Warped Passages - Lisa Randall [181]
You might have thought that if dimensions were as big as a millimeter (or even ten times smaller), we would surely know about them already. After all, anyone who can’t see a millimeter-size object needs new glasses. On the scales of particle physics, a millimeter is enormous.
To get an idea of how extraordinary extra dimensions a millimeter—or even one a tenth of a millimeter—in size would be, let us recap the sorts of length scale we have discussed so far. The Planck scale length, well out of any experimental reach, is 10-33 cm. The TeV scale, which experiments currently explore, is about 10-17 cm; physicists have tested electromagnetism down to distances as small as 10-17 cm. The sizes ADD were talking about are huge in comparison. In the absence of branes, millimeter-size extra dimensions would be an absurdity that would have been ruled out.
However, branes make far larger extra dimensions conceivable. Branes can trap quarks, leptons, and gauge bosons so that only gravity experiences the full higher dimensionality of space. In the ADD scenario, which assumes that everything other than gravity is confined to a brane, everything that doesn’t involve gravity would look exactly the same as it would without the extra dimensions, even if the extra dimensions were extremely large.
For example, everything you see would look four-dimensional. Your eye detects photons, and photons in the ADD model are trapped on a brane. Therefore all objects you see would look as if there were only three spatial dimensions. If photons are trapped on a brane, then no matter how strong your glasses you could never see any evidence of extra dimensions directly.
In fact, you could hope to see evidence of millimeter-size dimensions in the ADD scenario only with an extremely sensitive gravity probe. All of the usual particle physics processes, such as interactions mediated by the electromagnetic force, electron-positron pair creation, and the binding of the nucleus through the strong force, occur only on the four-dimensional brane and would be exactly the same as in a purely four-dimensional universe.
Charged KK particles would not be a problem either. The previous chapter explained that extra dimensions cannot be very big when all particles are in the bulk, because if they were, we would already have seen the KK partners of Standard Model particles. But this is not true in the ADD scenario because all Standard Model particles—the electron, for example—are bound to a brane. So the Standard Model particles, which don’t travel in the higher-dimensional bulk, wouldn’t carry extra-dimensional momenta. Standard Model particles, which are confined to a brane, therefore wouldn’t have KK partners. And since there would be no KK partners, the constraints based on KK particles such as the ones considered in the last chapter wouldn’t apply.
In fact, in the ADD model, the only particle that must have KK partners is the graviton, which we know must travel in the higher-dimensional bulk. However, the graviton’s KK partners interact far more weakly than the Standard Model KK partners. Whereas Standard Model KK partners interact via electromagnetism, the weak force, and the strong force, the KK partners of the graviton interact only with gravitational strength—as weakly as the graviton itself. The graviton’s KK partners would therefore be much harder to produce and detect than the KK partners of Standard Model particles. After all, no