Warped Passages (54 page)

Until recently, physicists thought that symmetries were the only way to avoid the anarchic principle. But as Raman and I saw, once we’d eaten enough ice cream, separated branes are another way. A crucial reason why extra dimensions initially appeared so promising to me is that they suggested a reason, apart from symmetry, that restricted or unusual types of interactions could be natural. Sequestering unwanted particles can prevent unwanted interactions because they won’t generally occur between particles that are separated on different branes.

Particles on different branes don’t interact strongly because interactions are always local—only particles in the same place interact directly. Sequestered particles can make contact with particles on other branes, but only if there are interacting particles that can travel from one brane to the other. Like Ike on the Jailbrane, particles on different branes have only restricted means of communication with each other because they have no options apart from invoking an intermediary. Even if such indirect interactions do occur, they are often extremely small, since intermediary particles in the bulk, particularly ones with mass, only rarely travel long distances.

This suppression of interactions between particles sequestered in different places would be similar to the suppression of international information in a country, which I’ll call Xenophobia, where the government carefully controls the borders and the media. In Xenophobia, information not provided locally could be acquired only from foreign visitors who manage to enter, or from newspapers or books that get smuggled in.

Similarly, separated branes provide a platform from which to evade the anarchic principle, thereby doubling the set of tools at nature’s disposal for guaranteeing the absence of unwanted interactions. A further merit of sequestering is that it can even protect particles from the effects of symmetry breaking. So long as symmetry breaking happens sufficiently far away from those particles, it will have very little effect on them. When symmetry breaking is sequestered, it is quarantined, much as a contagious disease is contained when everyone with the disease is kept within a restricted region. Or, to use our other analogy, dramatic events that occur outside Xenophobia would have no effect in Xenophobia without an intervening communicator. Without porous borders, Xenophobia could function independently of the rest of the world.

Sequestering and Supersymmetry

The particular problem that Raman and I investigated in the summer of 1998 dealt with how sequestering might operate in nature to yield a universe with broken supersymmetry that has the properties of the universe we see. We have seen that supersymmetry can elegantly protect the hierarchy and guarantee that all the large quantum mechanical contributions to the Higgs particle’s mass add up to zero. But, as we saw in Chapter 13, even if supersymmetry exists in nature, it must be broken in order to explain why we’ve observed particles but not their superpartners.

Unfortunately, most models with broken symmetry predict interactions that don’t occur in nature, and such models cannot possibly be right. Raman and I wanted to find a physical principle that nature might use to protect itself from these unwanted interactions so that we could incorporate it into a more successful theory.

We focused on supersymmetry breaking in a braneworld context. Braneworlds can preserve supersymmetry. But just as in four dimensions, supersymmetry can be spontaneously broken when some part of the theory contains particles that don’t preserve supersymmetry. Raman and I realized that if all the particles responsible for supersymmetry breaking were separated from the Standard Model
particles, the model with broken supersymmetry would be less problematic.

We therefore assumed that Standard Model particles were confined to one brane, and that the particles responsible for supersymmetry breaking were sequestered on another. We observed that with such a setup, the dangerous interactions that quantum mechanics could induce don’t necessarily occur. Apart from the supersymmetry-breaking effects that might be communicated via intermediary particles in the bulk, the interactions of Standard Model particles would be the same as in a theory with unbroken supersymmetry. So just as in a theory with exact supersymmetry, unwanted flavor-changing interactions that are inconsistent with experiments should not happen. Bulk particles that interact with particles on both the supersymmetry-breaking brane and the Standard Model brane would determine precisely which interactions are possible—and they wouldn’t necessarily include the forbidden ones.

Of course, some supersymmetry breaking has to be communicated to the Standard Model particles. Unless supersymmetry breaking is communicated to them, nothing will raise the superpartners’ masses. Although we don’t know the exact values for the superpartners’ masses, experimental constraints, combined with supersymmetry’s role in protecting the hierarchy, tell us approximately what the superpartners’ masses should be.

The constraints tell us the qualitative relationships among the masses of the superpartners. Roughly speaking, all the superpartners have about the same mass, and those masses are all approximately the weak scale mass, 250 GeV. We needed to ensure that the masses of the superpartners fell in this range, while still preventing unwanted interactions from occurring. All the pieces had to fit for the theory of sequestered supersymmetry breaking to have a chance of being right.

The key to our model’s success was finding the intermediary particle that could carry the news of supersymmetry breaking to the Standard Model particles and give the superpartners the masses they needed to have. But we also wanted to be sure that our intermediary would not incite impossible interactions.

The graviton, a bulk particle that interacts with energetic particles
no matter where they are, looked like the perfect candidate. The graviton interacts with particles on the supersymmetry-breaking and on the Standard Model branes. Furthermore, the interactions of the graviton are known—they follow from the theory of gravity. We could show that the graviton’s interactions, while generating the necessary superpartner masses, do not generate the interactions that would cause quarks or leptons to confuse their identities—the interactions that are known not to occur in nature. The graviton therefore looked like a promising choice.

When Raman and I worked out the superpartner masses that would follow from a mediating messenger graviton, we found that, despite the simple elements, the calculation was surprisingly subtle. Classical contributions to supersymmetry-breaking masses turn out to be zero, and only quantum mechanical effects communicated supersymmetry breaking. When we realized this, we called the graviton-induced communication of supersymmetry-breaking
anomaly mediation
. We chose the name because, like the anomalies I discussed in Chapter 14, the specific quantum mechanical effects broke a symmetry that would otherwise be present. The great thing was that since the masses of the superpartners depended on known quantum effects in the Standard Model, rather than unknown higher-dimensional interactions, we could predict the relative sizes of the superpartners’ masses.

It took a few days to get it all straight, which meant that I could go from disappointment to relief in the same day. I remember startling my dinner companion one evening when I became completely distracted because I recognized an error and solved a problem that had worried me earlier in the day. In the end, Raman and I discovered that if gravity communicates supersymmetry breaking, sequestered supersymmetry breaking works surprisingly well. All the superpartners had the right masses, and the relationship between the gaugino and squark masses was in the range where we wanted it to be. Although not everything worked quite as simply as we had initially hoped, important relations among the superpartners’ masses fell into place without inducing the impossible interactions that are problematic for other supersymmetry-breaking theories. And with only slight modifications, everything worked.

And, best of all, thanks to the distinctive predictions for the
superpartners’ masses, our idea can be tested. A very significant feature of sequestered supersymmetry breaking is that, even though the extra dimension could be extraordinarily tiny, something like 10
^-31
cm in size, only about a factor of a hundred bigger than the minuscule Planck scale length, there would still be visible consequences. This goes against standard wisdom, which says that only much larger dimensions could have visible consequences, through either a modified gravitational force law or new heavy particles.

Although it is indeed true that we won’t see either of the above experimental consequences when the extra dimension is small, the graviton communicates supersymmetry breaking to the gauginos in a very particular way that we could calculate from the known gravitational interactions and the known interactions that occur in a theory with supersymmetry. The sequestered supersymmetry-breaking model predicts distinctive mass ratios for the gauginos, the partners of the gauge bosons, and those masses can be measured.
³⁰

This is very exciting. If physicists discover superpartners, they can then determine whether the relationships among their masses agree with what we predict. An experiment to search for these gauge superpartners is under way right now at the Tevatron—the proton-antiproton collider at Fermilab in Illinois. If we are very lucky, we will see results in the next few years.

In the end, Raman and I were both reasonably confident that we had discovered something interesting. But we both had some residual concerns. I was a little afraid that such an interesting idea, if true, couldn’t have been overlooked, and that we still needed to ensure that we hadn’t missed some hidden flaw in our model. Raman, too, thought the idea too good to have been overlooked. But he was confident it was right, and was afraid only that we might have missed a similar idea in the physics literature.

He wasn’t far from the truth. Anomaly mediation of supersymmetry breaking was independently discovered around the same time by Gian Giudice at CERN, Markus Luty at Maryland, Hitoshi Murayama at Berkeley, and Riccardo Rattazzi at Pisa, who had been working together that same summer. They released a paper the day after ours came out. Their research was amazing to me. I couldn’t see how two
groups of physicists could have traced the same tortuous journey through ideas in a single summer, but Raman had correctly guessed that others might have had similar interests. In fact, we were both right in a way. Although the other group had similar ideas, they developed them independently of the extra-dimensional motivation—without which anomaly-mediated masses were just a curiosity. As Riccardo generously said to the physicist Massimo Porrati, a mutual friend, Raman and I had done it better, not because our version of anomaly mediation was more correct, but because we had a reason anyone would care in the first place! That reason was extra dimensions. Without extra dimensions, supersymmetry breaking wouldn’t be sequestered and anomaly-mediated masses would be swamped by larger effects.

Other physicists have since gone on to investigate sequestered models of supersymmetry breaking. They have found ways to join this with other, older ideas to make even more successful models, ones that might represent the real world. People have even found ways to extend the lesson of sequestering back to four dimensions.

There are too many models to enumerate, but let me just mention two ideas I found particularly interesting. The first idea arose from a collaboration between Raman and Markus Luty. They used the insights from the warped geometry (described in Chapter 20) to reinterpret the consequences of sequestering in four dimensions. With these ideas, they developed a new class of four-dimensional symmetry-breaking models.

Another interesting idea was called
gaugino mediation
. The idea was to communicate supersymmetry breaking not through the graviton, but instead through gauginos, the supersymmetric partners of the gauge bosons. For this to work, gauge bosons and their partners couldn’t be stuck on a brane; they would have to be free to travel in the bulk. Raman reminded me that gaugino mediation was actually one of the many ideas we had dismissed early on. But the excellent model builders David E. Kaplan, Graham Kribs, and Martin Schmaltz, and, separately, Zacharia Chacko, Markus Luty, Ann Nelson, and Eduardo Ponton, demonstrated that we had been too hasty, and that gaugino mediation might work beautifully in communicating
supersymmetry-breaking masses while preserving all the advantages of sequestered supersymmetry breaking.
^*

Sequestering and Shining Masses

Sequestered symmetry breaking is a powerful tool for model building. The real world could contain separated branes, and by constructing models with this assumption, physicists can explore the range of possibilities.

The previous section explained how problems with flavor-changing interactions might be solved in theories with supersymmetry. But another question challenging the model builder is why there should be different flavors of quarks and leptons with different masses in the first place. The Higgs mechanism gives particles their masses, but the precise values are different for each flavor. This can be true only if each of the flavors interacts differently with whatever plays the role of the Higgs particle. Given that the three flavors of each particle type, such as the up, charm, and top quarks, have exactly the same gauge interactions, it’s mysterious that they should all have different masses. Something has to distinguish them, but the particle physics of the Standard Model doesn’t tell us what.

We can try to make models that explain different masses. But almost invariably, any model would also contain unwanted interactions that would change flavor identities. What we need is something that can safely distinguish flavors without producing these problematic interactions.

Nima Arkani-Hamed and the German-born physicist Martin Schmaltz assumed that different Standard Model particles were housed on separate branes and that they could explain some masses. Nima and Savas Dimopoulos found another, even simpler possibility. They assumed that there was a brane on which particles of the Standard Model were confined, and that the interactions among particles on this brane treated all flavors identically. But with only
flavor-symmetric interactions, which treat all the flavors the same, all particles would have exactly the same mass. Clearly, we can explain the different masses only if something treats the particles differently.