Knocking on Heaven's Door (46 page)

For example, if there were two Higgs fields responsible for electroweak symmetry breaking rather than one, it could significantly alter the Higgs boson interactions that would be observed. In alternative models, the rate for Higgs boson production could be different than anticipated. And if other particles charged under Standard Model forces exist, they could influence the relative decay rates of the Higgs boson into the possible final states.

This brings us to the third reason to study the Higgs boson—we don’t yet know what really implements the Higgs mechanism. The simplest model—the one this chapter has focused on so far—tells us that the experimental signal will be a single Higgs boson. However, even though we believe the Higgs mechanism is responsible for elementary particle masses, we aren’t yet confident about the precise set of particles involved in implementing it. Most people still think we are likely to find a light Higgs boson. If we do, it will be an important confirmation of an important idea.

But alternative models involve more complicated Higgs sectors with an even richer set of predictions. For example, supersymmetric models—to be further considered in the following chapter—predict more particles in the Higgs sector. We would still expect to find the Higgs boson, but its interactions would differ from a model with only a single Higgs particle. On top of that, the other particles in the Higgs sector could give interesting signatures of their own if they are light enough to be produced.

Some models even suggest that a fundamental Higgs scalar does not exist but that the Higgs mechanism is implemented by a more complicated particle that is not fundamental but is rather a bound state of more elementary particles—akin to the paired electrons that give mass to the photon in a superconducting material. If this is the case, the bound state Higgs particle should be surprisingly heavy and have other interaction properties that distinguish it from a fundamental Higgs boson. These models are currently disfavored, since they are hard to match to all experimental observations. Nonetheless, LHC experimenters will search to make sure.

THE HIERARCHY PROBLEM OF PARTICLE PHYSICS

And the Higgs boson is only the tip of the iceberg for what the LHC might find. As interesting as a Higgs boson discovery will be, it is not the only target of LHC experimental searches. Perhaps the chief reason to study the weak scale is that no one thinks the Higgs boson is all that remains to be found. Physicists anticipate that the Higgs boson is but one element of a much richer model that could teach us more about the nature of matter and perhaps even space itself.

This is because the Higgs boson and nothing else leads to another enormous enigma known as the
hierarchy problem
. The hierarchy problem concerns the question of why particle masses—and the Higgs mass in particular—take the values that they do. The weak mass scale that determines elementary particle masses is ten thousand trillion times smaller than another mass scale—the Planck mass that determines the strength of gravitational interactions. (See Figure 54.)

The enormity of the Planck mass relative to the weak mass corresponds to the feebleness of gravity. Gravitational interactions depend on the
inverse
of the Planck mass. If it is as big as we know to be the case, gravity must be extremely weak.

[
FIGURE 54
]
The hierarchy problem of particle physics: The weak energy scale is 16 orders of magnitude smaller than the Planck scale associated with gravity. The Planck length scale is correspondingly shorter than the distances probed by the LHC.

The fact is that fundamentally, gravity is by far the weakest known force. Gravity might not seem feeble, but that’s because the entire mass of the Earth is pulling on you. If you were instead to consider the gravitational force between two electrons, you would find the force of electromagnetism is 43 orders of magnitude larger. That is, electromagnetism wins out by 10 million trillion trillion trillion. Gravity acting on elementary particles is completely negligible. The hierarchy problem in this way of thinking is: Why is gravity so much more feeble than the other elementary forces we know?

[
FIGURE 55
]
Quantum contribution to the Higgs boson mass from a heavy particle—for example with GUT-scale masses—and its antiparticle (
left
) and from a virtual top quark and its antiparticle (
right
).

Particle physicists don’t like unexplained large numbers, such as the size of the Planck mass relative to the weak mass. But the problem is even worse than an aesthetic objection to mysterious large numbers. According to quantum field theory, which incorporates quantum mechanics and special relativity, there should be barely any discrepancy at all. The urgency of the hierarchy problem, at least for theorists, is best understood in these terms. Quantum field theory indicates that the weak mass and the Planck mass constant should be about the same.

In quantum field theory, the Planck mass is significant not only because it is the scale at which gravity is strong. It is also the mass at which both gravity and quantum mechanics are essential and physics rules as we know them must break down. However, at lower energies, we do know how to do particle physics calculations using quantum field theory, which underlies many successful predictions that convince physicists that it is correct. In fact, the best measured numbers in all of science agree with predictions based on quantum field theory. Such agreement is no accident.

But the result when we apply similar principles to incorporate quantum mechanical contributions to the Higgs mass due to virtual particles is extraordinarily perplexing. The virtual contributions from just about any particle in the theory seem to give a Higgs particle a mass almost as big as the Planck mass. The intermediate particles could be heavy objects, such as particles with enormous GUT-scale masses (see left-hand-side of Figure 55) or the particles could be ordinary Standard Model particles, such as top quarks (see right-hand-side). Either way, the virtual corrections would make the Higgs mass much too large. The problem is that the allowed energies for the virtual particles being exchanged can be as big as the Planck energy. When this is true, the Higgs mass contribution too can be almost this large. In that case, the mass scale at which the symmetry associated with the weak interactions is spontaneously broken would also be the Planck energy, and that is 16 orders of magnitude—ten thousand trillion times—too high.

The hierarchy problem is a critically important issue for the Standard Model with only a Higgs boson. Technically, a loophole does exist. The Higgs mass, in the absence of virtual contributions, could be enormous and have exactly the value that would cancel the virtual contributions to just the level of precision we need. The problem is that—although possible in principle—this would mean 16 decimal places would have to be canceled. That would be quite a coincidence.

No physicist believes this fudge—or fine-tuning as we call it. We all think the hierarchy problem, as this discrepancy between masses is known, is an indication of something bigger and better in the underlying theory. No simple model seems to address the problem completely. The only promising answers we have involve extensions of the Standard Model with some remarkable features. Along with whatever implements the Higgs mechanism, the solution to the hierarchy problem is the chief search target for the LHC—and the subject of the following chapter.

THE WORLD’S NEXT TOP MODEL

In January 2010, colleagues gathered at a conference in Southern California to discuss particle physics and dark matter searches in the LHC era. The organizer, Maria Spiropulu, a CMS experimenter and member of the Caltech physics department, asked me to give the first talk and outline the LHC’s major issues and physics goals for the near future.

Maria wanted a dynamic conference, so she suggested we start with a “duel” among the three opening speakers. As if the term “duel” applied to three people wasn’t confusing enough, the audience of invited guests posed an even greater challenge since it ranged from experts in the field to interested observers from the California technology world. Maria asked me to dig deep and look into subtle and overlooked features of current theories and experiments, while one of the attendees, Danny Hillis—a brilliant nonphysicist from the company Applied Minds—suggested I make everything as basic as possible so the nonexperts could follow.

I did what any rational person would do in the face of such contradictory and impossible-to-satisfy advice: procrastinate. The result of my web surfing was my first slide (see Figure 56), which ended up in Dennis Overbye’s
New York Times
article on the subject—typo and all.

The topics referred to the subject matter that the subsequent speakers and I were scheduled to cover. But the humor in the sound effects I inserted to accompany the entrance of each of the dueling cats (which I can’t reproduce here) was meant to reflect both the enthusiasm and the uncertainty associated with each of these models. Everyone at the conference, no matter how strongly convinced of an idea he or she had worked on, knew that data were coming soon. And data would be the final arbiter of who had the last laugh (or a Nobel Prize).

[
FIGURE 56
]
Candidate models, as I presented on a slide at a conference.

The LHC presents us with a unique opportunity to create new understanding and new knowledge. Particle physicists hope to soon know the answers to the deep questions we have been thinking about: Why do particles have the masses they do? What is dark matter composed of? Do extra dimensions solve the hierarchy problem? Are extra symmetries of spacetime involved? Or is there something completely unforeseen at work?

Proposed answers include models with names like supersymmetry, technicolor, and extra dimensions. The answers could turn out to be different from anything anticipated, but models give us concrete targets of what to look for. This chapter presents a few of the candidate models that address the hierarchy problem and gives a flavor of the type of explorations that the LHC will perform. Searches for these and other models happen concurrently and will provide valuable insights no matter what turns out to be the true theory of nature.

SUPERSYMMETRY

We’ll begin with the bizarre symmetry called supersymmetry and the models that incorporate it. If you did a survey among theoretical particle physicists, a good fraction of them would likely say that supersymmetry solves the hierarchy problem. And if you asked experimenters what they wanted to look for, a large fraction of them would suggest supersymmetry as well.

Since the 1970s, many physicists have considered the existence of supersymmetric theories so beautiful and surprising that they believe it has to exist in nature. They have furthermore calculated that forces should have the same strength at high energy in a supersymmetric model—improving on the near-convergence that happens in the Standard Model, allowing the possibility of unification. Many theorists also find supersymmetry to be the most compelling solution to the hierarchy problem, despite the difficulty in making all the details agree with what we know.