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Physics + MathPhysics & Math

Maybe Higgs: What the LHC Might or Might Not Have Seen

ByFrank WilczekThe Nature of RealityThe Nature of Reality


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big announcement from CERN was that something important might or might not have been discovered at the Large Hadron Collider (LHC). That something, if it’s anything, could well be the long-awaited Higgs particle, also called the God particle.

“Higgs” is Peter Higgs, a professor at Edinburgh, who made some interesting suggestions along the lines I’ll discuss below in 1964. The name “Higgs particle,” though standard, is not entirely fair, for several reasons: the basic idea has a significant pre-history; what’s original with Higgs has co-claimants; and the modern, mature version of the theory involves many ideas that were not anticipated in 1964. I’ll leave those issues for historians of science and the Swedish Academy to sort out.

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God on the other hand deserves full credit, or blame.

Herewith a brief introduction, in question and answer format, for the buzz-curious.

What’s the basic idea?

Suppose that a species of fish evolved to the point that some of them became physicists, and began to ponder how things move. At first the fish-physicists would, by observation and measurement, derive very complicated laws. But eventually a fish-genius would imagine a different, ideal world ruled by much simpler laws of motion–the laws we humans call Newton’s laws. The great new idea would be that motion looks complicated, in the everyday fish-world, because there’s an all-pervasive medium–water!–that complicates how things move.

Modern physics proposes something very similar for our world. We can use much nicer equations if we’re ready to assume that the “space” of our everyday perception is actually a medium whose influence complicates how matter is observed to move.

Are there precedents for such an outrageous dodge?

Yes. In fact it’s a time-honored, successful strategy.

For example: In its basic equations, Newtonian mechanics postulates complete symmetry among the three dimensions of space. Yet in everyday experience there’s a big difference between motion in vertical, as opposed to horizontal, directions. The difference is ascribed to a medium: a pervasive gravitational field.

A much more modern example occurs in quantum chromodynamics (QCD), our fundamental theory of the strong force between quarks and gluons. There we discover that the universe is filled with a medium, the sigma (σ) field, that forms a sort of cosmic molasses for protons and neutrons. The σ field slows protons and neutrons down. Allowing a bit of poetic license, we can say that the σ field gives protons and neutrons mass. Many consequences of the σ field have been calculated and successfully observed, so that to modern physicists it is now every bit as real as Earth’s gravity field. But the σ field exists everywhere and everywhen; it is not tied to Earth.

What’s the new idea, then?

In the theory of the weak force, we need to do a similar trick for less familiar particles, the W and Z bosons. We could have beautiful equations for those particles if their masses were zero; but their masses are observed not to be zero. So we postulate the existence of a new all-pervasive field, the so-called Higgs condensate, which slows them down. This proposal, which here I’ve described only loosely and in words, comes embodied in specific equations and leads to many testable predictions. This proposal has been resoundingly successful.

What is the Higgs particle, conceptually?

Trouble is, no known form of matter has the right properties to make the Higgs condensate. In order to build that medium, we need to add to our inventory of world-ingredients. The simplest, “minimal” implementation introduces exactly one new elementary particle: the Higgs particle.

What is the Higgs particle, specifically?

There’s a quotation I love from Heinrich Hertz, about Maxwell’s equations, that’s relevant here.

To the question: “What is Maxwell’s theory?” I know of no shorter or more definite answer than the following: “Maxwell’s theory is Maxwell’s system of equations.”

Similarly, Higgs particles are the entities that obey the equations of Higgs particle theory. Those equations prescribe everything about how Higgs particles move, interact with other particles, and decay—with just one, albeit glaring, exception: The equations do not determine the mass of the Higgs particle. The theory can accommodate a wide range of values for that mass.

What is a Higgs particle, operationally?

A Higgs particle is a highly unstable particle, visible only through its decay products. It has zero electric charge, and—unlike all other known elementary particles—no intrinsic rotation, or “spin.” These null properties reflect the fact that many Higgs particles, uniformly distributed through space, build up the Higgs condensate, which we sense as emptiness or pure vacuum. (Although individual Higgs particles are highly unstable, a uniform distribution of them is stabilized through their mutual interactions. Visible Higgs particles are disturbances above that uniform background.)

As mentioned before, theory does not predict what mass a Higgs particle should have. Masses anywhere from 10 Giga-electron Volts (GeV) to 800 GeV might be accommodated, though problems start to emerge near either extreme. (Physicists commonly use GeV as the unit of mass for elementary particles. One GeV is close to, but slightly more than, the mass of one proton.)

Because Higgs particles are unstable, to study them one must produce them. That requires concentrating lots of energy into a very small space to create enormous energy density. The required concentration of energy is achieved at particle colliders. At the LHC, two counter-rotating beams of high energy protons are made to pass through one another, or cross, at a few points. At each crossing some fraction of the protons, which are moving in opposite directions at very close to the speed of light, collide. The collisions produce fireballs that explode into tens or hundreds of stable or near-stable particles including electrons and positrons, pi mesons, photons, protons and antiprotons, and several other possibilities.

Known physical processes account for the vast majority of this debris. Production and decay of Higgs particles, if they exist, will produce some additional debris. To get evidence for the existence of Higgs particles, therefore, one must identify some distinctive patterns in the observed debris that could result from Higgs particle decays but which are difficult to produce with conventional processes.

Putting it another way: If you’re looking for needles in a haystack, you’d better have a really good grip on what hay can look like—and it helps to look for needles that are hard to mistake!

Several patterns play an important role in the analysis, but I’ll discuss just one—a crucial one—to give a flavor of what’s involved. One process of Higgs particle production and decay is depicted in this sketch:

Maybe Higgs: What the LHC Might or Might Not Have Seen-morley-231x300.jpg

The sequence of events in the sketch above unfolds reading upwards. Gluons inside the fast-moving protons convert, by quantum fluctuations, into a “virtual” top quark and its antiparticle. The virtual top quark and antiquark swiftly recombine into a Higgs particle. Then the Higgs particle decays by a similar mechanism: quantum fluctuations convert it into a particle-antiparticle pair, which recombine into two photons. At the end of the day, it is those two photons that are observed. (I’m particularly fond of this exotically beautiful quantum process, which I discovered theoretically in 1977.) The point is that more conventional processes, i.e. processes that don’t involve Higgs particles, but which produce two energetic photons are fairly rare. Thus the calculated contribution from Higgs particles, should they exist, can be discerned above the background.

So, does it exist?

Short answer: We still don’t know for sure. There’s been dramatic progress on the question, however.

A very large range of potential mass-values has been ruled out. Only a small window in the range between 115 and 127 GeV remains viable.

On the other hand, an excess of events, above expectations from known processes, has been observed in the two-photon channel mentioned above and (less clearly) in several others. The excesses are compatible with, and could be explained by, the existence of Higgs particles with mass close to 125 GeV.

The observed excess might also be compatible with a statistical fluctuation in the background processes—e.g., an improbable run of normal processes leading to photon pairs, comparable to rolling four consecutive sixes at dice. With more data a true signal will grow more rapidly than any plausible fluctuation, so the ambiguity in interpretation will disappear. If the LHC continues to function brilliantly, as it has so far, we should have a definitive answer within the next few months.

What will it mean, if the hints pan out?

First of all, it will be a dazzling triumph for theoretical physics. Physicists will have used intricate equations and difficult calculations to predict not only the mere existence of the Higgs particle, but also (given its mass) its rate of production in the complex, extreme conditions of ultra high energy proton-proton collisions. Those equations will also have accurately rendered the relative rates at which the Higgs particle decays in different ways. Yet the most challenging task of all may be computing the much larger, competing background “noise” from known processes, in order to successfully contrast the Higgs’ “signal.” Virtually every aspect of our current understanding of fundamental physics comes into play, and gets a stringent workout, in crafting these predictions.

The animating spirit of research in fundamental physics, captured in the maxim “Today’s sensation is tomorrow’s calibration,” will not rest in that triumph, however. A Higgs particle at mass 125 GeV would portend a new level of fundamental understanding and discovery. Let me explain why.

Within our current theories of the fundamental interactions, embodied in the so-called Standard Model , the Higgs particle mass might, as previously mentioned, have any value within a wide range. Yet there are good reasons to suspect that despite its many virtues, the Standard Model is incomplete. Notably, its equations postulate four different forces (strong, weak, electromagnetic and gravitational) and six different materials they act on. It would be prettier to have a more coherent, unified theory. And in fact there are beautiful, concrete proposals for unified field theories, within which we have just one force and just one kind of material. But to make the unified theory work quantitatively, in detail, we need to expand the equations of the Standard Model so that they integrate a concept called supersymmetry.

Supersymmetry has many aspects and ramifications, but two are most relevant here. First, supersymmetry (for experts: more specifically, focus point supersymmetry) predicts that the Higgs particle mass should lie in the range 120-130 GeV. Finding Higgs particles with mass in that range would give strong circumstantial evidence both for supersymmetry and for the unification that supersymmetry enables.

Second, supersymmetry predicts the existence of many additional new fundamental particles, besides the Higgs particle, that should be accessible to the LHC. So if supersymmetry is right, the LHC will have many more years of brilliant discovery in front of it.

And if not?

I’ll be heartbroken. Mother Nature will have shown that Her taste is very different from mine. I don’t doubt that it’s superior, but I’ll have to struggle to understand it.

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.