Warped Passages - Lisa Randall [201]
If gauge bosons in the warped scenario are present in the bulk, they could have energy much bigger than a TeV. The gauge bosons, which would hang out in the bulk, would experience the entire energy range. No longer tethered to the Weakbrane, they could travel anywhere in the bulk, and have energies as high as the Planck scale energy. Only on the Weakbrane does energy have to be less than a TeV. Because the forces would be in the bulk and could therefore operate at high energies, unification of forces would be a possibility. This is exciting because it means that the forces can unify at high energy, even in a theory with an extra dimension. And Pomarol found the very interesting result that unification did indeed occur, almost as if the theory were truly four-dimensional.
But it gets even better. Unification and the warped hierarchy mechanism can be combined. Pomarol showed that forces unify, but he assumed that supersymmetry addressed the hierarchy problem. But the hierarchy problem’s solution in warped geometry requires only that the Higgs particle be on the Weakbrane, so that its mass will be about the same as the weak scale energy, between 100 GeV and a TeV. The gauge bosons need not be stuck there.
In the warped geometry, all you need in order to solve the hierarchy problem is that the Higgs particle’s mass be low. That is because the Higgs field is responsible for the spontaneous symmetry breaking that is the source of all elementary particle masses. Gauge bosons and fermions won’t have a mass unless the weak force symmetry is broken. So long as the Higgs particle has a weak scale mass, the weak gauge boson masses will turn out correct. The warped gravity solution to the hierarchy really only requires the Higgs particle to be on the Weakbrane.
What this all means is that if the Higgs particle is on the Weakbrane, but quarks, leptons, and gauge bosons are in the bulk (see Figure 83), you can have your cake and eat it too. The weak scale would be protected and would be about a TeV, but unification could still occur at very high energies—on the GUT scale. My former student Matthew Schwartz and I showed that supersymmetry isn’t the only theory that can be consistent with unification—a warped extra-dimensions theory can be, too!
Figure 83. Nongravitational forces can also be in the bulk. In that case, forces can unify at high energies.
Experimental Implications
The natural scale on the Weakbrane is about a TeV. Should this warped geometry scenario prove to be a true description of our world, the experimental consequences at the Large Hadron Collider at CERN in Switzerland will be tremendous. Signatures of the warped five-dimensional spacetime could include Kaluza-Klein particles, five-dimensional black holes of anti de Sitter space, and TeV-mass strings.
The KK particles of the warped spacetime are likely to be the most accessible experimental herald of this geometry. As always, KK particles are particles with momentum in the extra dimension. But the new wrinkle in this model is that because the space is curved—not flat—the masses of the KK particles would reflect the idiosyncrasies of the warped geometry.
Since the only particle that we know for certain traverses the bulk is the four-dimensional graviton, let’s concentrate on its KK partners. As was true in flat space, the lightest of the KK partners of the graviton will be the one with no momentum at all in the fourth dimension. This particle would be indistinguishable from a particle of genuine four-dimensional origin: it’s the graviton that would communicate gravity in what looks like a four-dimensional world and it is the graviton whose probability function we