Warped Passages - Lisa Randall [187]
However, you should bear in mind that, impressive as it is to rule out deviations of gravity at millimeter distances, this doesn’t test most of the currently proposed extra-dimensional models. Remember, only the model with two large extra dimensions produces effects that would be visible on the millimeter scale. If a theory with more than two large extra dimensions solves the hierarchy problem (or if one of the models we’ll consider in the next chapter applies to the world), deviations from Newton’s law would occur only at much shorter distances.
We don’t know for sure what the gravitational attraction between two objects less than a tenth of a millimeter apart will look like. No one has ever tested it. So we don’t know whether extra dimensions open up at a tenth of a millimeter, which, if you think about it, is not all that small. Relatively large extra dimensions—though not quite as big as a millimeter—remain a viable possibility. To test such models we’ll have to wait for collider tests, the subject of the next section.
Collider Searches for Large Extra Dimensions
High-energy particle colliders are well-suited to discover KK particles from large extra dimensions, even if there are more than two of them. In the ADD large extra-dimensions models, the KK partners of the graviton are always incredibly light. If the large-dimension proposal applies to the real world, the graviton KK partners would be light enough to be produced at accelerators, no matter how many extra dimensions there were. That tells us that even if dimensions are smaller than a millimeter, current and future accelerator searches should be able to discover them. Current colliders create more than enough energy to make such low-mass particles. In fact, if the only relevant quantity were energy, KK particles would already have been produced in abundance.
However, there is a catch. The graviton’s KK partners interact only incredibly feebly—as feebly, in fact, as the graviton itself. Since a graviton’s interactions are so negligible that gravitons are never produced or detected at colliders at a measurable rate, an individual graviton KK partner wouldn’t be either.
But the potential for detecting KK particles from higher dimensions is actually much more promising than this dismal assessment might lead you to believe. This is because, if the ADD proposal is correct, there would be so many light KK partners of the graviton that together they could leave detectable evidence of their existence. If the large-dimensions scenario is true, then even though any individual KK particle could be produced only rarely, the probability of producing one of the large number of light KK particles would be measurably large. For example, if there were two extra dimensions, about one hundred billion trillion KK modes would be light enough to be produced at a collider operating at an energy of about a TeV. The rate of producing at least one of these particles would be fairly high, even if the rate of producing any single one of them were extremely low.
It would be as if someone hinted something to you in such a subtle manner that you didn’t take it to heart the first time you heard it. But afterwards, fifty people repeated the same thing. Even though you wouldn’t take much notice the first time you heard the message, by the fiftieth time the message would register. Similarly, although the light KK particles are light enough to be produced at current accelerators, they interact so weakly that we can’t detect any individual one. However, when an accelerator achieves sufficiently high energy to produce a lot of them, KK particles will leave observable signals.
The Large Hadron Collider, which will study TeV-scale energies, could produce KK particles at a measurable rate if the ADD idea is correct. That might sound like a fortunate coincidence—why should an energy of about a TeV be relevant to KK production rates when neither the KK masses nor the mass that determines the interaction strength of the KK particles (that is, MPl)