The Particle at the End of the Universe: How the Hunt for the Higgs Boson Leads Us to the Edge of a New World (32 page)

In 1964, the year the Beatles took America by storm, three independent groups of physicists came up with very similar proposals that showed how spontaneous breakdown of a local symmetry doesn’t produce any massless bosons at all, only massive ones that lead to short-range forces. The first to appear was a paper by François Englert and Robert Brout of the Université libre de Bruxelles in Belgium. Next up was Peter Higgs from Edinburgh, Scotland, with two papers in rapid succession. And then Americans Carl Richard Hagen and Gerald Guralnik (who had been Walter Gilbert’s PhD student) teamed up with Englishman Tom Kibble to write a paper. All three groups worked independently, and all three deserve some of the credit for inventing what we now know as the “Higgs mechanism”—but the very precise apportionment of credit continues to be debated.

The Englert and Brout paper was short and to the point. The two physicists had met in 1959, when Englert came to Cornell as a postdoc to work with Brout. The first day they met, they went out for a drink, which turned into several drinks, as the two hit it off immediately. When Englert returned to Belgium in 1961 to take up a faculty position there, Brout and his wife arranged a temporary visit to Brussels and soon decided to stay there for good. They remained close friends and collaborators until Brout passed away in 2011.

They have two kinds of fields in their discussion: the force-carrying gauge boson and a set of two symmetry-breaking scalar fields that take on a nonzero value in empty space. It’s a similar setup as in Goldstone’s work on global symmetry breaking, with the addition of the gauge field required by a local symmetry. But they don’t devote much attention to the properties of the scalar fields, concentrating instead on what happens to the gauge field. They show, using Feynman diagrams, that it gets a mass without violating the underlying symmetry—perfectly in accord with the requirements of relativity, and in contradiction to Gilbert’s worry. All this was done apparently without knowing anything of Anderson’s paper from the previous year.

1964: Higgs

Peter Higgs, after receiving a PhD from University College London, returned to his native Scotland to take up a lectureship at the University of Edinburgh in 1960. He was aware of Anderson’s work and was interested in showing explicitly how Goldstone’s theorem could be avoided in a relativistic theory. In June 1964, Higgs opened the latest issue of
Physical Review Letters
(
PRL
), the premier physics journal from the United States, and came across Gilbert’s paper. He later recalled: “I think my reaction was to say ‘shit’ because he seemed to have closed the door on the Nambu programme.” But Higgs didn’t give up. He remembered that Schwinger had found a loophole in the usual argument that gauge bosons must be massless because of symmetry considerations, and thought it should be possible to extend the loophole to the case of spontaneously broken symmetries. Realizing that these were important issues, Higgs quickly wrote a short paper that was published in
Physics Letters
, the European counterpart to
Physical Review Letters
. Here, for the first time, it was shown explicitly how the assumptions behind Goldstone’s theorem can be sidestepped in the case of a gauge symmetry, even when relativity is completely respected.

What Higgs didn’t have in that first paper was a specific model in which the massless bosons were actually eradicated. In the second paper he provided exactly that, examining the behavior of a Goldstone-style pair of symmetry-breaking scalar fields coupled to a force-carrying gauge field, showing that the gauge field gobbled up the Nambu-Goldstone boson to make a single massive gauge boson. He sent this second paper to
Physics Letters
again—where it was promptly rejected. This was surprising to Higgs, who couldn’t understand why a journal would publish a paper saying, “Massive gauge bosons are possible” but not one saying, “Here is an actual model with massive gauge bosons.” But once again Higgs refused to give up; he added a couple of paragraphs elaborating on the physical consequences of the model, and sent it off to
Physical Review Letters
in the United States, where it was accepted. The reviewers there—who Higgs later learned was Nambu—suggested adding a reference to the Englert and Brout paper, which had just appeared.

Among the additions Higgs made after his second paper was rejected was a comment noting that his model didn’t only make the gauge bosons massive, it also predicted the existence of a massive scalar boson—the first explicit appearance of what we now know and love as the “Higgs boson.” Remember that Goldstone’s model of broken global symmetry predicted a number of massless Nambu-Goldstone bosons, but also a leftover massive scalar. In the case of a local symmetry, the would-be massless scalar bosons get eaten by the gauge fields, which become massive. But the massive scalar field from Goldstone’s theory is still there in Higgs’s theory. Englert and Brout didn’t discuss this other particle, although in hindsight it’s implicit in their equations (as it was in Anderson’s work).

Looking ahead a bit, in the real-world implementation of the Higgs mechanism in the Standard Model, before symmetry breaking we start with four scalar bosons and three massless gauge bosons. When the symmetry is broken by the scalars getting a nonzero value in empty space, three of the scalar bosons are eaten by the gauge bosons. We’re left with three massive gauge bosons: the Ws and the Z, and one massive scalar—the Higgs. Another gauge boson starts off massless and stays that way—that’s the photon. (The photon is actually a mixture of some of the original gauge bosons, but this is getting complicated enough.) In one sense, we discovered three-quarters of the Higgs bosons out in the 1980s, when we found the massive Ws and Z.

What happens when you spontaneously break a local (gauge) symmetry, which can be contrasted with the global case previously considered. Now the symmetric situation has massless gauge bosons as well as massive scalars; the bosons that would be massless after symmetry breaking are eaten by the gauge bosons, which become massive. The single massive leftover scalar boson is still there: That’s the Higgs.

While one might argue about whether it was Anderson, Englert and Brout, or Higgs who first proposed the Higgs
mechanism
by which gauge bosons become massive, Higgs himself has a good claim to the first appearance of the Higgs
boson
, the particle that we are now using as evidence that this is how nature works. (Others might point out—and they have—that the earlier papers could have mentioned the Higgs boson but didn’t, because its existence should be obvious once the rest of the work is done.) In a follow-up paper in 1966, Higgs examined the properties of this boson in greater detail. But if his original submission of the paper hadn’t been rejected by
Physics Letters
, he may never have drawn attention to the boson at all.

Higgs was well aware of Anderson’s paper from 1963. He tends to give Anderson substantial credit, but argues that Anderson didn’t go far enough: “Anderson should have done basically the two things that I did. He should have shown the flaw in the Goldstone theorem, and he should have produced a simple relativistic model to show it happened. However, whenever I give a lecture on the so-called Higgs mechanism I start off with Anderson, who really got it right, but nobody understood him.”

1964: Guralnik, Hagen, and Kibble

Guralnik, Hagen, and Kibble completed their own paper after—but only just barely—the papers by Englert and Brout, and Higgs had already been published. The GHK paper grew out of long-standing discussions between Guralnik and Hagen, who had been undergraduates together at MIT and wrote their first paper together after Hagen stayed at MIT for graduate school and Guralnik moved up the river to Harvard. Those discussions blossomed after Guralnik took a postdoc at Imperial College in London, where Abdus Salam was a faculty member and spontaneous symmetry breaking was a hot topic. Kibble was also there as a faculty member, and he and Guralnik talked frequently about evading the Goldstone theorem. A visit from Hagen provided the impetus for the trio to write up their results in a paper.

According to later recollections, in October 1964, Hagen and Guralnik “were literally placing the manuscript in the envelope to be sent to
PRL
, [when] Kibble came into the office bearing two papers by Higgs and the one by Englert and Brout.” The Englert-Brout paper had been submitted on June 26, 1964, and was published in August; Higgs’s two papers were submitted on July 27 and August 31, and appeared in September and October, respectively; the GHK paper was submitted on October 12, and appeared in November. Their immediate reaction was to recognize that these heretofore unsuspected works were relevant, but they didn’t feel they quite counted as “being scooped.” GHK judged that Englert-Brout and Higgs had successfully addressed the question of how gauge bosons could get mass via spontaneous symmetry breaking, but hadn’t confronted head-on the issue of what precisely went wrong with Goldstone’s theorem, which was a central concern of the Anglo-American triumvirate. They felt that the Englert-Brout discussion of what happened to the various vibrating fields was somewhat obscure, and Higgs’s papers were completely classical, not cast in the language of quantum mechanics.

With that in mind, GHK took their paper out of the envelope and added a reference to the slightly earlier works: “We consider, as our example, a theory which was partially solved by Englert and Brout, and bears some resemblance to the classical theory of Higgs.” Because nearly simultaneous invention of ideas is fairly common, a convention has arisen in the physics literature: If another paper comes along before yours is quite done, you include a note at the end that references it, with the explanation, “While this work was being completed, we received a related paper by . . .” GHK neglected to do that explicitly, but nobody doubts that their paper was substantially complete before they ever heard of the competing works. It’s sufficiently different, and was submitted so soon after the others appeared, that there’s no chance they were simply building on the Englert-Brout and Higgs papers.

Guralnik, Hagen, and Kibble undertake a thoroughly quantum-mechanical treatment of the problem of spontaneous breaking of a gauge symmetry. They focus very carefully on the question of how the assumptions of Goldstone’s theorem are sidestepped. They do not, however, get the Higgs boson quite right. While the real Higgs is expected to be massive, GHK set its mass to zero by choice. Their explicit statement about this particle is simply, “While one sees by inspection that there is a massless particle in the theory, it is easily seen that it is completely decoupled from the other (massive) excitations, and has nothing to do with the Goldstone theorem.” Those statements are true in the model they consider, but only because they set the couplings and mass to zero by hand; in the real world, we expect the Higgs to be massive and coupled to other particles.

There was yet another team pushing in the same direction, although slightly later (by a few months). At the time, scientific communication between the Soviet Union and the West was hampered by numerous bureaucratic restrictions. So in 1965, when physicists Alexander Migdal and Alexander Polyakov—both nineteen years old at the time—were thinking about spontaneous symmetry breaking in gauge theories, they weren’t aware of any of the 1964 papers. Their independent work had to suffer a thicket of skeptical reviewers, and didn’t appear until 1966.

Despite all this simultaneous activity, many physicists remained skeptical that local symmetries offered a way to escape from the massless particles. Higgs tells the story of giving a seminar at Harvard, where theorist Sidney Coleman had primed his students to “tear apart this joker who thinks he can outsmart Goldstone’s theorem.” (I can vouch for the veracity of this story, as Coleman related it himself when I took his class on quantum field theory many years later.) But Englert, Brout, Higgs, Guralnik, Hagen, and Kibble had one important fact on their side: They were right. Very soon, their ideas would be put to use in one of the major triumphs that are now incorporated into the Standard Model.

The weak interactions

All of this discussion of different kinds of spontaneous symmetry breaking was concerned with basic questions within quantum field theory: What can happen, and under what circumstances? It remained to be seen whether the phenomena that were described are actually relevant to the real world. It wasn’t long, however, before they found a permanent home in our understanding of the weak interactions.

The first promising theory of the weak interactions was invented by Enrico Fermi in 1934. Fermi took advantage of the new idea of the neutrino, which had recently been proposed by Wolfgang Pauli, to develop a model of neutron decay, which we would now say is mediated by the weak interactions. Fermi’s calculation was also an early success of quantum field theory, as we discussed in Chapter Seven.