The Particle at the End of the Universe: How the Hunt for the Higgs Boson Leads Us to the Edge of a New World (37 page)

Standard Model particles (below) and their superpartners (above). Bosons are circles, fermions are squares. Three copies of each quark and squark, and eight copies of the gluons and gluinos, represent different colors. The supersymmetric Standard Model has five Higgs bosons rather than the usual one. The superpartners of the W bosons and charged Higgs bosons mix together to make charginos, while the superpartners of the Z, the photon, and the neutral Higgs bosons mix to make neutralinos.

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 dimensions 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, 10
¹⁸
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 10
⁵⁰⁰
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.”