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

  Apart from the search for the Higgs, searching for supersymmetry is probably the highest-priority task of the LHC. Given the messiness of the theory, even if we find it there will be a great challenge in figuring out that supersymmetry is really what we’ve found. Interestingly, one implication of supersymmetry is that a single Higgs boson is not enough. Remember from Chapter Eleven that the Higgs field in the Standard Model starts off as four scalar fields of equal mass; after symmetry breaking, three of those fields get eaten by the W and Z bosons, leaving just one Higgs for us to detect. In supersymmetric versions of the Standard Model, however, it turns out for technical reasons that we need to double the amount of scalar fields we start with, from four to eight. (That’s not including the fermionic higgsino superpartners; here we’re just talking about boson fields.) One of those groups of four gives mass to the up-type quarks, while the other gives mass to the down-type quarks. We still just have three W and Z bosons; when the Higgs gets a nonzero value and breaks the electroweak symmetry, three of the scalar fields are eaten, and that leaves us with five different Higgs bosons running free. That’s right: A simple consequence of supersymmetry is that we have five Higgs bosons rather than the usual one. One will have a positive electric charge, one will be negative, and the other three will be neutral.

  Five Higgs bosons is obviously a field day for experimenters. This is one of the reasons why the LHC physicists were so cautious when announcing that they had found a new particle at 125 GeV; it could be a Higgs boson, without necessarily being the Higgs boson. When people try to construct supersymmetric models, it’s easy to make one Higgs lighter than all the rest, so maybe we’ve just discovered that one. However, it’s also a generic feature that the lightest Higgs tends to be quite light—usually 115 GeV or less. It’s possible to nudge it up to 125 GeV, but it requires a few unnatural-seeming contortions. There is a pressing need for more data, both to get a better handle on the particle that has been discovered, and to keep looking for more.

  Having extra particles to detect makes physicists happy, but it doesn’t really count as an advantage to supersymmetry as a theory. Here is a more tangible advantage: It helps solve the hierarchy problem.

  The hierarchy problem comes about because we expect the effects of virtual particles to push the value of the Higgs field up to the Planck scale. Closer examination, however, reveals that virtual bosons tend to push the Higgs field one way, and virtual fermions push it the other way. In general, there’s no reason to expect these effects to cancel each other; usually, subtracting a random big number from another random big number gives a third (positive or negative) big number, not a small one. But with supersymmetry, all that changes. Now there are exactly matching fermion and boson fields, and the effects from their virtual fluctuations can precisely cancel, leaving the hierarchy intact. This is one of the primary motivations physicists have for taking supersymmetry seriously.

  Another motivation comes from the idea of WIMP dark matter. In viable supersymmetric models, the lightest superpartner is a completely stable particle with a mass and interaction strength close to the weak scale. If that particle has no electric charge—i.e., if it’s a neutralino—it is a perfect candidate for dark matter. A great deal of theoretical work has gone into calculating the relic abundance of neutralinos in different supersymmetric models. Precisely because there are so many new particles and interactions, a wide range of abundances is possible, but it’s not hard to get the correct dark-matter density. If superpartners exist at energies accessible to the LHC, we may be able to achieve a spectacular synthesis of particle physics and cosmology. It’s good to aim high.

  Strings and extra dimensions

  String theory is one of the simplest ideas of all time. Just imagine that the elementary constituents of nature, rather than being pointlike particles, are instead small vibrating strings. The concept can be traced back to separate papers in 1968 and 1969 by Yoichiro Nambu, Holger Nielsen, and Leonard Susskind, who independently suggested that certain mathematical relationships in particle scattering could be simply explained if the particles were replaced by strings. As long as the loops or segments of string are sufficiently small, they will look like particles to us. You’re not supposed to ask, “What are the strings made of?” just as you were never tempted to ask, “What is an electron made of?” The string-stuff is the fundamental substance out of which other things are made.

  The original string theories described only bosons, and they were plagued by an apparently fatal flaw: Empty space was unstable and would quickly dissolve into a cloud of energy. To fix it, string pioneers Pierre Ramond, André Neveu, and John Schwarz showed how to add fermions to the theory. In the process, they ended up inventing one of the first examples of supersymmetry. Thus was “superstring theory” born. To be clear: Viable models of string theory seem to necessarily be supersymmetric, but there are supersymmetric models that aren’t necessarily connected to string theory in any way. If we were to find supersymmetric particles at the LHC, it would improve the chance that string theory is on the right track, but it wouldn’t be direct evidence for strings.

  Superstrings solved the stability problem of the early string models, but they came with a frustrating feature: a massless particle that coupled to the energy of everything. This was annoying because the early goal of string theory was to explain the strong force, and there wasn’t any such particle in nuclear interactions. Then in 1974, Joël Scherk and Schwarz pointed out that there is a famous massless particle that couples to the energy of everything: the graviton. Instead of being a theory of the strong interactions, they suggested, maybe string theory is a theory of quantum gravity, as well as all the other known forces—a theory of everything.

  This idea was originally met with bemused stares, as particle theorists in the 1970s weren’t that concerned with gravity. By 1984, however, it was clear that the Standard Model was doing a good job at explaining particle physics, and theorists were looking for new challenges. In that year, Michael Green and Schwarz showed that superstring theory was able to avoid a mathematical consistency challenge that many thought would render the theory nonviable. Just as the electroweak theory burst into popularity once ’t Hooft showed it is renormalizable, the string theory bandwagon took off after the Green-Schwarz paper and has been a major part of particle theory in the years since.

  There is yet another problem that string theory needs to solve: the dimensionality of spacetime. Quantum field theory is more flexible than string theory, and there are sensible field theories in all sorts of different spacetimes. But superstring theory is more restrictive; early investigations found that the theory naturally wants to live in precisely ten dimensions of spacetime. That’s nine dimensions of space and one of time, in contrast with our usual three dimensions of space and one of time. At this point, the faint of heart would be excused for moving on to other ideas.

  But string theorists were entranced by the possibility of bringing gravity into the fold of the known forces, and they persevered. They borrowed an old idea that had been investigated in the 1920s by Theodor Kaluza and Oskar Klein: Perhaps some dimensions of space are hidden from our view by being curled up into a tiny ball, too small to be seen or even probed in high-energy particle accelerators. A cylinder like a straw or a rubber hose has two dimensions—up and down the length, and around the circle—but if you look at it from far away it will appear as a one-dimensional line. From that perspective, a faraway cylinder is a line with a tiny compact circle located at each point. Remember that short wavelengths correspond to high energies; if a compact space is sufficiently small, only extremely high-energy particles will even notice it is there.

  This idea of “compactification” of extra dimensions became an important part of attempts to connect string theory with observable phenomena. At a fundamental level, there is very little freedom in creating different versions of string theory; work in the 1980s showed that there are really only five string theories. But each of those five features ten d
imensions of spacetime, and when we hide six of them we find out that there can be many different ways to perform the compactification. Even though it would take very high energies (presumably of the order of the Planck energy of quantum gravity, 1018 GeV) to directly probe a compact manifold, features of the compactification directly affect the kinds of physics we see at low energies. By “features of the compactification” we mean its volume, its shape, and its topology; compactifying on a torus (the surface of a doughnut) will be very different from compactifying on a sphere (the surface of a ball). And by “the physics we see at low energies” we mean what kind of fermions there are, which forces exist, and the values of the various masses and interaction strengths.

  Three different models of compactification. What looks like a point to a macroscopic observer is revealed, on closer inspection, to be a higher-dimensional space. From left to right: a torus (surface of a doughnut), a sphere (surface of a ball), and a warped space stretching between two branes. Realistic compactifications will involve a larger number of extra dimensions, which are hard to illustrate.

  Therefore, while string theory itself is fairly unique, connecting it to experiments has proven to be extremely difficult. Without knowing how the extra dimensions are compactified, it’s impossible to say much about what predictions string theory would make for the observable world. This is a pretty general problem with any attempt to apply quantum mechanics to gravity, not just string theory: Direct experimental probes require energies at the Planck scale, and no feasible particle accelerator is going to reach that. That’s not to say there can never be data that helps us test models of quantum gravity, but the tests are going to require subtlety rather than brute force.

  Branes and the multiverse

  In the 1990s, the way people tried to connect string theory with reality underwent a dramatic shift. The impetus for this change was the discovery by Joseph Polchinski that string theory isn’t simply a theory of one-dimensional strings. There are also higher-dimensional objects that play a crucial role.

  A two-dimensional surface is called a “membrane,” but string theorists needed to be able to describe three-dimensional and higher-dimensional objects as well, so they adopted the terminology “2-brane” and “3-brane” and so on. A particle is a zero-brane, and a string is a 1-brane. Using these extra branes, string theorists showed that their theory is even more unique than they thought: All five of the ten-dimensional superstring theories—as well as an eleven-dimensional “supergravity” theory that doesn’t have strings at all—are simply different versions of one underlying “M-theory.” To this day, nobody really knows what the “M” in “M-theory” is supposed to stand for.

  The bad news is that this menagerie of branes nudged string theorists into discovering even more ways to compactify the extra dimensions. Partly this was driven by attempts to find compactifications that featured a positive amount of vacuum energy, which was demanded by the 1998 discovery that the universe is accelerating—one of the rare times that progress in string theory was instigated by experiment. Lisa Randall and Raman Sundrum used brane theory to develop an entirely new kind of compactification, in which space “warped” in between two branes. This led to a rich variety of new approaches to particle physics, including new ways of addressing the hierarchy problem.

  It also, unfortunately, seemingly dashed remaining hopes that finding the “right” compactification would somehow allow us to connect string theory with the Standard Model. The number of compactifications we’re talking about is hard to estimate, although numbers like 10500 have been bandied about. That’s a lot of compactifications, especially when the task before you is to search through all of them looking for one that matches the Standard Model.

  In response, some proponents of string theory took a different tack: Rather than finding the one true compactification, they imagine that different parts of spacetime feature different compactifications, and that every compactification is realized somewhere. Because compactifications define the particles and forces seen at low energies, this is like having different laws of physics in different regions. We can then call each such region a separate “universe,” and the whole collection of them is the “multiverse.”

  It might seem that such a scheme gives up on any pretense of making testable predictions. It’s certainly difficult, but advocates of the multiverse argue that there is still hope. In many parts of the multiverse, they argue, conditions are so inhospitable that no intelligent life can possibly arise. Maybe there are no appropriate forces, or the vacuum energy could be so high that individual atoms would be torn apart by the expansion of the universe. One problem is that we don’t have a very good understanding of the conditions under which life can form. If we can overcome such mundane considerations, however, optimists hold out hope that they can make predictions for what typical observers in the multiverse would actually observe. In other words, even if we don’t see other “universes” directly, we might be able to use the idea of the multiverse to make testable predictions. The “anthropic principle” is the idea that there is a strong selection effect that limits the conditions we can possibly observe to those that are compatible with our existence.

  It’s an ambitious plan, and possibly doomed to failure. But people try, and in particular they have applied this idea to properties of the Higgs boson. These are treacherous waters; back in 1990, Mikhail Shaposhnikov and Igor Tkachev tried to predict the value of the Higgs mass under certain anthropic assumptions and came up with the answer 45 GeV. That’s clearly incompatible with the data as we now understand it, so something was wrong about those assumptions. Under different assumptions, in 2006, another group predicted a value of 106 GeV; closer, but still no cigar. Now that we have a Higgs boson at 125 GeV, it is unlikely that many predictions will be published that don’t somehow manage to reach that value.

  To be fair, we need to mention the most impressive success of anthropic reasoning: predicting the value of the vacuum energy. In 1987, more than ten years before the discovery of the acceleration of the universe, Steven Weinberg pointed out that a very high (or large and negative) vacuum energy would inhibit the formation of galaxies. Therefore, most observers in a multiverse should see small but nonzero values of the vacuum energy. (Zero is allowed, but there are more nonzero numbers than numbers equal to zero.) The value we think we have observed is perfectly consistent with Weinberg’s prediction. Granted, Weinberg was implicitly imagining a multiverse in which only the value of the vacuum energy changed from place to place; if we let other parameters change, the agreement becomes much less impressive.

  Despite the pessimistic, even curmudgeonly tone of this section, I believe the multiverse scenario is actually quite plausible. (In From Eternity to Here, I suggested that it might be helpful in explaining the low entropy of the early universe.) If string theory or some other theory of quantum gravity allows for different manifestations of local laws of physics in different regions of spacetime, the multiverse might be real, whether we can observe it or not; I’m always an advocate for taking seriously things that might be real. At the current state of the art, however, we are very far from being able to turn the multiverse into a predictive theory for particle physics. We can’t let our personal distaste color our judgment of cosmological scenarios, but neither can we let our enthusiasm get in the way of our critical faculties.

  Venturing forth

  There is much more to be discovered in the realm of the very small, and there are many aspects to particle physics beyond the Standard Model. Why is there more matter than antimatter in the universe? Several scenarios for generating such an asymmetry involve the cosmological evolution of the Higgs field, so it’s plausible that a better understanding of its properties will lead to new insights on this problem. There are also interesting “technicolor” models, according to which the Higgs is a composite particle like the proton rather than something fundamental. Current versions of technicolor tend to be disfavored by other particle-physics data, but studyi
ng the actual Higgs itself might very well lead to surprises.

  Discovering the Higgs is not the end of particle physics. The Higgs was the final piece of the Standard Model, but it’s also a window onto physics beyond that theory. In the years to come, we’ll be using the Higgs to search for (and hopefully study) dark matter, supersymmetry, extra dimensions, and whatever other phenomena prove to be needed to fit the new data that is rapidly coming in. The Higgs discovery is the end of one era and the beginning of another.

  THIRTEEN

  MAKING IT WORTH DEFENDING

  In which we ask ourselves why particle physics is worth pursuing, and wonder what comes next.

  Robert Wilson, the physicist who was in charge of building Fermilab, was dragged before the Congressional Joint Committee on Atomic Energy in 1969 to help senators and representatives understand the motivation behind the multimillion-dollar project. It was a turning point in the history of particle physics in the United States; the Manhattan Project had given physicists easy access to influence and funding, but it was unclear how the search for new elementary particles was going to lead to anything as immediately valuable as a new kind of weapon. Senator John Pastore of Rhode Island asked Wilson directly: “Is there anything connected with the hopes of this accelerator that in any way involves the security of the country?”