist but that their non-existence could now be regarded as proven.

Theory, in the guise of the cqm, intervened into this context of experimental uncertainty in two ways. First, cqm analyses offered experimenters specific targets to aim at in succeeding generations of experiment. Thus, for example, Zweig argued in 1964 that the strange resonance Λ(1520) had been misidentified as a member of an su(3) octet: according to his formulation of the cqm, the genuine octet member should have a mass of around 1635 MeV. Zweig noted that experiments had observed structure in cross-sections in this energy region, but that this had been ascribed to another nearby resonance, the Σ(1660). The Λ(1635) and Σ(1660) resonances had isospin 0 and 1 respectively, so further experiment using different beams and targets could attempt to disentangle them.⁵² Examples of this kind of heuristic feedback from theory to experiment could be multiplied almost indefinitely throughout the history of the cqm.⁵³

The more general influence which the cqm exerted on experiment was that it made experimental resonance physics interesting — a field worthy of the expenditure of considerable amounts of time, money and effort.⁵⁴ It seems implausible that, without the sustaining interest of quark modellers, experimenters would have persisted in the painstaking exploration of the low-energy resonance regime. There would have been little point to such activity, and experimenters would have found other ways of exploiting the finite resources available for research.⁵⁵ As it was, the flourishing of the cqm tradition translated in experimental terms into determined programmes of precision measurements of cross-sections for a variety of choices of

Table 4.2(a). Mesons listed in Review of Particle Properties, 1982.

**** Good, clear, and unmistakeable.

*** Good, but in need of clarification or not absolutely certain.

** Needs confirmation

* Weak

beam, target and decay channels, and into the development of increasingly sophisticated techniques of data analysis.⁵⁶ In connection with the former, it is significant to note that although hadron-beam experiments at pss had led the way in resonance physics, the electromagnetic couplings calculated in the cqm could more readily be measured in ‘photoproduction’ experiments at electron accelerators.⁵⁷ As expected in the cqm, it also proved to be the case that certain resonances could only be detected in photoproduction experiments, and thus resonance physics became a principal preoccupation of research at electron accelerators as well as pss in the latter half of the 1960s.

The upshot of the increasingly diversified and precise programme of experimental resonance physics was the steady flow of new resonances encapsulated in Figure 4.5.⁵⁸ This shows how the lists of resonances recorded in the Tables of Review of Particle Properties grew over two decades. Figure 4.5(a) refers to mesons, and includes both ‘well understood’ particles, for which all quantum numbers were known, and those which were simply ‘listed’ as having been sighted in one or more experiments. Figure 4.5(b) refers only to those baryons whose spin and parity had been determined, and reflects the intensity with which their properties had been investigated. It is important to note here that the ‘properties’ count is almost entirely made up of ‘branching ratios’. These express how often a given resonance decays to a given decay channel and are precisely the quantities described by cqm calculations of resonance couplings.

Figure 4.5(a). Growth of information on mesons.

Figure 4.5(b). Growth of information on baryons.

Thus the activity of cqm modellers served to sustain and motivate a growing programme of experimental resonance physics. This programme generated more and more information on resonances and their properties, which, in turn, served to sustain and motivate more work on the cqm. The theoretical and experimental wings of resonance physics grew together in a symbiotic relationship through the 1960s and into the 1970s.⁵⁹

The Death of Quantum Field Theory

One last point remains to be made before moving on from the cqm.  {107}  Two theoretical traditions dominated the old physics of the 1960s and early 1970s. At high energies there was the Regge analysis of soft scattering, discussed in Chapter 3.4; at low energies there was the cqm analysis of resonances. Neither of these traditions drew significantly upon the resources of quantum field theory. Indeed field theory was anathema to the bootstrappers amongst Regge theorists, while the cqm was itself repellent to the field-theory purists. Thus during the 1960s, the field approach to elementary-particle physics fell largely into disuse. Many of the older generation of field theorists ceased actively to practise their art, and many of the younger generation of hep theorists — rapidly expanding in this period — received their training in a context from which field theory was effectively absent.⁶⁰ From a sociological perspective, the decline of field theory in the 1960s creates an apparent problem in understanding its resurrection in the new physics of the 1970s: where did the required pool of theoretical expertise come from? Fortunately, the problem is only apparent. In the shadow of the cqm and Regge lay two lesser traditions oriented around the field-theory approach. One was devoted to the elaboration of the prototypical field theory, qed. The other was the ‘current algebra’ tradition discussed below. Together, these traditions offered a refuge wherein committed field theorists could make constructive use of their expertise and at the same time make contact with experiment. The qed and current algebra traditions kept the flame of field theory alive during the 1960s, and were the training ground for a new generation of field theorists. As discussed in Chapter. 8.3, the advanced guard of the 1970s new-physics resurgence of field theory was drawn from the ranks of qed theorists and, especially, current algebraists. I have already outlined the qed approach to electromagnetic phenomena and I will not go into further details here.⁶¹ But some discussion of current algebra is needed. It was within this tradition that Gell-Mann grounded his earliest discussion of quarks and, as one of the leading figures in theoretical hep, it was surely Gell-Mann rather than Zweig who first persuaded physicists to entertain the quark concept.⁶²

4.3 Quarks and Current Algebra

There were two ways of formulating and elaborating the quark concept: the straightforward cqm way, and Gell-Mann's way. Gell-Mann's ‘current algebra’ approach was highly esoteric compared with the cqm, and had relatively little impact upon the overall practice of the hep community.⁶³ I will therefore discuss it only briefly, and without going very far into technical details.⁶⁴ To begin the discussion it is illuminating to compare Gell-Mann's first quark  {108}  paper with that of George Zweig.⁶⁵ Both authors listed the quark quantum numbers and stressed the importance of looking for free quarks, but there the resemblance ends. In his lengthy first draft (24 pages in preprint form) Zweig laid out the straightforward consequences of the composite analogy, writing down quark assignments for the spin 0 and spin 1 meson nonets, and the baryon octet and decuplet. Gell-Mann did no such thing. His paper covered less than two pages, and the only equations are ‘commutators’ for hadronic ‘weak currents’, evaluated for free quarks. I will come back to ‘commutators’ and ‘weak currents’ in a moment; initially I want just to emphasise that spectroscopic considerations, drawing directly on the composite analogy, were completely absent from this paper — Gell-Mann's interests were elsewhere. As he indicated in the text and footnotes, his aim was to plug in quarks as a new resource into an already evolving tradition which he had himself founded some years earlier. This was the tradition devoted to ‘current algebra’. To understand the form it took it is useful to know something about Gell-Mann's approach to particle physics.⁶⁶

Above all else, Gell-Mann was a field theorist. His first publication (written with F.E.Low in 1951) was portentously entitled ‘Bound States in Quantum Field Theory’.⁶⁷ We noted in Chapter 3.2 how his enthusiasm for gauge field theory influenced his 1961 proposal of the Eightfold Way. We have also remarked on the obstacles theorists encountered during the 1950s in trying to extend the qed-type approach to any field theory of the weak and strong interactions. Like all of the theorists of this period, Gell-Mann was aware of these problems, but his response was a novel one. Characteristic of his work was the idea that one should take traditional field theory (the standard perturbative form, modelled on that of qed) and extract whatever might be useful in practice. He sought, that is, to use field theory heuristically, in order to arrive at new formulations or models which could then stand in their own right, independent of their origins. In Chapter 3.4 one way in which Gell-Mann attempted to do this was discussed: the exploration of the analytic properties of the S-matrix using perturbative quantum field theory as a guide. The other was the current-algebra approach, which led through su(3) and quarks. The S-matrix approach related exclusively to the strong interactions of hadrons, while current algebra focused on their properties with respect to the weak and electromagnetic interactions.

In 1958 Feynman and Gell-Mann had written down the pheno-menologically successful V–A field theory of the weak interactions. This theory was directly modelled on qed, the weak interactions taking place between weak currents just as in qed electromagnetic  {109}  interactions take place between electromagnetic currents. Questions arose, however, as to the nature of the weak currents. For the purely leptonic sector — the weak interactions of electrons, muons and neutrinos — the situation was clear: the currents were to be constructed from the relevant fields as in qed. But for hadrons the waters were murky. One problem concerned the population explosion: was every hadron to be ascribed its own personal field, contributing to an equation several pages long for the hadronic weak current? If so, was there any relation between the individual contributions to this current? These were some of the questions which Gell-Mann addressed in a 1962 publication — his first writings on the Eightfold Way to appear in a refereed journal.⁶⁸ The ideas in this paper were characteristic of his previous work and foreshadowed what was to follow. In effect, he proposed that in discussing both the weak and electromagnetic properties of hadrons one should forget about traditional quantum field theory, and instead regard weak and electromagnetic currents as the primary variables. At the same time, however, he used field theory as an aid to guessing the properties of the currents themselves. In particular, he hypothesised that the relationships between the various hadronic currents — technically speaking, the ‘equal-time commutators’ between the currents — could be modelled on those believed to hold in the V–A theory for the leptonic currents. If one considered a world containing only leptons one could show that the currents generated an su(2) algebra, and Gell-Mann proposed that the hadronic currents similarly generated an su(3) algebra — or, to be more precise, that the two orthogonal linear combinations of V (vector) and A (axial vector) currents generated two independent su(3) algebras. In technical terms, the hadronic currents were postulated to obey an su(3) × su(3) algebra — hence the name ‘current algebra’ for the work which grew up around this proposal.⁶⁹

There are two characteristic points to note about Gell-Mann's strategy in arriving at the current-algebra formulation. First, current algebra had immediate phenomenological applications since currents were directly related to experimentally observable quantities via standard theoretical techniques (see below). Secondly, although Gell-Mann was clearly working within the field-theory idiom — his 1962 publication is littered with suggestive field-theoretic calculations — the algebraic structure relating the currents could not be said to be derived from any field theory. This was so because a derivation required a fully calculable theory of the strong interactions (recall that hadrons were at issue) and no such theory existed. Thus the invention of current algebra offers a perfect illustration of Gell-Mann's  {110}  strategy for arriving at self-sustaining theoretical structures from a shaky field-theoretic base, a strategy which he encapsulated in a culinary metaphor:

In order to obtain such relations that we may conjecture to be true, we use the method of abstraction from a Lagrangian field theory model. In other words we construct a mathematical theory of the strongly interacting particles, which may or may not have anything to do with reality, find suitable algebraic relations that hold in the model, postulate their validity, and then throw away the model. We may compare this process to a method sometimes employed in French cuisine: a piece of pheasant meat is cooked between two slices of veal, which are then discarded.⁷⁰

Having discussed the pre-existing current-algebra tradition, we are now in a position to understand the distinctive features of Gell-Mann's 1964 quark paper. In 1963, building upon Gell-Mann's 1962 current-algebra/Eightfold Way paper, the Italian theorist Nicola Cabibbo (working at cern) had written down a general expression for the hadronic weak interactions, and in a detailed phenomenological analysis had shown this to be in agreement with the available experimental data on hadronic weak decays.⁷¹ Gell-Mann, in turn, pointed out in 1964 that if one constructed suitable weak currents from free, non-interacting, quark fields, one could re-derive the current commutators he had postulated earlier in his Eightfold Way paper, and hence recover Cabibbo's successful phenomenological analysis of the weak interactions. Gell-Mann was careful to point out that he was not suggesting that hadrons were really made up of non-interacting quarks since, with no forces to bind them together, non-interacting quarks would simply fly apart from one another. In accordance with his standard strategy, he simply observed that the relationships between the weak currents required to explain the experimental data were the same as those between currents constructed from free quark fields.

Thus, working from his individual field-theoretic viewpoint, Gell-Mann used quarks to underpin su(3) results on hadronic weak interactions, just as Zweig and others were to use quarks to underpin the su(3) spectroscopy of hadronic resonances and their strong interactions. Also, as in the spectroscopic tradition, the introduction of the new quark degree of freedom enabled theorists to go beyond simple su(3) considerations in the current-algebra tradition, too. The point here was this. Gell-Mann had conjectured the su(3) × su(3) structure of current algebra on the basis of heuristic field-theoretic models. It turned out that certain current commutators were  {111}  independent of the models used to arrive at them, in the sense that it appeared that whichever model one chose one arrived at the same result. It was thus reasonable to suppose that these commutators would remain unchanged in a full field-theoretic calculation (as distinct from the heuristic and approximate calculations actually done). On the other hand, certain other commutators depended crucially on the model field theory chosen — the free quark field theory, for instance, leading to different results from other theories. Thus, to the extent that theorists used the quark model commutators, and that these led to successful predictions, the quark model was centrally implicated within the current-algebra tradition.

Theorists tended initially to work with safe, model-independent, commutators and, in its early years at least, current algebra did not lend such persuasive support to quarks as did the cqm tradition.⁷² The significance of current algebra lay rather in the fact that, although Gell-Mann advocated only a heuristic use of field theory, currents remained explicitly field-theoretic constructs and were manipulated and explored using characteristically field-theoretic techniques. And, since the problems entailed in extending the traditional field-theory approach beyond electromagnetism were manifest to all, current algebra became a haven in the 1960s for the majority of committed field theorists.

We can turn now from the conceptual roots of current algebra to the phenomenological uses which theorists found for it. Central to many applications was pcac: the ‘partially conserved axial current’ hypothesis. Pcac was another instance of Gell-Mann prising a pheasant from the veal of perturbative field theory. In 1958, in their ‘V–A’ paper, Feynman and Gell-Mann had proposed that the weak vector current was exactly conserved, just like the electromagnetic current (another vector quantity). The conserved vector current (cvc) hypothesis explained the ‘universality’ of strength of weak decays: the fact that the muon and neutron beta-decay coupling appeared experimentally to be the same. In 1960, Gell-Mann and M. Levy (of the University of Paris, which Gell-Mann was then visiting) went on to propose that the axial weak current was not exactly conserved, but partially. They supposed that the ‘divergence’ of the axial current (a measure of its non-conservation) came about through its coupling to the pion.⁷³ The pcac hypothesis was, quite typically, argued heuristically to be true from a variety of field-theoretic models, and then postulated as a truth in its own right. To back this up, Gell-Mann and Levy offered a pcac re-derivation of the ‘Goldberger-Treiman relation’ — a quantitative relationship between the weak- and strong-interaction couplings of the pion which was  {112}  known to hold experimentally to within around ten per cent.⁷⁴ Subsequently the pcac hypothesis became an important adjunct to the current-algebra approach in the construction of low-energy theorems for processes involving pions. A range of phenomenological applications were devised in the mid-1960s, most of which seemed to agree quite well with the data.⁷⁵ (A notable exception was the calculation of the η ⟶ 3π decay rate, which came out quite wrong, and of which all that could be said was: ‘The reason for this failure of the current algebra is not understood’.⁷⁶ This decay process remained an intransigent anomaly until the resurgence of gauge theory in the 1970s and, even then, the solution to the problem remained controversial.)

Another significant and popular line of development of the current-algebra approach was the construction of ‘sum-rules’.⁷⁷ The first of these, dating from 1965, was the ‘Adler-Weisberger relation’.⁷⁸ This was a relation between the axial vector weak-coupling strength (g_A) and an energy integral over pion-nucleon scattering cross-sections. One could attempt to evaluate this relation from experimental data (although, since the integral extended to infinite centre-of-mass energy, some theoretical assumptions were required) and it appeared to be reasonably well satisfied. The success of this sum-rule was regarded as a successful test of the underlying current algebra, and encouraged the formation of a sum-rule industry which was, in general, phenomenologically successful. On the one hand, sum-rules could be used to re-derive the low-energy theorems mentioned above, and hence take over their successes (and failures). On the other, the first new sum-rule which could be numerically evaluated from experimental data seemed to work. This was the Cabibbo-Radicati sum-rule, proposed in 1966,⁷⁹ and it may be useful to explain what I mean by ‘seemed to work’, in order to give a feeling for the kind of phenomenology at issue. The Cabibbo-Radicati sum-rule asserted that a certain mathematical integral over photon-nucleon cross-sections had the value zero. As usual, this integral extended over an infinite range of centre-of-mass energies and could only be evaluated approximately from the data. The four dominant contributions to the measurable, low-energy end of the integral were evaluated to be –0.8, +1.6, –2.8, and +1.6.⁸⁰ These added up to –0.4: a small number, but whether it was near enough to the predicted value of zero was clearly a matter of personal choice. Later sum-rules met with a similar degree of numerical success.⁸¹

The elaboration of sum-rules together with exploration of the meaning and consequences of pcac constituted the principal lines of development of current algebra in the 1960s. In the early 1970s a third  {113}  variant appeared, the ‘light cone algebra’. This was again Gell-Mann's brainchild, and depended decisively upon the use of quark fields. Before we discuss it (in Chapter 7) we must review the phenomenon it was designed to explain: scaling. Scaling is the subject of the next chapter, which begins the analysis of the new physics. Here one topic remains to be explored . . .

4.4 The Reality of Quarks

In the latter half of the 1960s it was unarguable that the constituent quark model provided the best available tools for the analysis of hadronic resonances — the low-energy domain of the old strong-interaction physics. Likewise, there was no doubt that the current-algebra tradition, in which quarks were frequently called upon, was the cutting edge of theoretical research into the weak and electromagnetic interactions of hadrons. But particle physicists did not extrapolate from this considerable body of theoretical, phenomenological and experimental practice to the assertion that the existence of quarks was established. Throughout the 1960s and into the 1970s, papers, reviews and books on quarks were replete with caveats concerning their reality. As the British quark modeller Frank Close wrote in 1978 (when quarks had at last been certified as real):

The quark model had some success in the 1960s; in particular it enabled sense to be made out of the multitude of meson and baryon resonances then being found. When interpreted as excited states of multi-quark and quark-antiquark systems, these resonances and their properties were understood. Even so, there was much argument at the time as to whether these quarks were really physical entities or just an artefact that was a useful mnemonic aid when calculating with unitary symmetry groups.⁸²

The reasons for this state of affairs are not hard to find. Most obviously, quarks, with their fractional electric charges, were supposed to be highly conspicuous entities; yet repeated experimental searches had failed to turn up any communally acceptable candidates. This in itself was not immediately damning, since theorists could argue that quarks were too heavy to be produced in contemporary accelerator experiments. But even if this empirical problem were set on one side, it remained difficult to argue for the reality of quarks from their phenomenological utility. In the first instance the problem was that, as George Zweig put it, ‘the quark model gives an excellent description of half the world’.⁸³ Whilst the quark model was central to the world of low-energy resonance physics, it was at most peripheral to the world of high-energy soft-scattering. In the former,  {114}  hadrons indeed appeared to be quark composites, while in the latter they were Regge poles. Hadronic structure differed according to who was analysing it, making it very difficult to assert that hadrons actually were quark composites (or Regge poles). This manifest social and conceptual division of the theoretical hep community encouraged an instrumentalist attitude towards hadronic structure. Quark and Regge modellers existed in a state of peaceful coexistence, each group focusing upon its own chosen domain of phenomena in its own terms, and generally claiming no special ontological priority for its description of hadrons.

Such social and conceptual divisions extended, moreover, into the quark theorists’ camp itself. Even if one were willing to forget that the cqm was theoretically disreputable, and that the current-algebra tradition drew upon unrealistic quark models in a purely heuristic fashion, the fact remained that the image of hadrons and quarks differed between the two. This was a subtle point which caused some confusion in the early days of quarks, but in outline went as follows. In the cqm, theorists used ‘constituent quarks’ to represent hadrons of definite spin. The latter were the physical particles observed in experiment. In the current-algebra approach, theorists built hadrons out of ‘current quarks’, but these were not the individual hadrons observed in experiments: they were combinations of different hadrons having different spins. (Hence the succession of terms appearing in the current-algebra sum-rules, corresponding to an infinite sequence of hadronic resonances.) Current and constituent quarks were therefore in some sense different objects. Gell-Mann's view was that they were, nevertheless, related — that constituent quarks represented some complicated combination of current quarks, and vice-versa. A considerable amount of work was done in exploring the form of this relation and led to several new insights into the classification and properties of hadrons, but a full understanding was never achieved.⁸⁴ The cqm and current-algebra traditions remained separate, each with its own practitioners, its own quark concept and its own routines of phenomenological application.

The theoretical wing of the old physics in the mid-1960s was thus constituted from three principal traditions: Regge theory, the cqm and current algebra. In the first of these it was quite possible to discuss hadron dynamics without reference to quarks. In the second, quarks were central to any discussion. In the third, quarks were an optional heuristic extra but led to a different image of hadrons from that of the cqm. This social and conceptual diversity of theoretical practice fostered an instrumentalist rather than a realist view of quarks. In the 1970s a unification of practice around gauge field  {115}  theory eventually made possible a consensual realist perspective on quarks. But the situation got worse before it got better. In the next chapter we will be discussing the arrival in the late 1960s of the quark-parton model: yet another variant on the quark theme, and distinct from both the cqm and current algebra.

NOTES AND REFERENCES

5
SCALING, HARD SCATTERING AND THE QUARK-PARTON MODEL

The new physics began, appropriately enough, in California. In the late 1960s, experiments at the Stanford Linear Accelerator Center (slac) saw the discovery of the first new-physics phenomenon: scaling.¹ The circumstances of the discovery itself are the subject of Section 1 of this chapter. Section 2 deals with the explanation of scaling offered by Richard Feynman's ‘parton’ model, and aims to explore the central analogy of Feynman's approach. Sections 3 and 4 review the phenomenological applications of the parton model to electron scattering at slac, and to neutrino scattering at the cern ps. These applications led to the identification of Feynman's partons with the quarks of Gell-Mann and Zweig. Section 5 outlines the applications of the parton model to other lepton-hadron processes and to unexpected hard-scattering phenomena seen in purely had-ronic reactions in the first round of experiments at the cern isr. Experimental investigation of the phenomena to which the parton model was held to apply came, in the 1970s, to constitute the empirical backbone of the new physics. The parton model itself was subsequently subsumed into the gauge field theory of the strong interaction, qcd, as we shall see in Chapter 7.

5.1 Scaling at slac

Construction of a 22 GeV, two-mile long linear electron accelerator at the Stanford Linear Accelerator Center was first formally proposed in 1957 and began in 1962. By January 1967 the design energy had been achieved and the physics programme got under way.² At this time several lower-energy electron machines were in operation around the world, but had contributed little of major impact to the development of hep. As discussed in the previous chapter, the principal focus of electron-beam experiments was the exploration of the detailed properties of hadronic resonances.

Amongst the 19 experimental proposals which had been approved at slac by July 1967 were three by a collaboration of physicists drawn from slac, Caltech and Massachusetts Institute of Technology (mit).³ These were typical first-round experiments at a new accelerator, conceived to ‘act as a shakedown of the spectrometers’  {125}  — major items of experimental apparatus, designed to measure the energies and momenta of scattered electrons — and to ‘provide a general survey of the basic cross-sections which will be useful for future proposals’.⁴ The experiments in question aimed at measurements of the elastic scattering of electrons and positrons from protons, and of inelastic electron-proton scattering. The discovery of scaling emerged from the last of these measurements, but a discussion of the first will provide some necessary conceptual background.⁵

Elastic Electron-Proton Scattering

An elastic scattering process is one in which beam and target particles retain their identity and no new particles are produced. Elastic electron-proton scattering is, in obvious notation, the process ep ⟶ ep. Electrons are believed to be immune to the strong interaction. Thus the routine assumption in analysing electron-scattering processes is that they are predominantly electromagnetic and well described in terms of the exchange of a single photon between the incoming electron and the target proton (Figure 5.1).

Figure 5.1. Elastic electron-proton scattering via single photon exchange.

The primary interest of all electron-proton scattering experiments derived from the belief that electron-photon interactions were fully understood in terms of qed. Experimental measurements could therefore be construed as exploring the details of photon-proton interactions. As discussed further in Section 5.2, according to qed (in first-order approximation) electrons interacted as structureless point particles, occupying an infinitesimal volume in space, while protons, by virtue of their strong interactions, were expected to have structure and to be extended over a finite volume of space. Measurements of electron-proton scattering could therefore be considered to probe the proton's structure and, in particular, to explore the distribution in space of the proton's electric charge.

The first electron-proton scattering measurements were made at  {126}  Stanford using the lower-energy electron accelerators which were the predecessors of the slac machine. These early experiments served to mark out a significant difference between elastic electron-electron and electron-proton scattering. It was found that cross-sections at large scattering angles for the latter were much smaller than those for the former (see Figure 5.4, below). Electrons frequently scattered from other electrons at large angles, while electron-proton cross-sections peaked at small angles, with very few electrons being scattered at large angles. In loose but suggestive language, electrons seemed to act as ‘hard’ objects, bouncing violently off one another, while protons seemed to be ‘soft’ and capable only of giving a gentle nudge to passing particles. This was the origin of the terminology of hard and soft scattering which serves to characterise many of the phenomena of the old and new physics. Speaking more formally, the observed angular dependence of the electron-electron cross-section was that predicted by qed for point-like electrons, while the angular dependence of the electron-proton cross-section resembled that familiar to physicists from optical diffraction phenomena. And, indeed, in the pre-slac era the accepted explanation of the elastic electron-proton scattering data was that the proton was a diffusely extended object which served to diffract the incoming electron beam. As in optical physics, a connection could be made between the dimensions of the diffracting object and the shape of the diffraction pattern it produced, and the electron-proton scattering data were taken to show that the proton had a finite diameter of around 10^–13 cm.

In 1961, R. Hofstadter was awarded the Nobel Prize for Physics for his pioneering work at Stanford on electron scattering. The slac-mit-Caltech experiment made measurements of elastic electron scattering at hitherto inaccessible energies, but no major discoveries resulted.⁶ For our purposes, the point to note is that the observed electron-proton cross-sections retained their characteristic diffraction peak at high energies, and continued to be identifiable with a diffusely extended proton structure.

Inelastic Electron-Proton Scattering

When the elastic electron (and positron) measurements were complete, the Caltech group decided not to take part in the third experiment. The slac-mit group led by Richard Taylor (slac) and Henry Kendall and Jerome Friedman (mit) went on alone to measure inelastic electron-proton scattering.⁷ The experimental runs took place in the second half of 1967 and the procedure was a simple one. The experimenters fired the electron beam at a proton (liquid  {127}  hydrogen) target, and counted how many electrons emerged with given energies at given angles relative to the beam axis. They thus measured inclusive cross-sections for the process ep ⟶ eX, where X represents whatever hadronic debris resulted from the electron-proton collision. Such inclusive measurements were considered to be less informative than exclusive measurements in which the particles comprising X were detected and identified. But they were also much simpler, since no instrumentation was needed to register the hadronic debris. The slac-mit experiment was therefore regarded as a quick and crude survey, designed to investigate the new energy regime, in preparation for later exclusive measurements. As usual, inelastic electron-proton scattering was thought to be mediated by single-photon exchange (Figure 5.2(a)) and, in particular, it was expected that the most important process would be resonance production (Figure 5.2(b)).⁸

Figure 5.2. (a) Inelastic electron-proton scattering; (b) Resonance (N*) production in inelastic electron-proton scattering.

Analysis of the inelastic data began in the spring of 1968. For the small-angle scattering of lower-energy electrons the experimenters found what they expected. Figure 5.3 shows a typical plot of cross-sections versus the mass of the hadronic system produced, and three bumps are clearly evident, corresponding to the Δ(1232), N(1518) and N(1688) resonances.⁹

However, as the experimenters examined the data for larger angle scattering and higher beam energies they encountered a surprise. Their expectation was that resonance production cross-sections would decrease rapidly at large angles like elastic electron-proton cross-sections, exhibiting a diffractive fall-off characteristic of the spatial dimensions of the resonances. What the experimenters found was that although the individual resonance peaks quickly disappeared, the measured cross-sections remained large at large angles and high energies (technically, at high momentum transfers, q²). This behaviour is illustrated in Figure 5.4.¹⁰ Here the inelastic cross-sections are shown divided by the corresponding electron-electron

Figure 5.3. Inelastic cross-sections (d2σ/dΩdE') for small-angle (6°) scattering of relatively low-energy (10 GeV) electrons at slac. W is the mass of the hadronic system X.

scattering cross-section (σ_Mott). It is evident that the q²-dependence of the inelastic electron-proton and elastic electron-electron cross-sections is roughly the same. For comparison the elastic electron-proton cross-section is also shown, which falls off very quickly in proportion to σ_Mott.

From the preceding discussion it is perhaps clear that a straightforward inference from the parallelism between the high-q² inelastic cross-sections and ctmou was that the proton contained hard point-like scattering centres which, in some sense, resembled electrons. The significance of the large inelastic cross-sections was, however, far from immediately obvious to the slac-mit experimenters. Their initial reaction was to suspect that their findings were illusory. The grounds for this suspicion were that electrons were well known to radiate photons rather freely, and measurements of electron energy and scattering angle could therefore not be directly translated into values of momentum transfer to the target proton. Allowance had to be made for the possibility that radiated photons had carried off energy and momentum undetected. The experimenters suspected that the large inelastic cross-sections would disappear when the appropriate radiative corrections were made to allow for the effects of processes like that of Figure 5.5.

Radiative corrections could only be estimated approximately, and the appropriate calculations were, in Richard Taylor's words, ‘difficult and tedious’.¹¹ Nevertheless, such calculations went ahead at slac and mit, and it appeared that the radiative corrections could not account for the large cross-sections observed at high momentum-transfers.¹² This was the experimental situation in early 1968, but it

Figure 5.4. slac inelastic cross-sections (σ) as a function of momentum-transfer (q2). The lower curve represents elastic cross-section measurements.

Figure 5.5. Electron energy and momentum loss via photon radiation.

could not be said that at this stage a discovery had been made. The slac-mit experimenters felt fairly confident that their findings were genuine, but they had no idea what they meant: what had they found? At this point, the experimenters began to pay attention to a member of the slac hep theory group, James D.Bjorken.

Bjorken and Scaling

Bjorken was awarded a PhD in theoretical particle physics by Stanford University in 1959. After another four years there (as Research Associate and Assistant Professor) he joined the slac theory group at its foundation in 1963 (becoming a full Professor in 1967). At that time the slac accelerator was still under construction and Bjorken, like the other resident theorists, directed his efforts towards laying the groundwork for the interpretation of high-energy electron scattering. He was a field-theorist and a devotee of current algebra,¹³ and one task with which he became particularly ‘obsessed’ was that of predicting the behaviour of inelastic electron scattering. From a variety of non-rigorous perspectives — principally from consideration of a modified version of a neutrino scattering current-algebra sum-rule — he concluded that ‘the only credible guess’ was that the inelastic cross-sections would be large-as they indeed proved to be.¹⁴ He also derived a second and more quantitative result, which went as follows. In 1964, Stanford theorists S.D.Drell and J.D. Walecka had shown that in general the inelastic electron-proton scattering cross-section could be expressed in terms of two independent quantities, W₁ and W₂ known as ‘structure functions’.¹⁵ In principle, the two structure functions were each functions of two independent kinematic variables, usually chosen to be q² and ν (where ν was a measure of the energy lost by the electron in the collision). From his current-algebra calculations, Bjorken inferred that in an appropriate kinematic limit where q² and ν became large but with a fixed ratio (the ‘Bjorken limit’, as it became known), W₁ and the product νW₂ should not depend upon ν and q² independently. Rather, W₁ and νW₂ should only be functions of the ratio ν/q²: W₁ and νW₂ should fall upon unique curves when plotted against the variable ω = 2Mν/q² (M is the mass of the proton).¹⁶

Perplexed by their observations, the slac-mit experimenters were readily prevailed upon by Bjorken to plot their data against ν/q², and the data were indeed seen to exhibit the required features, at least approximately, and for values of ν and q² greater than around one or two GeV, the so called ‘deep inelastic’ region. For illustration, the universal curves for W₁ and νW₂ are shown in Figure 5.6.¹⁷ These became known as ‘scaling’ curves — because the ν-dependence of the  {131}  data points could be compensated for by an appropriate scaling of q² — and the phenomenon they enshrined became known as ‘scaling’. In passing, it is interesting to note that the variable ω' measured along the horizontal axis of Figure 5.6 is closely related but not identical to the scaling variable ω chosen by Bjorken as the relevant parameter.¹⁸ When plotted against ω, scaling was clearly only an appropriate phenomenon; ω' was a so-called ‘improved scaling variable’, chosen to display scaling as an exact phenomenon. With the advent of qcd (Chapter 7) theorists became interested in measurements of deviations from exact scaling, and the use of improved scaling variables went out of fashion. For simplicity, I will therefore refer to ω as the scaling variable in what follows.

Once their puzzling observations had been transmuted into the discovery of the scaling phenomenon, the slac-mit experimenters decided to make their findings public. The first presentations were made at the Vienna hep Conference in September 1968. In a rapporteur's talk, slac's Director, Wolfgang Panofsky, mentioned the scaling property of the deep-inelastic data,¹⁹ but this created little excitement at the time.²⁰ The problem was that, despite Bjorken's work, the significance of scaling remained unclear. Bjorken's calculations were not only heuristic: to experimenters and the many theorists unfamiliar with the outer reaches of current algebra they were esoteric to the point of incomprehensibility. When the deep-inelastic data appeared in a refereed journal in 1969 the response of the hep community was more enthusiastic.²¹ But by 1969 the theoretical context had been transformed by the intervention of Caltech theorist Richard Feynman.

5.2 The Parton Model

Late in 1968, shortly after the Vienna conference, Feynman paid a brief visit to slac. While there, he formulated the ‘parton model’ explanation of scaling, an achievement which will reverberate throughout the remaining pages of this account. Here I will trace out Feynman's route to the parton model, and explain how it was applied to deep-inelastic electron scattering.²²

Feynman was a leading field theorist — we have already noted his work on the renormalisation of qed and on the V–A theory of the weak interactions — and during the 1960s he attempted to develop some useful field-theoretic insight into the strong interaction. The general obstacles encountered by field theorists in discussing the strong interaction have been outlined in Chapter 3, but it will be useful to reformulate them here in terms more appropriate to Feynman's approach.

Figure 5.6. Structure functions (νW2 and 2MpW1, Mp is the proton mass) for deep-inelastic electron-proton scattering as measured at slac. Note that measurements at different values of q2 all fall on the same curves when plotted against the scaling variable ω'.

Figure 5.7. Feynman diagrams for (a) non-interacting electron; (b) emission and reabsorption of a photon; and (c) photon conversion to an electron-positron pair.

I have referred to the electron as structureless and point-like, and to the proton as having structure, and these terms have a particular meaning for field theorists. To explain this, let us begin with the electron and consider an electron moving freely through space. If the electromagnetic interaction did not exist, the Feynman diagram for this electron would be that shown in Figure 5.7(a) corresponding to the motion of an entity occupying only a mathematical point in space. When the electromagnetic interaction is taken into account the situation becomes more complicated: the electron can emit and reabsorb photons as it travels along, and the photons themselves can convert back and forth into electron-positron pairs. Figure 5.7(b) shows the emission and reabsorption of a single photon, as given by the first-order approximation to qed, and Figure 5.7(c) shows how, in second-order approximation, the photon can itself convert to an electron-positron pair: At higher orders of approximation to qed ever more photons and electron-positron pairs appear. Thus, when these higher order terms are taken into account, the electron appears not as a single point-like entity, but as an extended cloud of electrons, positrons and photons, which together carry the quantum numbers, energy and momentum of the physically observed electron. However, because of the weakness of the electromagnetic interaction (the smallness of the fine-structure constant) the higher-order qed

Figure 5.8. Feynman diagrams for (a) non-interacting proton; (b) emission and reabsorption of a pion; and (c) pion conversion into a nucleon-antinucleon pair.

corrections to Figure 5.7(a) represent only small perturbations. Physically, this corresponds to the fact that for most practical purposes it is sufficient to regard electrons as point-like particles. This is the field-theoretic significance of describing the electron as structureless.

A similar argument can be made for the proton (or any hadron). Figure 5.8(a) shows a non-interacting proton travelling through space. However, in considering the proton's structure, the strong as well as the electromagnetic interactions have to be taken into account. Thus, for example, in strong interaction field theories of the type discussed in Chapter 3.3, mesons and nucleon-antinucleon pairs appear as indicated in Figures 5.8(b) and (c). By virtue of its strong interaction, the proton appears in field theory as a spatially extended cloud of nucleons, antinucleons and mesons. So far the analogy between electrons and protons is exact. But it breaks down when one recognises that the strong coupling constant is large and that, as explained in Chapter 3.3, successive terms in the perturbation expansion are larger than their predecessors (rather than smaller, as is the case in qed). From the perspective of field theory it is therefore not sufficient to regard the proton as the structureless entity of Figure 5.8(a). All of the higher-order perturbations — those of Figures 5.8(b) and (c) and infinitely more complex ones, too — have to be taken into  {135}  account. In field theory the proton has an intrinsically complex structure, constituted from a whole cloud of ephemeral particles.

This was the situation which Feynman confronted as a field theorist. In one way, the field-theory image of proton structure was welcome. The ascription of a finite size of around 10^–13 cm served to explain why the elastic electron-proton scattering cross-sections decreased diffractively with momentum transfer. In another way, the image was most unwelcome. To have to deal with the proton as a particle-cloud rather than as a single particle made the field theorist's task that much more difficult, and constituted another reason for the abandonment of the traditional field theory approach to strong interaction physics. Feynman, however, was not so easily deterred. He took the view that protons (and all hadrons) were indeed clouds of an indefinite number of particles. In a field theory of mesons and nucleons, the clouds would contain mesons, nucleons and antinuc-leons; in a quark theory, they would contain quarks and antiquarks. Feynman was agnostic: he simply assumed that the swarms contained entities of unspecified quantum numbers, and christened them ‘partons’.

Suppose, reasoned Feynman, one considers a high-energy collision between two protons. Because of their high relative velocity, each proton will see the other as relativistically contracted along its direction of motion to a flat disc or pancake. Furthermore, because the strong interactions are of short range, the two pancakes would only have a very short time to interact with one another, during which they would effectively see a frozen ‘snapshot’ of the partons within each pancake. Feynman therefore envisaged high-energy hadronic collisions as taking place between individual partons of each pancake and, because the available interaction time would be small, he regarded the interaction of partons within a given pancake as negligible: during a high-energy collision the partons of each proton would act as independent, quasi-free, entities. This image was the basis of the parton model; in technical language, the trick of visualising relativistic protons as frozen pancakes was known as working in the ‘infinite-momentum frame’ (a mathematical device which had been introduced into current-algebra calculations in 1965)²³ and the trick of treating partons as free particles was known as the ‘impulse approximation’ (familiar from nuclear physics).

Feynman developed this picture in the mid-1960s in an attempt to understand the interactions of hadrons and when, in 1969, he first published his work he addressed the problem of analysing multiparticle production in high-energy hadronic soft scattering.²⁴ However, this was the province of Regge-modellers,²⁵ and partons instead  {136}  found a home in the analysis of deep-inelastic electron scattering. During his 1968 visit to slac Feynman realised that, while his analysis of hadronic soft-scattering was qualitative and intuitive,²⁶ he could give a very simple and direct parton-model explanation of scaling. He visualised deep-inelastic scattering as a process wherein the incoming electron emits a photon which then interacts with a single free parton (Figure 5.9). By construction, each parton was itself supposed to be a structureless particle, which would interact with photons just like an electron. Thus the similarity between the momentum-transfer dependence of electron-proton and electron-electron scattering shown in Figure 5.4 was immediately explicable in terms of partons. Furthermore, the mathematical definition of the structure functions W₁ and W₂ was such that each received a contribution at a given value of the scaling variable ω only when the struck parton carried a fraction x = 1/ω of the total momentum of the proton. Effectively, then, the structure functions measured the momentum distribution of partons within the proton, and this measurement was dependent only upon ω, the ratio of ν and q², and not upon their individual values. Thus scaling emerged as an exact prediction of the parton model.

Figure 5.9. Deep-inelastic scattering in the parton model.

In the years which followed the discovery of scaling, the parton model became central to the practice of increasing numbers of hep experimenters and theorists. We can discuss below some of the uses to which it was put, but first some general discussion of its appeal is appropriate. It is instructive to compare the explanations of scaling offered by Feynman's parton approach and Bjorken's current-algebra calculations. The first point to stress is that the attraction of the parton model did not lie in its success in explaining scaling per se — Bjorken could provide an alternative explanation, and other theorists had other explanations which worked just as well.²⁷ Neither can the popularity of the parton model be ascribed to the uniform  {137}  validity of its predictions. As we shall see in the next section, straightforward extensions of the model often led to conflicts with observation. The difference between the parton and current-algebra approaches to deep-inelastic electron scattering lay rather in the different meanings with which each endowed scaling. Like Feynman, Bjorken related his prediction of scaling to the existence of point-like scattering centres within the proton,²⁸ but the two men interpreted the significance of this relation differently. Bjorken's calculations led first to the prediction of scaling, then to the observation that scaling could be said to correspond to point-like scattering (an observation which he traced back to the structure of the current-algebra commutators).²⁹ Feynman, instead, began with point partons, and thence arrived at scaling. Although, in the first instance, they led to the same predictions, the two approaches differed in the conceptual frameworks in which they were set and upon which physicists could draw for their elaboration. Only a few theorists counted themselves sufficiently expert to evaluate and exploit Bjorken's current-algebra approach. Feynman's parton model, in contrast, drew upon the common culture of all trained physicists, and was available for appreciation and exploitation by hep experimenters and theorists irrespective of their particular expertise: physicists found the parton model both comprehensible and convenient.

The comprehensibility of the parton model derived from its relation to models already established in other areas of physics. The success of the parton model in explaining scaling indicated that in some circumstances, at least, one could profitably view hadrons as composites of effectively free particles. This kind of picture was far from unfamiliar to physicists, as they repeatedly pointed out, to each other in the technical literature, and to the wider public in popular scientific accounts. In a generalised sense the parton model established an analogical connection between the novel phenomenon of scaling and composite systems known to physicists from their professional childhood.

The analogy most often presented in the popular writing of scientists was that between deep-inelastic scattering and Rutherford's experiments in the early years of this century. Rutherford had bombarded specimens with α-particles (helium nuclei) and had observed that a surprisingly large number of α-particles were scattered at large angles. The slac-mit group had observed similar behaviour with highly energetic electron beams. Just as Rutherford had interpreted his results in terms of a point-like scattering centre, the nucleus, within the atom, so Feynman's model showed how scaling could be interpreted in terms of point-like partons within the  {138}  proton. Thus, for example, Wolfgang Panofsky and Henry Kendall wrote in Scientific American that ‘the Stanford experiments are fundamentally the same as Rutherford's.’³⁰ In so doing, however, they were not quite telling the whole story. An atom, physicists believe, comprises a single central nucleus surrounded by an extended cloud of electrons. The parton model, on the other hand, asserted that the proton comprised a single amorphous cloud of partons. In this respect the proton was better to be conceptualised in terms of the electron cloud of the atom or the assemblage of nucleons within the nucleus, and this closer analogy with multi-constituent composite systems was brought out and exploited in many research papers and review articles in the technical literature.³¹

Even more significant than specific detailed analogies between protons and composite atoms or nuclei was the convenient way in which Feynman formulated the parton model. His approach served, in effect, to bracket off the still intransigent strong interactions in the application of the model: all of the effects of the strong interaction were contained in the parton momentum distributions. Knowing or guessing these distributions, calculations of electron-hadron scattering processes could be reduced to simple first-order qed calculations in which partons behaved like point-particles. The only difference between such calculations and those for electron-electron scattering was that the relevant quantum numbers of the partons were a priori unknown. Needless to say, various conjectures as to the nature of the partons and their quantum numbers were available in the late 1960s culture of hep. One popular speculation was that the partons had the same quantum numbers as quarks and, as we shall see, this quickly came to be generally accepted.

In general terms, then, the appeal of the parton model was very much the same as that of the constituent quark model: it provided a simple and readily understood framework, ready for elaboration for the various purposes of theorists and experimenters in terms of the various resources available within the culture of hep. We can examine in the following section the historical development of the model and the experimental traditions which sustained it, but two further points should be clarified in advance.

First, as a composite model, the parton approach to the structure of hadrons was very similar to that of the constituent quark model. The two models were, however, quite distinct; whilst the parton model came to inherit many resources from earlier quark models it remained a separately identifiable tradition. The reason for this was that in order to explain scaling one had to treat partons as free particles, whereas the existence of strong inter-quark interactions  {139}  binding quarks into hadrons were at the heart of the constituent quark model. Besides this conceptual division, it is also important to emphasise that the parton model and the cqm addressed different experimental domains. The cqm found its greatest success in low-energy resonance physics, whereas the parton model was applied to the newly discovered high-energy, high-momentum-transfer scaling regime. Whilst attempts were made to explain scaling in terms of sums of resonances, it was clearly impossible to explain the details of hadron spectroscopy in terms of free partons.

Secondly, the idea that the parton model ‘worked’ as an explanation of scaling requires some clarification. As we shall see below, partons quickly became identified with quarks by most particle physicists, and this had one unfortunate consequence. The quark-parton explanation of scaling required that the quark struck in the electron-proton interaction behave as a free particle. If this quark continued to behave as a free particle one would expect it to shoot out of the proton and appear amongst the debris of the collision. However, quarks were no more observed in the final-states of electron scattering than in any other class of reactions. The debris of electron scattering was just a shower of normal hadrons, and some assumption had to be added to the parton model to explain this. This assumption was simply that although the quark behaved as a free particle in the initial hard interaction, it must subsequently undergo a series of soft, low momentum-transfer, strong interactions with its fellow partons. These interactions were supposed somehow to ensure that hadrons and not quarks would appear in the final state and, being soft, were assumed not to invalidate the explanation of scaling itself. Such assumptions were unavoidable and theoretically unjustifiable but, as the quark-parton model became central to the practice of increasing numbers of particle physicists, the hep community learned to live with this unsatisfactory state of affairs.

5.3 Partons, Quarks and Electron Scattering

We can now turn from the conceptual foundations of the parton model to its historical evolution. Although the model was Feynman's creation, he did not publish on the analysis of scaling until 1972.³² Instead, the parton model was taken up at slac, and first appeared in the hep literature in 1969 (with ample acknowledgment to Feynman) in an article by Bjorken and E.A.Paschos.³³ A large and diverse body of theoretical and phenomenological work elaborating upon the basic form of the model quickly came into being.³⁴ Following Feynman's lead, field theorists began openly to practise their art in the realm of the strong interaction for the first time in more than a  {140}  decade. This work led eventually to the formulation of qcd, as we shall see in Chapter 7. In the present chapter, though, I will focus on the phenomenological use of the parton model, for two reasons. First, because this was the sense in which the model was used to give structure and coherence to the experimental programme at slac and, later, elsewhere: as Kendall and Panofsky wrote in 1971, the model ‘supplied the motivation for several experiments now in the planning stage’.³⁵ And, secondly, because the identification of quarks with partons was grounded in the phenomenological analysis of scaling.

Feynman's initial analysis showed that scaling should be observed in deep-inelastic scattering whatever the nature of the partons. Subsequent phenomenological work concentrated upon trying to make detailed fits to the available data with the aim of specifying more closely the attributes of partons. At issue here was the fact that besides their scaling property, the magnitudes and shapes of the structure functions could themselves be measured in a variety of processes. Each species of parton was supposed to contribute to the total structure functions in a calculable way, given by qed and dependent only upon the spin and electric charge of the parton in question. Thus, it was argued, measurements of different structure functions would yield information on the parton quantum numbers.

For example, one conclusion which followed directly from qed was that the relative magnitudes of the W₁ and W₂ structure functions in electron-proton scattering were determined just by the parton spins. A particular mathematical combination of W₁ and W₂ denoted by 'R’ was predicted to be zero in the Bjorken limit if the partons had spin ¹/₂ (as expected for quarks) and non-zero for spin 0 or 1 (as expected if the proton-cloud included elementary mesons).³⁶ The initial slac data were insufficient to determine R, but subsequent measurements covering a wider range of energies and momentum transfers yielded a value of R = 0.18 ± 0.10.³⁷ This was ‘certainly small’, as slac theorist Fred Gilman put it in a 1972 review, and ‘given possible systematic errors it is possible, although unlikely, that R = 0’.³⁸ In default of any better proposal than spin ¹/₂ quarks for the proton's constituents, Gilman continued: ‘since experiment suggests that R is small one thinks in terms of mostly spin-¹/₂ partons’.³⁹ Besides the measurement of electron-proton scattering, the slac-mit physicists also measured electron-deuteron scattering, and the scattering of muons from both protons and deuterons. In all of these processes deep-inelastic scaling was observed to hold, consistently with the identification of partons as spin ¹/₂ objects.⁴⁰ Theorists had little difficulty in concluding that the spin ¹/₂ objects were very possibly quarks.  {141} 

More information on the parton quantum numbers was sought from an examination of the individual structure functions. According to qed, each species of parton was supposed to contribute to the total structure function in proportion to the square of its electric charge. For example, the relative contributions from u, d and s quarks, having charges +²/₃, –¹/₃ and –¹/₃ respectively, were expected to be in the proportions ⁴/₉,¹/₉ and ¹/₉ (compared with a unit contribution expected from any unit-charge parton). Hence, by making assumptions about the parton composition of the proton, estimates of the proton structure functions could be made. Since the parton momentum distributions were a priori unknown, the estimates related to the overall size of the structure functions — mathematical integrals over the entire range of the scaling variable ω (i.e. the areas under the curves of Figure 5.6).

These estimates proved to be erroneous. The three-constituent (uud) quark-parton model overestimated the measured size of the proton structure functions by a factor of around two. Neutron structure functions could be extracted from measurements on deep-inelastic electron-deuteron scattering,⁴¹ and the cqm assumption that the neutron was a three-quark udd composite again led to a factor of two overestimate. But in such adversity the parton model flourished. Feynman's fundamental image of the proton and neutron was that of a cloud containing an indefinitely large number of partons, and theorists argued that to approximate the cloud by just three quarks was not likely to be realistic. The model was elaborated accordingly, by dividing the cloud of quark-partons into two components. One component contained the minimum number of quarks required to construct the su(3) quantum numbers of the hadron at issue — uud for the proton, for example. These were known as ‘valence’ quarks, in an explicit reference to the atomic analogy. The second component comprised a quark-antiquark ‘sea’: an su(3) singlet cloud containing an indefinite number of qq pairs. The relative magnitudes of the valence and sea components could not be calculated in advance, but inclusion of the sea lent an additional degree of interpretative flexibility to the phenomenological analysis of the structure functions. However, even when they allowed for an arbitrary sea component, theorists found that they still overestimated the measured structure functions.⁴²

Undeterred, theorists elaborated the quark-parton model still further, and introduced ‘glue’ into the constitution of the proton. The argument here was that if the nucleon was simply a composite of non-interacting quarks it would fall apart. Some interacting entity was required to ‘glue’ the quarks together: in field-theoretic terms, for  {142}  example, some other particle must interact with the quarks to provide the requisite attractive interquark forces. This hypothetical particle, about which much more will be said later, was known as the ‘gluon’.⁴³ Two theorists at mit, Victor Weisskopf and Julius Kuti (a visitor from Eotvos University in Budapest) took the gluon idea seriously, and in 1971 produced a detailed model of the structure functions.⁴⁴ They assumed that the gluons were electrically neutral and would therefore not contribute directly to electron scattering. The gluons would, however, share in carrying the total momentum of protons and neutrons. Thus the gluons would act as an important but invisible component of protons and neutrons in electron-scattering experiments. The effect of allowing for a gluonic component was to reduce still further the estimates of the size of the structure functions. Like the qq sea, the gluon component was a free parameter in the Kuti-Weisskopf model, and with this further degree of explanatory freedom it was found to be possible to achieve a ‘fair quantitative fit’⁴⁵ to the slac data.

By this stage, though, the quark-parton model was in danger of becoming more elaborate than the data which it was intended to explain. A critic could easily assert that the sea and gluon components were simply ad hoc devices, designed to reconcile the expected properties of quarks with experimental findings. Field theorists could argue that the sea and glue would be required in any sensible field theory of quarks (although they had no actual candidate for such a theory); but most particle physicists in the late 1960s and early 1970s were not field theorists, and many were openly sceptical of such arguments. Something more was required to persuade the hep community at large of the validity of the parton model, and of the equation of partons to quarks. Neutrino scattering experiments provided what was needed.

5.4 Neutrino Physics

One of the processes to which theorists quickly extended the parton model was neutrino (and antineutrino) scattering from nucleons.⁴⁶ Except for the fact that three independent structure functions were required to describe neutrino scattering (as against two for electron scattering), the weak neutrino-parton interaction could be seen as very similar to the electromagnetic electron-parton interaction.⁴⁷ This is indicated in Figure 5.10 where neutrino-parton scattering is depicted as mediated by exchange of a W-particle (see Chapter 3.3) in order to make the analogy with Figure 5.9 explicit. From a theoretical point of view the principal difference between electron and neutrino scattering lay in their different dependences upon the parton  {143}  quantum numbers: the photon coupled to the electric charges of the partons while the W coupled to the weak charges. Thus theorists argued that if one combined data on electron and neutrino scattering — assuming that scaling would hold for the latter — one could obtain more information than from electron scattering alone.

Figure 5.10. Inclusive neutrino-proton scattering in the parton model.

From an experimental point of view, the important difference between electron and neutrino scattering was one of reaction rates. Being mediated by the weak rather than the electromagnetic interactions, neutrino events were extremely infrequent and hard to observe. The first accelerator neutrino experiments were carried out in the early 1960s, using secondary neutrino beams produced at the newly operational Brookhaven ags and cern ps.⁴⁸ The objective of these experiments was three-fold: to demonstrate the technical feasibility of hep neutrino physics; to investigate the ‘two-neutrino hypothesis’; and to search for W-particles — the intermediate vector bosons (ivbs) of the weak interaction.⁴⁹ The first and second of these objectives were achieved in the earliest Brookhaven experiment and quickly confirmed at cern: events induced by neutrinos were identified, and the two-neutrino hypothesis was confirmed. The latter asserted that there were two distinct species of neutrinos, ν_e and ν_μ, associated with electrons and muons respectively.⁵⁰ None of the first round experiments was successful in detecting the production of ivbs.⁵¹ More neutrino experiments were performed during the 1960s, most of them at cern where neutrino physics became a local specialty, but they were now directed towards more mundane topics: ‘elastic’ neutrino scattering (e.g. νn ⟶ μ^–p) and resonance production.⁵² These exclusive processes, in which only a small number of particles were produced and all were experimentally identified, were those of principal theoretical interest at the time.⁵³  {144} 

This was the situation when the parton model entered the scene. In 1969 parton modellers began to argue, in analogy with electron scattering, that inelastic, inclusive neutrino scattering, in which any number of hadrons could be produced, was the truly interesting aspect of neutrino physics. The advocates of the parton model constituted a new audience for the neutrino experimenters, and the latter did their best to respond. The most extensive set of relevant neutrino data came from a series of bubble-chamber experiments carried out at cern between 1963 and 1967. Analysis of these data had hitherto focused upon the exclusive channels mentioned above but, by virtue of the indiscriminate character of bubble-chamber photographs, inclusive cross-sections could also be extracted from them. A total of around 900 neutrino events had been recorded on film. This was insufficient to provide detailed information on the three neutrino structure functions at different values of ν and q² and hence to test scaling directly, but it was sufficient to test a cruder prediction of the parton model. Bjorken and others had shown that if the neutrino structure functions did scale, then total neutrino cross-sections should be directly proportional to the energy of the neutrino beam.⁵⁴ The cern experimenters analysed their data accordingly and in September 1969 announced that, within considerable experimental uncertainties, a linear relation between beam energies and cross-sections did obtain.⁵⁵

Here matters rested until 1971, when the French-built bubble-chamber ‘Gargamelle’ was installed at cern.⁵⁶ Gargamelle was almost ten times larger than the bubble chambers used in previous neutrino experiments at cern, and promised to collect much more extensive data in a reasonable space of time.⁵⁷ In February 1964, when the construction of Gargamelle was first proposed, its virtues for the measurement of exclusive processes and searches for intermediate vector bosons had been stressed,⁵⁸ but as the time approached for its first operation priorities had begun to change. A quotation from Bernard Gregory, then Director-General of cern, serves to indicate both the response of the hep community to the slac data and the influence of the parton model on the planning of the forthcoming neutrino experiments: the slac scaling data, he wrote in 1970,

appear to be produced by the recoil of point-like constituents inside the proton. Here . . . we have a mathematical picture which may or may not have a direct physical significance. The name ‘partons’ has been given to these postulated constituents. It will be possible to repeat such experiments at cern, using the neutrino as an excellent probe. In a few months time, combining  {145}  a refined neutrino beam and the large Gargamelle bubble chamber, an experiment will be carried out on this important new subject.⁵⁹

In 1971, Gargamelle produced around 500,000 pictures; in 1972, 400,000; in 1973, 700,000 (despite a serious breakdown); in 1974, 240,000; and in 1975, the final year of Gargamelle's operation at the ps, 250,000.⁶⁰ In 1972 a team of more than 50 physicists, drawn from cern and six European universities,⁶¹ began to analyse the film. In 1973, the Gargamelle group published their first results.⁶² They had analysed 95,000 pictures taken in a neutrino beam and 174,000 pictures taken in an antineutrino beam, and had positively identified around 2,500 instances of neutrino interactions (neutrino events) and 1,000 antineutrino events. They were able to show that cross-sections increased linearly with neutrino energy, as expected from the parton model, albeit with very large uncertainties above 4 GeV where few events had been recorded. At this time, the Gargamelle group did not report a full analysis of the neutrino structure functions, but did report the overall size of W₂ (i.e. the integral of W₂ over all values of ω). This was given by the difference of the neutrino and antineutrino total cross-sections, and the observed value was quoted to be 0.49 ± 0.03. In the parton model, this number corresponded to the fraction of the proton momentum carried by non-interacting partons. Theorists assumed that the gluons were immune to the weak as well as the electromagnetic interaction, and therefore regarded the Gargamelle result as showing that around fifty per cent of the proton's momentum was carried by the gluon component — supporting the similar conclusion already reached in the analysis of deep-inelastic electron scattering.

In 1974 the Gargamelle group submitted for publication a more detailed study of their existing sample of neutrino and antineutrino events.⁶³ Here they announced that an analysis of the energy and momentum-transfer dependence of their data showed them to be consistent with scaling. They also announced two further results on the integrated magnitudes of the structure functions. First the ratio of the W₂ structure functions for neutrino- and electron-scattering was reported to be 3.6 ± 0.3. In the parton model this ratio was sensitive to the parton charges, and the experimental result supported the identification of partons with fractionally charged quarks. Indeed, the quark-parton model predicted a ratio of exactly 3.6 (18/5), while the assumption of integrally charged partons led to a ratio of 2.⁶⁴ Secondly, the Gargamelle experimenters reported that the integrated value of the W₃ structure function was 3.2 ± 0.6. The quark-parton prediction here was 3, corresponding to the three valence quarks of  {146}  the model. Again, different identifications of partons led to different numerical predictions.⁶⁵

The most detailed Gargamelle data appeared in a refereed journal in 1975. Preliminary announcements had, however, been made at conferences in the summer of 1973,⁶⁶ and by that time there was general agreement that the parton model, with the identification of quarks with partons, was a promising approach to the analysis of both electron and neutrino inelastic scattering. Theoretical arguments could still be brought against the quark-parton idea — why were quarks not produced as free particles in deep-inelastic scattering; what was the mysterious gluon component? — but Feynman felt justified in remarking that ‘There is a great deal of evidence for, and no experimental evidence against, the idea that hadrons consist of quarks. . . . Let us assume it is true.’⁶⁷ Many physicists did just that, and in the early 1970s the quark-parton model became central to the planning and interpretation of lepton scattering experiments.

5.5 Lepton-Pair Production, Electron-Positron Annihilation
and Hadronic Hard Scattering

The quark-parton model drew its early empirical support primarily from electron- and neutrino-scattering experiments. The model was, though, extended to certain other processes. In the late 1960s little experimental information was available on these processes but, in the fullness of time, they all came to constitute important strands of the new physics.

Inclusive Lepton-Pair Production

Inclusive lepton-pair production, the process pp ⟶ l⁺l^–X (where ‘l’ represents either an electron or muon, and ‘X’ represents any collection of hadrons) was readily conceptualised in the quark-parton model. As indicated in Figure 5.11, it could be visualised as the annihilation of a quark and an antiquark (coming from the sea of either the beam or the target proton) to form a photon which then materialised as a lepton pair. Many authors, amongst whom slac theorists Sidney Drell and Tung-Mow Yan were most influential, gave estimates of the appropriate cross-sections, using qed to evaluate the probabilities for the production and decay of the photon, and the measured deep-inelastic structure functions to specify the parton momentum distribution.⁶⁸

Experimentally, appropriate measurements were very hard to make. The major problem was to detect the few lepton pairs expected amongst the large numbers of hadrons produced in high-energy proton-proton collisions. In the late 1960s and early 1970s, the only

Figure 5.11. Lepton-pair production in the parton model.

relevant data came from an experiment performed at the Brookhaven ags in 1968.⁶⁹ Carried out by Leon Lederman and his colleagues from Columbia University, the primary aim of this experiment, like the neutrino experiments of the 1960s, was to search for ivbs.⁷⁰ Like the neutrino experiments, the Columbia dilepton experiment failed to find any ivbs and was, instead, embraced by the parton modellers. Cross-sections were found to fall off roughly as the sixth power of the combined mass of the lepton pair, and the Drell-Yan model gave a ‘qualitatively correct description’⁷¹ of this behaviour. More important than the qualitative agreement of prediction and data, the Columbia experiment showed that high-energy lepton-pair measurements were technically possible, and the parton model made them interesting (even if no ivbs were to be found). Further experiments were planned along similar lines, and developments in this area will be reviewed in Part in of this account.

Electron-Positron Annihilation

In the quark-parton model, electron-positron annihilation to had-rons was envisaged as shown in Figure 5.12.⁷² Here the electron and positron annihilate to form a photon which materialises as a quark-antiquark pair. This was the simplest of all processes to calculate in the parton model: since the momenta of the quark and antiquark were precisely determined by momentum conservation, no recourse to momentum distributions specified by measured structure functions was necessary. Of course, assumptions had to be made to explain how the produced quarks would rearrange themselves into hadrons, but theorists followed the usual route and asserted that such rearrangement would not affect the parton model predictions. In the late 1960s, the principal source of information upon electron-positron annihilation was the adone electron-positron collider which began operation at Frascati in Italy in 1967. Early data from adone confirmed the general expectations, at least, of the quark-parton model.⁷³ Quantitatively, however, the model failed to explain the  {148}  data. This merely encouraged theorists to endow quarks with yet another set of properties known as ‘colour’, but discussion of colour will be postponed to Chapter 7 when it can be related to several other developments connected with quarks and the parton model.

Figure 5.12. Electron-positron annihilation to hadrons in the parton model.

Hadronic Experiments

The earliest applications of the parton model were all to processes involving leptons in either the initial or final states. In the late 1960s and early 1970s there were no obvious analogues of scaling to be seen in the realm of purely hadronic experiment. Only with the advent in 1971 of the proton-proton collider, the Intersecting Storage Rings (isr) at cern, did this situation begin to change.

The isr made available a centre-of-mass energy considerably greater than that available at any other facility, and in the first round of isr experiments several groups set out to hunt for ivbs.⁷⁴ These hunts were extensions of the 1968 Brookhaven experiments discussed above. Any ivbs produced were to be identified by their decay to leptons, and the crucial technical problem at the isr was to detect the leptons against the large background of hadrons associated with high-energy collisions. Lower-energy experiments had shown that inclusive hadron production (e.g. pp ⟶ πX) showed similar diffractive characteristics to elastic electron-proton scattering. Most collisions were soft, and cross-sections decreased rapidly as a function of the transverse momentum (p_T) of the detected hadron. Typical inclusive hadron cross-sections fell-off exponentially fast, roughly as e^–6p_T. The experimenters therefore decided to look for high-transverse-momentum leptons, because at high transverse momenta the background of hadrons would be small and relatively easy to cope with.⁷⁵

As ivb searches, these experiments failed. It was found that although inclusive hadronic cross-sections did fall fast with p_T at the isr, they did not fall as fast as expected. Figure 5.13 shows an early compilation of isr cross-sections for inclusive pion production, pp ⟶ π⁰ X.⁷⁶ The straight line is an extrapolation of the low-p_T data,  {149}  and the high-p_T measurements stand well above this. Although the high-px cross-sections found at the isr were small in absolute terms, having fallen by six orders of magnitude in going from transverse momenta of 1 GeV to 4 GeV, they were still very large compared with prior expectations — by a factor of 10² to 10³ at a transverse momentum of 4 GeV. The consequence of this was that hadronic backgrounds remained sufficient, even at high p_T, to make it impossible to detect leptons with existing apparatus, and hence to vitiate the ivb searches. However, just because the hadronic high-p_T cross-sections were unexpectedly large, they could be argued to represent a new phenomenon in their own right. One of the first-round experimenters at the isr was Leon Lederman, pursuing the ivbs to higher energies after his earlier experience at the Brookhaven ags and, as he later remarked: ‘[The hadronic] background became the signal for a new field of high transverse momentum hadrons. This subject literally exploded in the period 1972–1975.’⁷⁷

The excess production of high-p_T hadrons was observed by three groups at the isr in 1972 and the first results were published in 1973.⁷⁸ The observations were quite unexpected, at least by the experimenters, but in the theoretical context of the time were immediately, if tentatively, interpreted as the first evidence in purely hadronic reactions for the hard scattering of point-like constituents — partons — within the proton. As W. Jentschke, cern's Director-General, wrote in 1972:

An intriguing question over the past few years was why partons were noticed only in electromagnetic but not in strong interaction processes . . . . However, two recent isr experiments have given results which might indicate point-like constituents also in strong interactions. . . . This is perhaps the most exciting, unexpected, result from the isr.⁷⁹

In ascribing the excess high-p_T production of hadrons to hard-scattering between point-like constituents, physicists were merely following the basic Rutherford-type analogy at the heart of the parton model. Indeed, the isr observations had been qualitatively predicted in advance by parton modellers.⁸⁰ However, problems arose when attempts were made at more quantitative analyses of the isr data. The high-p_T cross-sections were found to be several orders of magnitude larger than the earliest parton-model calculations. This was not very surprising. The calculations had assumed that hard hadronic scattering was mediated by photon-exchange between quark-partons, in direct analogy with the other processes discussed above. While such an assumption was routine for processes involving leptons (which

Figure 5.13. Inclusive pion-production cross-sections (Ed3σ/dp3) as a function of pion momentum transverse beam axis (pT), measured at the isr by the cern-Columbia-Rockefeller (ccr) collaboration. The different data point symbols correspond to the different centre-of-mass energies given in the key in the upper right.

were believed to couple only to photons and ivbs) it was neither routine nor plausible for quarks. One could easily imagine quarks interacting with one another by exchanging gluons, or even conventional mesons. Furthermore, if one took seriously the gluonic component of hadrons, then one had also to consider the possibility of gluon-gluon hard scattering (one gluon from each proton) and gluon-quark scattering.

Thus much of the simplicity of the parton model was lost when it was applied to processes in which no leptons were present to guarantee the primacy of photon (or W) exchange. It was not clear how the parton model should be extended to hadronic hard scattering, nor was it clear what was to be learned from such extensions.⁸¹ But, for the present, the significant point to note is that the interest of parton-modellers served to crystallise the isr discovery  {151}  of large high-p_T hadronic cross-sections as that of an important new phenomenon worthy of further exploration. From 1972 onwards a distinctive tradition of hard-scattering experiments emerged, first at the isr and later at Fermilab and the cern sps, which aimed at detailed investigation of large transverse momentum hadronic processes. And, under the aegis of the quark-parton model, this tradition found a place in the experimental new physics alongside the investigation of deep-inelastic lepton scattering, lepton-pair production and electron-positron annihilation. We will encounter all of these traditions again in subsequent chapters.

NOTES AND REFERENCES