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By Root 718 0

In a theory in which most Standard Model particles reside in the bulk, we might also see charged KK partners of quarks and leptons and gauge bosons. Those particles would be both charged and heavy. And they could ultimately give us even more information about the higher-dimensional world.* In fact, the model builders Csaba Csaki, Christophe Grojean, Luigi Pilo, and John Terning have shown that in extra-dimensional warped spacetime with Standard Model particles in the bulk, electroweak symmetry might be broken even without a Higgs particle, and the charged particles that experimenters might then detect could tell us whether this alternative model is true for the world in which we live.

An Even More Bizarre Possibility

I’ve described quite a few weird properties of extra dimensions. But the most extraordinary possibility is yet to come. We will shortly see that a warped extra dimension can actually stretch infinitely far, yet still be invisible, unlike a flat dimension, which always has to have a finite size to agree with observations.

This result was truly shocking. In Chapter 22, when we discuss this infinite extra dimension, we will focus on the geometry of space, not the hierarchy problem. But I’ll briefly mention here how you can solve the hierarchy problem in the infinite-extra-dimensional case as well.

So far, we have considered a model with two branes: the Gravitybrane and the Weakbrane, both of which bound a fifth dimension. However, the Weakbrane doesn’t have to be the end of the world (that is, the boundary of the fifth dimension). If the Higgs particle is confined to a second brane placed in the middle of an infinite extra dimension, such a model could also solve the hierarchy problem. The graviton’s probability function would be very small on the Weakbrane, gravity would be weak, and the hierarchy problem would be solved just as before when the Weakbrane bounded the extra dimension. The graviton’s probability function in the model with an infinite warped dimension would continue beyond the Weakbrane, but that wouldn’t affect the solution to the hierarchy problem, which relied only on the small graviton probability function on the Weakbrane.

However, because the dimension is infinite, the KK particles would have different masses and interactions, so the experimental implications of this model would be different than the ones I just described. When Joe Lykken and I first discussed this possibility at the Aspen Center for Physics (an inspirational venue if there ever was one, and also one of the reasons why many theoretical physicists like to hike), we weren’t sure whether this idea would actually work. If the fifth dimension didn’t end on the Weakbrane, not all the KK particles would be heavy (and have mass of about a TeV). Some KK particles would have very tiny masses. If these particles were detectable but experiments hadn’t yet discovered them, the model would be ruled out.

But it turns out that our model is safe. While sitting on a bench surrounded by gorgeous mountain scenery, I worked out the interactions of the KK particles (Joe did the same calculation, but I think he was inside his office at the Center). We calculated a result that told us that, although the KK particles’ interactions would be big enough to be interesting for future experiments, they would not be so big as to have already been seen.

In the future, the LHC will have a good chance of producing the KK particles of this model, should they exist. These particles won’t look like the ones from the finite-sized extra-dimensional warped model. Instead of nice KK particles that decay inside the detector, the KK particles in this model with an infinite extra dimension will escape into the extra dimension (similar to the KK particles’ behavior when there are large dimensions). So if there’s an infinite extra warped dimension and a Weakbrane that solves the hierarchy problem, experiments could only hope to discover events with missing energy. Even so, at sufficiently high energies, missing energy should be a sufficiently telling signal that