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Physics + MathPhysics & Math

My Enchanted Evening

Frank Wilczek recalls the most important night of his scientific career in this excerpt from A Beautiful Question.

ByFrank WilczekThe Nature of RealityThe Nature of Reality

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From A BEAUTIFUL QUESTION: Finding Nature’s Deep Design by Frank Wilczek. Reprinted by arrangement of Penguin Press, part of the Penguin Random House company. Copyright (c) 2015 by Frank Wilczek. Publication date July 14, 2015

Up until 10 PM or so, the day that would turn out to be the most productive in my scientific career seemed anything but promising. My very young daughter Amity had an ear infection, and all day long she was feverish, cranky, and needy. Betsy and I, inexperienced in parenting, newly arrived and on our own in Fermilab’s impromptu village, coped as best we could. As the dark midwestern night set in, Amity at last fell into exhausted sleep, and then Betsy too. They looked like angels of peace.

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The alertness and energy that coping with a stream of little crises had called forth was still with me, after the crises themselves had passed. Seeking an outlet, I decided, as I often do, to take a walk. The night was brilliantly clear, the sky radiant, the horizon sharp and distant, and even the ground, moonlit, seemed ethereal. With images of earthly angels lingering within me, and celestial spectacle surrounding me, I felt an unlikely elation. It was a time for big thoughts.


Over the preceding few years, theories of the strong, weak, and electromagnetic interactions based on local symmetry had matured from bold adventure to conventional wisdom. As I reviewed this situation, in my mind, it occurred to me that while the various quarks, leptons, gluons, and weakons—not to mention photons—had received a lot of attention, and were the focus of well thought-out experimental programs, the symmetry breaking was relatively unexplored.

A little story will set the stage:

On a water-covered planet in a galaxy far far away, fish have evolved to become intelligent—so intelligent, that some of them become physicists, and to study the ways things move. At first the fish-physicists would derive very complicated laws of motion, because (as we know) the motion of bodies through water is complicated. But one day a fish genius—Fish Newton—proposes that the basic laws of motion are much simpler and more beautiful: in fact, they are Newton’s Laws of Motion. She proposes that the observed motions look complicated due to the influence of a material—call it “water”—that fills the world. After a lot of work, the fish manage to confirm Fish Newton’s theory by isolating molecules of water.

According to the Higgs mechanism, we are like those fish. We are immersed in a cosmic ocean, which complicates the observed laws of physics.

Physicists had been invoking the Higgs mechanism for many years, and with its use have gone from success to success. Many aspects of the interactions of W and Z bosons, besides their masses, were predicted accurately by using the beautiful equations of massless particles and gauge symmetry, with their consequences suitably modified by a space-filling material. In this way, we built up a convincing case for the existence of our cosmic ocean. But ultimately that case rested on circumstantial evidence. There was no clear answer to an obvious question: What’s it made from?

No known substance could provide the cosmic ocean. No combination of the known quarks, leptons, gluons, or other particles has the right properties to make it. Something new was required.

But there wasn’t even a credible proposal to test the very simplest, “minimal” model, featuring a single Higgs particle. The basic problem is simple: the Higgs particle, in that model, likes to couple to heavy particles, but the particles of stable matter, that we can study directly or put into our accelerators, are very light. The color gluons have zero mass, as do photons, while the u and d quarks, and electrons, have negligible mass.

But recently (as of 1976) there had been a lot of interest in heavier quarks. The charmed quark c was a fairly recent discovery, and there were excellent reasons to suspect that two additional, still heavier kinds would also exist. (And they do. The bottom quark b was discovered not much later, in 1977, while the top quark t took until 1995. They had been named, and their properties—with the sole exception of their masses—had been calculated, even before their experimental observation.) So it was natural to consider whether new, heavier quarks could open a portal through which we’d get to the Higgs particle. I realized right away that they might. You can use the same tricks that people had used for charmed quarks, to produce produce mesons based on b b or t t . Those heavier quarks would couple vigorously to Higgs particles. If things broke right—basically, if the heavy quarks had more than half the mass of the Higgs particle—then Higgs particles would be produced in the decays of those mesons. That was my first important realization of the night.

Now it was important to consider how the Higgs particle decays, since its products might be indistinguishable from background, making the whole thing academic. One of the most important possibilities to consider is decay into color gluons. I couldn’t do an accurate calculation in my head, though it seemed OK, from rough estimates. (It is.) More importantly, this got me thinking: if the heavy quarks can couple to Higgs particles and to gluons, then they provide a way to connect gluons to Higgs particles! And at that moment, my brain had hatched the basic process you see in the bottom half of the figure below. Again, accurate calculation would be a chore, but I did some crude estimates in my head, and found the results encouraging. In particular, I realized that even if the missing quarks were very heavy, they’d still contribute—and that if there were even more, heavier quarks, they’d contribute too. It was clear to me, right away, that this was the dominant way Higgs particles would couple to stable matter, and a promising window into the unknown. That was my second important realization of the night.

At that point I’d reached the lab site, and I decided to turn back. I’d had good luck thinking about the minimal Higgs model, so I wanted to consider how the new ideas would apply to more complicated versions. The changes are easy to work out, for any given version, so I started considering what would be the most interesting complications to consider. An especially interesting possibility, is to have some extra symmetry, that gets broken spontaneously. This can lead to the existence of new massless particles—a spectacular possibility! That was my third important realization of the night.

This sketch depicts the process through which the Higgs particle was discovered experimentally. It is a tour de force, that puts many aspects of the Core, and deep principles of quantum theory, to work simultaneously. For a full explanation, see the text.

Back in Princeton, where I’d been teaching during the year, there’d been enormous excitement about something called instantons—which I won’t even try to explain here. Instantons break symmetry in particularly interesting ways, and I thought it would be fun to bring those in, so I’d have something to talk about, that my colleagues would be interested in hearing. I dimly perceived that the particle that would otherwise have been massless, according to my third realization, would instead get a tiny mass, and would have other interesting properties. That was my fourth important realization of the night, and brought me home.

Those four insights have had different fates. The first was a victim of bad luck. The b quark is not heavy enough, compared to the Higgs particle, while the t quark is so heavy and unstable that its mesons are useless.

The second is one of my proudest achievements. More than thirty years later, it was central to the actual discovery of the Higgs particle.

The third hasn’t borne fruit yet, but remains interesting. I eventually called the massless particles “familons,” and people continue to look for them.

The fourth turned out to be the most interesting, and possibly the most important. When I got back to the lab the next day, and consulted the literature on these things, I discovered a very interesting paper by Roberto Peccei and Helen Quinn. They’d looked at the kind of model I’d been playing with, and pointed out that it could solve a very important problem, the so-called θ problem. It would require a long digression to explain that problem here. The essence of it is, that there’s a number—θ—that the Core says could be anything between -π and π, but which is observed to be very very small. That’s either a coincidence, or an indication that the Core is incomplete. In Peccei and Quinn’s model, the “coincidence” got explained as the residue of a new (spontaneously broken) symmetry. Peccei and Quinn didn’t notice, however, that their model had a light particle in it! And so I got to name the thing. I had noticed, several years before, that there was a detergent, Axion, whose name sounded like a particle. I resolved that if got the chance, I’d make it so. Now the θ problem, along the way, involves an axial current. That gave me an opening, to sneak the name past the watchful, conservative editors of Physical Review Letters, which I did. (Steven Weinberg also noticed this new particle, independently. He’d been calling it the “higglet.” We agreed, deo gratias, to use axion.)

The axion has had a long, winding, and still unresolved history. It is a subject I’ve returned to many times, developing the theory of its production in the early universe, and suggesting the possible existence of an axion background, analogous to the famous microwave background. According to this work, the axion background will be difficult, but not impossible, to observe. A hardy band of brilliant experimentalists are actively searching. Some day soon, the axion may deserve a book of its own, for it has become a leading contender to provide the dark matter of the universe. Or it may not exist at all. Time will tell.

This project/research was supported by grant number FQXi-RFP-1822 from the Foundational Questions Institute and Fetzer Franklin Fund, a donor-advised fund of Silicon Valley Community Foundation.