The God Particle

by Leon Lederman

  Jesse, a horseman, lived in Spain to train with the Spanish cavalry. When he learned I had three horses, he ran off to ride with my wife and the Fermilab horse club. A real expert, he gave everybody pointers. Pretty soon the prairie riders were trading tips on flying changes, passages, lavade, corbette, and capriole maneuvers. We now have a trained Fermilab cavalry to defend the lab should the hostile forces from CERN or SLAC decide to attack on horseback.

  Friday we installed all the cards, testing each one carefully. By Saturday morning we were up and running, and a few days later a quick analysis showed that the bump was still there. Jesse stayed on for two weeks, riding horses, charming everyone, advising on fire prevention. We never got a bill from him, but we did pay for the chemicals. And that was how the world acquired a third generation of quarks and leptons.

  The very name "bottom" suggests that there must be a "top" quark. (Or if you prefer the name "beauty," then there is a "truth" quark.) The new periodic table now reads:

  First generation Second generation Third generation

  QUARKS

  up (u) charm (c) top? (t)

  down (d) strange (s) bottom (b)

  LEPTONS

  electron neutrino (νe) muon neutrino (νμ) tau neutrino (ντ)

  electron (e) muon (μ) tau (τ)

  At this writing, the top quark has yet to be found. The tau neutrino has also never been pinned down experimentally, but no one really doubts its existence. Various proposals for a "three-neutrino experiment," a souped-up version of our two-neutrino experiment, have been submitted over the years at Fermilab, but all have been rejected because such a project would be enormously expensive.

  Note that the lower left-hand grouping (νe-e-vμ-μ) in our table was established in the 1962 two-neutrino experiment. Then the bottom quark and the tau lepton put the (almost) finishing touches on the model in the late 1970s.

  The table, once the various forces are added to it, is a compact summary of all the data emerging from all of the accelerators since Galileo dropped spheres of unequal weights from the nearly vertical tower at Pisa. This table is called the standard model or, alternately, the standard picture or standard theory. (Memorize.)

  In 1993 this model is still the ruling dogma of particle physics. The machines of the 1990s, primarily Fermilab's Tevatron and CERN's electron-positron collider (called LEP), are concentrating the efforts of thousands of experimentalists on clues to what lies beyond the standard model. The smaller machines at DESY, Cornell, Brookhaven, SLAC, and KEK (Tsukuba, Japan) are also attempting to refine our knowledge of the many parameters of the standard model and trying to find clues to a deeper reality.

  There is much to do. One task is to explore the quarks. Remember in nature only two kinds of combinations exist: (1) quark plus antiquark ()—these are the mesons—and (2) three quarks (qqq)—the baryons. Now we can play and compose hadrons such as and ... Have fun! And uud, ccd, ttb ... Hundreds of combinations are possible (somebody knows how many). All are particles that either have been discovered and listed in the tables or are ready to be discovered. By measuring the mass and the lifetimes and the decay modes, one learns more and more about the strong quark force mediated by gluons and about weak-force properties. Much to do.

  Another experimental high point is called "neutral currents," and it is crucial to our story of the God Particle.

  The Weak Force Revisited

  By the 1970s lots of data had been collected on the decay of unstable hadrons. This decay is really the manifestation of the constituent quarks undergoing reactions—for example, an up quark changing to a down quark or vice versa. Even more informative were the results of several decades of neutrino-scattering experiments. Together, the data insisted that the weak force had to be carried by three massive messenger particles: a W+, a W−, and a Z0. These had to be massive because the weak force has a very small sphere of influence, reaching no farther than approximately 10−19 meters. Quantum theory enforces a rough rule that the range of a force varies inversely as the mass of the messenger particle. The electromagnetic force reaches out to infinity (although it gets weaker with distance), and its messenger particle is the zero-mass photon.

  But why three force carriers? Why three messenger particles—one positively charged, one negatively charged, and one neutral—to propagate the field that induces the changes of species? To explain, we're going to have to do some physics bookkeeping, making sure that things come out equal on both sides of the arrow (→). This includes the electric-charge signs. If a neutral particle decays into charged particles, for example, the positive charges have to offset the negatives.

  First, here's what happens when a neutron decays into a proton, a typical weak-force process. We write it like this:

  We have seen this before: a neutron decays into a proton, an electron, and an antineutrino. Note that the positive proton cancels the negative charge of the electron on the right side of the reaction, the antineutrino being neutral. Everything works out. But this is a superficial view of the reaction, like watching an egg hatch into a blue jay. You don't see what the fetus is doing inside. The neutron is really a conglomerate of three quarks—one up and two downs (udd); a proton is two ups and a down (uud). So when a neutron decays into a proton, a down quark changes into an up quark. Thus it's more instructive to look inside the neutron and describe what's happening to the quarks. And in quark language, the same reaction can be written:

  That is, a down quark in the neutron changes to an up quark, emitting an electron and an antineutrino. However, this too is a simplified version of what really happens. The electron and antineutrino don't come directly out of the down quark. There's an intermediate reaction involving a W−. The quantum theory of the weak force therefore writes the neutron decay process in two stages:

  1) d− ⅓ → W− + u+⅔

  and then

  Note that the down quark decays first into a W− and an up quark. The W in turn decays into the electron and antineutrino. The W is the mediator of the weak force and participates in the decay reaction. In the above reaction it must be a negative W to balance the change in electric charge when d goes to u. When you add the −1 charge of the W− to the +⅔ charge of the up quark, you get −⅓, the charge of the down quark that started the reaction. Everything works out.

  In nuclei, up quarks can also decay into down quarks, turning protons into neutrons. In quark language the process is described: u → W+ + d and then W+ → e+ + νe. Here we need a positive W to balance the change of charge. Thus the observed decays of quarks, via the changes of neutrons to protons and vice versa, require both a W+ and a W−. But that's not the whole story.

  Experiments carried out in the mid-1970s involving neutrino beams established the existence of "neutral currents," which in turn required a neutral heavy force carrier. These experiments were stimulated by theorists like Glashow who were working the unification-of-forces frontier and were frustrated by the fact that weak forces seemed to require only charged force carriers. The hunt was on for neutral currents.

  A current is basically anything that flows. A current of water flows in a river or a pipe. A current of electrons flows in a wire or through a solution. The W− and W+ mediate the flow of particles from one state to another and the need to keep track of the electric charge probably generated the "current" concept. The W+ mediates a positive current; the W− mediates the negative current. These currents are studied in spontaneous weak decays, such as those just described. But they can also be generated by neutrino collisions in accelerators, made possible by the development of neutrino beams in the Brookhaven two-neutrino experiment.

  Let's look at what happens when a muon neutrino, the kind we discovered at Brookhaven, collides with a proton—or more specifically, with an up quark in the proton. The collision of a muon antineutrino with an up quark generates a down quark and a positive muon.

  Or, in English, muon antineutrino plus up quark → down quark plus positive muon. Effectively, when the neutrino
and up quark collide, the up turns into a down and the neutrino converts to a muon. Again, what really happens in the weak-force theory is a two-reaction sequence:

  The antineutrino collides with the up quark and leaves the collision as a muon. The up turns into a down, the whole reaction mediated by the negative W. So we have a negative current. Now, even as early as 1955, theorists (notably Glashow's teacher Julian Schwinger) noted that it would be possible to have a neutral current, like so:

  νμ + u → u + νμ

  What's happening here? We have muon neutrinos and up quarks on both sides of the reaction. The neutrino bounces off the up quark but emerges as a neutrino, not a muon as in the previous reaction. The up quark gets nudged but remains an up quark. Since the up quark is part of a proton (or a neutron), the proton, albeit jostled, remains a proton. If we were to look at this reaction superficially, we would see a muon neutrino hitting a proton and bouncing off intact. But it's more subtle than that. In the previous reactions, either a negative or a positive W was required to help facilitate the metamorphosis of an up quark into a down or vice versa. Here, the neutrino must emit a messenger particle to kick the up quark (and be swallowed by it). When we try to write this reaction, it's clear that this messenger particle must be neutral.

  This reaction is similar to the way we understand the electrical force, say between two protons; there is an exchange of a neutral messenger, the photon, and this produces the Coulomb law of force, which allows one proton to kick another. There is no change of species. The similarity is not fortuitous. The unification crowd (not the Reverend Moon but Glashow and his friends) needed such a process if they were to have a prayer of unifying the weak and electromagnetic forces.

  So the experimental challenge was: can we do reactions in which neutrinos collide with nuclei and come out as neutrinos? A crucial ingredient is that we observe the impact on the struck nucleus. There was some ambiguous evidence of such reactions in our two-neutrino experiment at Brookhaven. Mel Schwartz called them "crappers." A neutral particle goes in; a neutral particle comes out. There's no change in electric charge. The struck nucleus breaks up, but very little energy appears in the relatively low-energy neutrino beam at Brookhaven—hence Schwartz's description. Neutral currents. For reasons I forget, the neutral weak messenger particle is called Z0 (zee zero, we say), rather than W0. But if you want to impress your friends, use the term "neutral currents," a fancy way of expressing the idea that a neutral messenger particle is required to kick off a weak-force reaction.

  TIME TO BREATHE FASTER

  Let's review a bit of what the theorists were thinking.

  The weak force was first recognized by Fermi in the 1930s. When he wrote down his theory, Fermi modeled it in part on the quantum field theory of the electromagnetic force, quantum electrodynamics (QED). Fermi tried to see if this new force would follow the dynamics of the older force, electromagnetism (older, that is, in terms of our knowledge of it). In QED, remember, the field idea is carried by messenger particles, the photons. So the Fermi theory of the weak force should have messenger particles, too. But what would they be like?

  The photon has zero mass, and that gives rise to the famous long-range inverse-square law of the electric force. The weak force was very short range, so in effect Fermi simply gave his force carriers infinite mass. Logical. Later versions of the Fermi theory, most notably by Schwinger; introduced the heavy W+ and W− as weak-force carriers. So did several other theorists. Let's see: Lee, Yang, Gell-Mann ... I hate to credit any theorists because 99 percent of them will be upset. If I occasionally neglect to cite a theorist, it's not because I've forgotten. It's probably because I hate him.

  Now comes the tricky part. In program music, a recurring theme introduces an idea or person or animal—like the leitmotif in Peter and the Wolf that tells us Peter is about to come onstage. Perhaps more appropriate in this case is the ominous cello that signals the appearance of the great white shark in Jaws. I am about to slip in the first thematic notes of the denouement, the sign of the God Particle. But I don't want to reveal her too early. As in any tease show, slow is better.

  In the late sixties and early seventies, several young theorists began to study quantum field theory in the hopes of extending the success of QED to the other forces. You may recall that these elegant solutions to action-at-a-distance were subject to mathematical troubles: quantities that should be small and measurable appear in the equation as infinite—and that's a lot. Feynman and friends invented the process of ›normalization to hide the infinities in the measured quantities, for example, e and m, the charge and mass of the electron. QED was said to be a renormalizable theory; that is, you can get rid of the stultifying infinities. However; when quantum field theory was applied to the other three forces—the weak force, the strong force, and gravity—it met with total frustration. It couldn't have happened to nicer guys. With these forces infinities ran wild, and things got so sick that the entire usefulness of quantum field theory was questioned. Some theorists reexamined QED to try to understand why that theory worked (for electromagnetism) and the other theories did not.

  QED, the super-accurate theory that gives the g-value to eleven significant places, belongs to a class of theories known as gauge theories. The term gauge in this context means scale, as in HO-gauge model railroad tracks. Gauge theory expresses an abstract symmetry in nature that is very closely tied to experimental facts. A key paper by C. N. Yang and Robert Mills in 1954 stressed the power of gauge symmetry. Rather than proposing new particles to explain observed phenomena, one sought for symmetries that would predict these phenomena. When applied to QED, gauge symmetry actually generated the electromagnetic forces, guaranteed the conservation of charge, and provided, at no extra cost, a protection against the worst infinities. Theories exhibiting gauge symmetry are renormalizable. (Repeat this sentence until it rolls trippingly from the tongue, then try it out at lunch.) But the gauge theories implied the existence of gauge particles. They were none other than our messenger particles: photons for QED, and W+ and W− for weak. And for strong? Gluons, of course.

  Some of the best and brightest theorists were motivated to work on the weak force for two, no three, reasons. The first is that the weak force was full of infinities, and it was not clear how to make it into a gauge theory. Second was the quest for unification, extolled by Einstein and very much on the minds of this group of young theorists. Their focus was on unifying the weak and electromagnetic forces, a daunting task since the weak force is vastly weaker than the electric force, has a much, much shorter range, and violates symmetries such as parity. Otherwise, the two forces are exactly alike!

  The third reason was the fame and glory that would accrue to the guy who solved the puzzle. The leading contestants were Steven Weinberg, then at Princeton; Sheldon Glashow, a fellow science fiction club member with Weinberg; Abdus Salam, the Pakistani genius at Imperial College in England; Martinus Veltman at Utrecht, Netherlands; and his student Gerard't Hooft. The more elderly theorists (well into their thirties) had set the stage: Schwinger, Gell-Mann, Feynman. There were lots of others around; Jeffrey Goldstone and Peter Higgs were crucial piccolo players.

  Eschewing a blow-by-blow account of the theoretical brouhaha from about 1960 to the mid-1970s, we find that a renormalizable theory of the weak force was finally achieved. At the same time it was found that a marriage with the electromagnetic force, QED, now seemed more natural. But to do all this, one had to assemble a common messenger family of particles for the combined "electroweak" force: W+, W−, Z0, and the photon. (It looks like one of those mixed families, with stepbrothers and stepsisters from previous marriages trying to live, at all odds, in harmony while sharing a common bathroom.) The new heavy particle, Z0, helped to satisfy the demands of gauge theory, and the foursome satisfied all the requirements of parity violation, as well as the apparent weakness of the weak force. Yet at this stage (before 1970) not only hadn't the W's and Z been seen, but neither had the reactions that Z0 might prod
uce. And how can we talk about a unified electroweak force, when any child in the laboratory can demonstrate huge differences in behavior between the electromagnetic and weak forces?

  One problem that the experts confronted, each in his own aloneness, at office or home or airplane seat, was that the weak force, being short range, needed heavy force carriers. But heavy messengers are not what gauge symmetry predicted, and the protest came in the form of infinities, sharp steel into the intellectual guts of the theorist. Also, how do three heavies, W+, W−, and Z0, coexist in a happy family with the massless photon?

  Peter Higgs, of the University of Manchester (England), supplied a key—yet another particle, to be discussed soon—which was exploited by Steven Weinberg, then at Harvard, now at the University of Texas. Clearly, we plumbers in the lab see no weak-electromagnetic symmetry. The theorists know that, but they desperately want the symmetry in the basic equations. So we are faced with finding a way to install the symmetry, then break it when the equations get down to predicting the results of the experiment. The world is perfect in the abstract, see, but then it becomes imperfect when we get down to details, right? Wait! I didn't think up any of this.

  But here's how it works.

  Weinberg, via the work of Higgs, had discovered a mechanism by which a pristine set of zero-mass messenger particles, representing a unified electroweak force, acquired mass by feeding, in a very poetic manner of speaking, on the unwanted components of the theory. Okay? No? Using Higgs's idea to destroy the symmetry, lo!—the W's and Z's acquired mass, the photon remained the same, and in the ashes of the destroyed unified theory there appeared: the weak force and the electromagnetic force. Massive W's and Z's waddled around to create the radioactivity of particles and the reactions that occasionally interfered with neutrino transits of the universe, whereas the messenger photons gave rise to the electricity we all know, love, and pay for. There. Radioactivity (weak force) and light (electromagnetism) neatly(?) tied to one another. Actually, the Higgs idea didn't destroy the symmetry; it just hid it.