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Home , Elementary particle, Steven Weinberg

What Is An Elementary ? by

HEN A STRANGER, hearing that I am a physi- W cist, asks me in what area of I work, I generally reply that I work on the theory of elementary . Giving this answer always makes me nervous. Suppose that the stranger should ask, “What is an elemen- tary particle?” I would have to admit that no one really knows. Let me declare first of all that there is no difficulty in saying what is meant by a particle. A particle is simply a physical system that has no continuous degrees of freedom except for its total mo- mentum. For instance, we can give a complete description of an by specifying its momentum, as well as its around any given axis, a quantity that in mechanics is discrete rather than continuous. On the other hand, a system consisting of a free electron and a free is not a particle, because to describe it one has to specify the momenta of both the electron and the proton— not just their sum. But a of an electron and a proton, such as a hydrogen in its state of lowest , is a particle. Everyone would agree that a hydrogen atom is not an , but it is not always so easy to make this distinction, or even to say what it means.

Copyright © 1996 by Steven Weinberg. Research supported in part by the Robert A. Welch Foundation and NSF Grant PHY 9511632.

BEAM LINE 17 OR THE FIRST FEW decades .) It was the 1936 discovery of this century there did not of the independence of nuclear Fseem to be any trouble in say- forces by Merle Tuve et al. that ing what is meant by an elementary showed clearly that and particle. J. J. Thomson could use the have to be treated in the electric field in a cathode-ray tube to same way; if protons are elementary, pull electrons out of , so atoms then neutrons must be elementary were not elementary. Nothing could too. Today, in speaking of protons be pulled or knocked out of electrons, and neutrons, we often lump them so it seemed that electrons were el- together as . ementary. When atomic nuclei were This was just the beginning of a discovered in Ernest Rutherford’s lab- great increase in the roster of so- oratory in 1911, it was assumed that called elementary particles. they were not elementary, partly be- were added to the list in 1937 (though cause it was known that some ra- their was not understood un- dioactive nuclei emit electrons and til later), and and strange par- other particles, and also because nu- ticles in the 1940s. had clear charges and could be ex- been proposed by in plained by assuming that nuclei are 1930, and made part of beta-decay composed of two types of elementary theory by in 1933, but who discovered the particles: light, negatively charged were not detected until the Reines- in 1932. (Courtesy AIP Meggers electrons and heavy, positively Cowan experiment of 1955. Then in Gallery of Nobel Laureates) charged protons. the late 1950s the use of particle ac- Even without a definite idea of celerators and bubble chambers re- what is meant by an elementary par- vealed a great number of new parti- ticle, the idea that all consists cles, including of spin higher of just two types of elementary par- than 0 and of spin higher ticle was pervasive and resilient in a than 1/2, with various values for way that is difficult to understand to- charge and strangeness. day. For instance, when neutrons On the principle that—even if were discovered by James Chadwick there are more than two types of el- in 1932, it was generally assumed ementary particles—there really that they were bound states of pro- should not be a great number of tons and electrons. In his paper an- types, theorists speculated that most nouncing the discovery, Chadwick of these particles are composites of offered the opinion: “It is, of course, a few types of elementary particles. possible to suppose that the neutron But such bound states would have to is an elementary particle. This view be bound very deeply, quite unlike has little to recommend it at present, atoms or atomic nuclei. For instance, except the possibility of explaining pions are much lighter than nucle- the statistics of such nuclei as N14.” ons and antinucleons, so if the (One might have thought this was were a bound state of a and a pretty good reason: molecular spec- an antinucleon, as proposed by Fer- tra had revealed that the N14 nucle- mi and Chen-Ning Yang, then its us is a , which is not possible would have to be if it is a bound state of protons and large enough to cancel almost all of

18 SPRING 1997 the of its constituents. The composite nature of such a particle would be far from obvious. How could one tell which of these particles is elementary and which composite? As soon as this question was asked, it was clear that the old answer—that particles are elemen- tary if you can’t knock anything out of them—was inadequate. Mesons come out when protons collide with each other, and protons and antipro- tons come out when mesons collide with each other, so which is a com- posite of which? Geoffrey Chew and Jr. Ehrenfest, P. others in the 1950s turned this ONG BEFORE Heisenberg , left, talking with dilemma into a point of principle, reached this rather exaggerat- Neils Bohr at the Copenhagen Conference, Bohr Institute, 1934. known as “nuclear democracy,” ed conclusion, a different sort L (Courtesy AIP Emilio Segrè Visual Archives) which held that every particle may of definition of elementary particle be considered to be a bound state of had become widespread. From the any other particles that have the ap- perspective of quantum field theory, propriate quantum numbers. This as developed by Heisenberg, Pauli, view was reflected decades later in a and others in the period 1926–34, the 1975 talk to the German Physical So- basic ingredients of Nature are not ciety by Werner Heisenberg, who particles but fields; particles such as reminisced that: the electron and are bundles of energy of the electron and the elec- In the experiments of the fifties and sixties . . . many new particles tromagnetic fields. It is natural to de- were discovered with long and fine an elementary particle as one short lives, and no unambiguous whose field appears in the funda- answer could be given any longer mental field equations—or, as the- to the question about what these orists usually formulate these the- particles consisted of, since this ories, in the Lagrangian of the theory. question no longer has a rational It doesn’t matter if the particle is meaning. A proton, for example, could be made up of neutron and heavy or light, stable or unstable—if pion, or Lambda- and , its field appears in the Lagrangian, it or out of two nucleons and an anti- is elementary; if not, not. nucleon; it would be simplest of all This is a fine definition if one to say that a proton just consists of knows the field equations or the La- continuous matter, and all these grangian, but for a long while physi- statements are equally correct or cists didn’t. A fair amount of theo- equally false. The difference be- tween elementary and composite retical work in the 1950s and 1960s particles has thus basically disap- went into trying to find some objec- peared. And that is no doubt the tive way of telling whether a given most important experimental dis- particle type is elementary or com- covery of the last fifty years. posite when the underlying theory is

BEAM LINE 19 We will not be

able to say

which particles

are elementary

until we have not known. This turned out to be composites of and , not a final theory possible in certain circumstances because we can knock quarks and in nonrelativistic quantum me- of force and matter. gluons out of them, which is believed chanics, where an elementary par- to be impossible, but because that is ticle might be defined as one whose the way they appear in the theory. coordinates appear in the Hamilton- The one uncertain aspect of the ian of the system. For instance, a becomes incorrect, and instead we is the mechanism theorem due to the mathematician get a formula for the length that breaks the electroweak gauge Norman Levinson shows how to in terms of the nucleon mass, the symmetry and gives the W and Z par- count the numbers of stable non- deuteron binding energy, and the ticles their masses, thereby adding elementary particles minus the num- fraction of the time that the deuteron an extra helicity state to what would ber of unstable elementary particles spends as an elementary particle (that have been the two helicities of a in terms of changes in phase shifts is, the absolute value squared of the massless W or Z particle of spin 1. as the kinetic energy rises from zero element between the physi- Theories of electroweak symmetry to infinity. The trouble with using cal deuteron state and the elemen- breakdown fall into two categories, this theorem is that it involves the tary free-deuteron state). Comparing according to whether these extra he- phase shifts at infinite energy, where this formula with experiment licity states are elementary, as in the the approximation of nonrelativistic showed that the deuteron spends original form of the Standard Model, potential scattering clearly breaks most of its time as a composite par- or composite, as in so-called tech- down. ticle. Unfortunately, arguments of nicolor theories. In a sense, the prime I worried about this a good deal in this sort cannot be extended to task driving the design of both the the 1960s, but all I could come up deeply bound states, such as those Large and the ill- with was a demonstration that the encountered in elementary particle fated SSC was to settle the question deuteron is a bound state of a proton physics. of whether the extra helicity states and neutron. This was not exactly The lack of any purely empirical of the W and Z particles are ele- a thrilling achievement—everyone way of distinguishing composite and mentary or composite particles. had always assumed that the elementary particles does not mean deuteron is a bound state—but the that this distinction is not useful. In demonstration had the virtue of re- the 1970s the distinction between el- HIS MIGHT have been the lying only on nonrelativistic quan- ementary and composite particles end of the story, but since the tum mechanics and low-energy neu- seemed to become much clearer, Tlate 1970s our understanding tron-proton scattering data, without with the general acceptance of a of has taken any specific assumptions about the quantum field theory of elementary another turn. We have come to un- Hamiltonian or about what happens particles known as the Standard derstand that particles may be de- at high energy. There is a classic for- Model. It describes , , and scribed at sufficiently low mula that gives the spin triplet s- gauge fields, so these are the ele- by fields appearing in so-called ef- wave neutron-proton scattering mentary particles: six varieties or fective quantum field theories, length in terms of the nucleon mass “flavors” of quarks, each coming in whether or not these particles are tru- and the deuteron binding energy, but three colors; six flavors of , ly elementary. For instance, even the derivation of this formula actu- including the electron; and twelve though nucleon and pion fields do ally relies on the assumption that the gauge , including the photon, not appear in the Standard Model, we deuteron is a bound state. If we as- eight gluons, and the W+, W–, and Z0 can calculate the rates for processes sume instead that the free-particle particles. The proton and neutron involving low-energy pions and nu- part of the Hamiltonian contains an and all of the hundreds of mesons and cleons by using an effective quantum elementary deuteron state, then this baryons discovered after World War II field theory that involves pion and formula for the scattering length are not elementary after all; they are nucleon fields rather than quark and

20 SPRING 1997 fields. In this field theory pi- ons and nucleons are elementary, though nuclei are not. When we use a field theory in this way, we are sim- ply invoking the general principles of relativistic quantum theories, to- gether with any relevant symmetries; we are not really making any as- sumption about the fundamental structures of physics. From this point of view, we are en- titled only to say that the quarks and gluons are more elementary than nu- cleons and pions, because their fields appear in a theory, the Standard Model, that applies over a much wider range of energies than the ef- fective field theory that describes nu- cleons and pions at low energy. We cannot reach any final conclusion about the elementarity of the quarks and gluons themselves. The Standard Model itself is probably only an effective quantum field theory, matter. When we have such a theo- Elementary particles today. There are which serves as an approximation to ry, we may find that the elementary three known families of quarks and some more fundamental theory structures of physics are not parti- leptons in the Standard Model. whose details would be revealed at cles at all. Many theorists think that energies much higher than those the fundamental theory is something available in modern accelerators, and like a , in which which may not involve quark, lep- quarks, leptons, etc. are just differ- ton, or gauge fields at all. ent modes of vibration of the strings. One possibility is that the quarks It seems impossible in principle to and leptons and other particles of the identify one set of strings as truly el- Standard Model are themselves com- ementary, because, as recently real- posites of more elementary particles. ized, different theories with The fact that we see no structure in different types of strings are often the quarks and leptons only tells us equivalent. that the energies involved in their There is a lesson in all this. The binding must be quite large—larger task of physics is not to answer a set than several trillion electron volts. of fixed questions about Nature, such But so far no one has worked out a as deciding which particles are ele- convincing theory of this sort. mentary. We do not know in advance We will not be able to give a fi- what are the right questions to ask, nal answer to the question of which and we often do not find out until we particles are elementary until we are close to an answer. have a final theory of force and

BEAM LINE 21