The Particle at the End of the Universe: How the Hunt for the Higgs Boson Leads Us to the Edge of a New World

by Sean Carroll

  The problem of infinite answers wasn’t confined to the weak interactions; it even plagued electromagnetism, which should be one of the simplest and easiest-to-understand quantum field theories there is. There, however, it turns out that the infinities can be tamed. The process for doing so is known as “renormalization,” and it’s what won the Nobel for Feynman, Schwinger, and Tomonaga.

  Some field theories are renormalizable—there are well-defined mathematical techniques for getting finite answers—and some are not. In modern quantum field theory, when a theory fails to be renormalizable, we don’t simply throw it away. We just admit that it’s an approximation at best, perhaps valid only at very low energies, and that some new physics must be present up at high energies to tame the infinities. For a long time, however, nonrenormalizability was taken as a sign that a theory was simply sick. Fermi’s theory of the weak interactions turns out to be nonrenormalizable; it gives infinite answers when we press too hard, and there’s no way to fix them beyond coming up with a better theory.

  Julian Schwinger, who had been intrigued by the Yang-Mills idea that more elaborate symmetries could produce connection fields that accounted for nature’s forces, tried to apply the idea to the weak interactions. There is an immediate problem, of course: The Yang-Mills bosons are supposed to be massless, implying a long-range force, while the weak interaction is clearly short-range. Schwinger simply put that problem aside: He started with a Yang-Mills model and made two of the force-carrying bosons massive by hand. This was the first appearance of what we now know as the W+ and W- bosons. (One of the first, anyway. In Leon Lederman’s words: “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.”)

  Changing views of the weak interactions, as exemplified by neutron decay. In Fermi’s theory, a neutron decays directly to a proton, an electron, and an antineutrino. Schwinger suggested that a charged W- boson was emitted by the neutron, and then decayed into an electron and an antineutrino. He was right, but we now know the neutron is made of three quarks, one of which changes from a down to an up by emitting a W-.

  The reason why the Yang-Mills bosons were massless in the first place was because of the symmetry on which the theory was based. When Schwinger gave mass to the bosons it implied that this symmetry was broken, but in this case it was an explicit breaking, not a spontaneous breaking in which the symmetry was hidden by some field that was nonzero in empty space (which hadn’t been invented yet). It wasn’t broken because of a field, it was broken because Schwinger said so. As you might guess, this somewhat ad hoc construction wreaked havoc with the model. For one thing, the renormalizability of electromagnetism depends crucially on the symmetry underlying the theory, and disregarding that symmetry rendered Schwinger’s model nonrenormalizable. Eventually it was realized that a theory of massive gauge bosons would be renormalizable if and only if the masses came from spontaneous symmetry breaking; but that was years down the road.

  Nevertheless, Schwinger didn’t persevere with a dodgy theory just because he was stubborn. One property of genius is that you can recognize which kinds of ideas are worth pursuing even though they don’t seem to be working quite yet. A nice property of Schwinger’s model is that it actually predicted three gauge bosons: the two charged W bosons, which were given a mass, and a single neutral gauge boson, which was allowed to remain massless. We all know about a neutral massless gauge boson, of course: It’s the photon. Schwinger was encouraged by the notion that this approach held out the promise of unifying electromagnetism with the weak interactions, which would represent a major step forward in physics. That’s probably what kept him going in the face of the problems with the model.

  He didn’t keep going for very long. Schwinger’s paper came out in 1957, and in that same year it was discovered that the weak interactions violate parity. Remember from Chapter Eight (and Appendix One) that particles are either left-handed or right-handed, depending on how they are spinning. Parity violation implied that the weak interactions couple to left-handed particles but not right-handed ones. It’s possible to invent Yang-Mills symmetries that involve only left-handed particles, but we know that electromagnetism doesn’t violate parity—it treats left and right on equal footing. This discovery seemed to put the kibosh on Schwinger’s hope of unifying the weak and electromagnetic forces.

  Electroweak unification

  Sometimes, as a professor, the thing to do is to not give up; it’s to hand off your questions to a graduate student. Happily, Schwinger had a very talented young student available: Sheldon Glashow, who was given the task of thinking about unifying electromagnetism and the weak interactions. Glashow has an expansive and charismatic personality, and as a physicist he enjoys hopping quickly from idea to idea. This propensity served him well in the quest for unification, as he was always very willing to propose one theory and then move on quickly to the next one. After thinking about the question on and off for a few years, he hit on a promising scheme for what would ultimately be called “electroweak unification.”

  The sticking point was parity: Electromagnetism preserves it, while the weak interactions violate it. How could they be unified? Glashow’s idea was to introduce two different symmetries: one that treated left-handed and right-handed particles the same, and one that treated them differently. Now, you might think this isn’t a step forward; having two different symmetries doesn’t sound very unified at all. The secret in Glashow’s model was that both symmetries were broken, but in just such a way that a certain combination of the two was left unbroken.

  Think of two gear wheels. Either of them can rotate independently; that’s like Glashow’s original two symmetries. But bring them together, the teeth of both wheels meshing with each other. Now they can still move, but they must move together rather than separately. There is less freedom than before. In Glashow’s model, the unbroken symmetry is like the ability to move the wheels together, while the broken symmetry is like the inability to move them at different speeds. The massless, neutral gauge boson corresponding to Glashow’s unbroken symmetry is of course the photon.

  This idea seemed to be able to accommodate the known features of both the weak and electromagnetic interactions. (It still suffered from the problem that the gauge boson masses were just put in by hand, and the theory wasn’t renormalizable.) But it deviated from what was known by predicting a new gauge boson: something that was neutral but massive, what we now call the Z. There was no evidence for such a particle at the time, so the model didn’t capture many people’s attention.

  While the ingredients Glashow put together in his attempt to unify electromagnetism with the weak interactions might seem a bit arbitrary, there was clearly something sensible about them: Across the ocean in Britain, at Imperial College London, almost exactly the same theory was being put together by Abdus Salam and John Ward. Each physicist individually was very accomplished. Ward, who was born in Britain but spent various years living in Australia and the United States, was a pioneer of quantum electrodynamics. He is probably best known within physics for the “Ward identities” in quantum field theory, mathematical relations that enforce local symmetries. Salam, who was born in Pakistan when it was still joined with India under British control, would eventually become politically active and serve as an advocate for science in the developing world. They were frequent collaborators, and some of their most interesting work was done together, on the question of unifying the forces.

  Following very similar logic as Glashow’s, Salam and Ward invented a model with two different symmetries, one of which violated parity and the other which did not, and which predicted a massless photon and three massive weak gauge bosons. Their paper was published in 1964, apparently without being aware of Glashow’s earlier work. Like Glashow, they broke symmetries by hand in their model. Unlike Glashow, they had no excus
e for doing so: They were working literally down the hall from Guralnik, Hagen, and Kibble, who were concentrating full-time on spontaneous symmetry breaking.

  Part of the failure of communication might have been due to Ward’s naturally reticent nature. In his book The Infinity Puzzle, Frank Close relates a revealing story told by Gerald Guralnik:

  Guralnik and Ward were having lunch together in a local pub, and Guralnik started to talk about his work—yet to be completed—on hidden symmetry. “I did not get far before [Ward] stopped me. He proceeded to give me a lecture on how I should not be free with my unpublished ideas, because they would be stolen, and often published before I had a chance to finish working on them.” As a result of this admonishment, Guralnik did not ask Ward about the work that he himself was doing with Salam.

  Even if one takes such a cautious approach to discussing unpublished work, the most secretive physicist usually isn’t reluctant to talk about published results. For whatever reason, however, Salam and Ward didn’t catch on to what Guralnik, Hagen, and Kibble had proposed until several years later. Eventually Salam learned of the work through conversations with Tom Kibble, and for years thereafter would refer to it as the “Higgs-Kibble mechanism.”

  Putting it all together

  The final pieces of the puzzle were put together in 1967. Steven Weinberg had been high school classmates with Sheldon Glashow at the Bronx High School of Science, but they never directly collaborated on the work in theoretical physics that would lead to them sharing the Nobel Prize with Salam in 1977. Today Weinberg is a respected elder statesman of physics, the author of several influential books as well as frequent essays in The New York Review of Books and elsewhere. He also was a major advocate for the Superconducting Super Collider—which he would have been even if the accelerator hadn’t been located in Texas, where he had moved in 1982.

  In 1967 Weinberg was a young professor at MIT, driving a red Camaro to campus each day. He was deeply invested in spontaneous symmetry breaking, but he was using it to try to understand the strong interactions. Inspired by a recent paper by Kibble, Weinberg was playing with a set of symmetries that, unbeknownst to him at the time, bore a close resemblance to those considered by Glashow and Salam and Ward before. The problem was that he kept predicting a massless, neutral, gauge boson, which didn’t seem to be there in the strong interactions.

  In September of that year, Weinberg suddenly realized that he had been thinking about the wrong problem. His problematic model of the strong interactions worked very well as a theory of the weak and electromagnetic interactions. The annoying massless boson was a feature, not a bug: It was the photon. In a short paper entitled “A Theory of Leptons,” Weinberg put together what every modern graduate student in particle physics would immediately recognize as what’s known as the “electroweak” sector of the Standard Model. In the references he cited Glashow’s paper, but he still wasn’t aware of the one by Salam and Ward. Using Kibble’s ideas, he was able to make a direct prediction for the masses of the W and Z bosons—something Glashow and Salam and Ward weren’t able to do, as they had inserted the masses by hand. Weinberg accounted for the mechanism by which all the fermions in the theory acquired mass, as well as the gauge bosons. He even noted that the model might possibly be renormalizable, although he wasn’t able to offer any convincing arguments at the time. A coherent theory of electroweak unification had finally been assembled.

  At almost precisely the same time, Kibble and Salam finally realized their mutual interest in symmetry breaking, and Kibble explained the theory to Salam. Salam figured out that he could rework the unified model he had proposed with Ward to include symmetry-breaking scalar bosons, and gave lectures on his ideas to a small audience at Imperial. For unknown reasons, Salam didn’t write up these ideas right away; he was extremely prolific as a physicist, but his major focus in those days was on gravity, not on subatomic forces. Consequently, his proposal to add a Higgs mechanism to the Salam-Ward model didn’t appear in print until a year later, when he included it in the proceedings from a conference talk (where he also cites Weinberg’s paper).

  The separate papers by Weinberg and Salam had all the impact, as Kurt Vonnegut once said in a different context, of a pancake twelve feet in diameter dropped from a height of two inches. In academia, and science in particular, the most concrete way of quantifying the influence of a piece of research is to count how many times the paper has been cited by other papers. Between 1967 and 1971, Weinberg’s paper was cited just a handful of times. The two authors did not even pursue their own ideas to any great extent in the years immediately thereafter. Since 1971, however, Weinberg’s paper has been cited more than 7,500 times—an average of more than once every two days for four decades.

  What happened in 1971? Some surprising experimental result? No, a surprising theoretical result: Gerard ’t Hooft, a young graduate student in the Netherlands, working under Martinus “Tini” Veltman, proved that theories with spontaneously broken gauge symmetries are renormalizable, even though the gauge bosons are massive. In other words, ’t Hooft showed that the electroweak theory made mathematical sense. This had been conjectured by both Weinberg and Salam, but many people in the field had remained skeptical, which partly accounts for the obscurity of these ideas up to that point. In Sidney Coleman’s words, ’t Hooft “revealed Weinberg and Salam’s frog to be an enchanted prince.” Gerard ’t Hooft has since gone on to earn a reputation as one of the most creative and brilliant minds in physics. He and Veltman shared the Nobel Prize in 1999 for their work on the electroweak theory and spontaneous symmetry breaking.

  The surprising experimental results weren’t long in coming, however. The main novel prediction of the Glashow, Salam-Ward, and Weinberg models was the existence of a heavy neutral boson, the Z. The effects of the W bosons were well-known: They change the identity of a fermion when they are emitted (for example, changing a down quark to an up during neutron decay). If the Z existed, it would imply a version of the weak interactions in which particles kept their identities; for example a neutrino could scatter off an atomic nucleus. Events of precisely this kind were observed at CERN’s Gargamelle detector in 1973, setting the stage for Glashow, Salam, and Weinberg to share the Nobel Prize in 1979. (Ward was left out, but only three people can share the prize in any one year.) The W and Z bosons themselves, as opposed to their indirect effects, weren’t discovered until Carlo Rubbia found them a few years afterward.

  All that remained was to discover the Higgs boson.

  The name game

  Physicists are human beings. They are typically motivated by what Richard Feynman called “the pleasure of finding things out,” but once they find out something interesting they appreciate getting credit for their work. Throughout this book, following nearly universal practice within the physics community, I’ve been referring to the “Higgs mechanism” for given mass to gauge bosons via spontaneous symmetry breaking, as well as the “Higgs boson” for the scalar particle that this model predicts. It’s clear, however, that while Higgs’s contributions were important, he was hardly alone. Why is that the name, and what should be the name?

  Nobody is precisely sure where the name “Higgs boson” originally came from; it certainly wasn’t from Higgs himself. Particle physics lore points the finger at Benjamin Lee, a talented Korean-American physicist who died in a tragic car accident in 1977. Lee had learned about spontaneous breakdown of gauge symmetries from talking with Higgs, and the story goes that he gave an influential talk at a conference at Fermilab in 1972, where he repeatedly referred to the “Higgs meson.” That was in the immediate aftermath of ’t Hooft’s revolutionary result, when everyone was scrambling to learn about these ideas. Precisely because physicists are human beings, they tend to lazily stick with the first words they hear attached to the subject, so a widely heard talk can spread a piece of nomenclature far and wide.

  Another theory goes back to Weinberg’s 1967 paper. When the original papers came out in 1964, not too many
physicists were thinking about spontaneous symmetry breaking in gauge theories; after ’t Hooft’s breakthrough in 1971, many rushed to catch up, and Weinberg’s paper was a good starting point. In his discussion of the Higgs mechanism, he references three papers by Higgs, as well as the paper by Englert and Brout and the one by Hagen, Guralnik, and Kibble. However, Higgs comes first in his reference list, due to a mix-up between Physical Review Letters (where Higgs’s second paper appeared) and Physics Letters (where the paper by Englert and Brout appeared). From such minor lapses are long-lasting consequences forged.

  Perhaps most important, “Higgs boson” sounds like a good name for a particle. It was Higgs’s papers that first drew close attention to the boson particle rather than the “mechanism” from which it arose, but that’s not quite enough to explain the naming convention. We might ask, however, what is the alternative? There may have been a chance, in the early days, to come up with a label that wasn’t derived from the name of a person. The “radial boson,” perhaps, or the “relicon,” since the boson is the only surviving relic of the symmetry-breaking process. The “electroweak boson” would work, although it runs the danger of being confused with the W and Z bosons, so the “electroweak scalar boson” might be most accurate.