Warped Passages - Lisa Randall [202]
Only the more massive KK particles could communicate the secrets of the five-dimensional theory. But they have to be light enough to be produced. Calculating the KK particles’ masses in this theory is a little tricky, however. Because of the distinctive geometry, the KK particles would not have masses proportional to the inverse size of the dimension, as was the case for rolled-up dimensions of flat space. A mass proportional to the inverse size would have been extremely surprising, since, for the small extra dimension we are considering, that would be the Planck scale mass. On the Weakbrane nothing much heavier than a TeV can exist; one certainly wouldn’t ever find anything there with the Planck scale mass.
Since a TeV is the mass associated with the Weakbrane, it shouldn’t come as too big a surprise that when you do the calculations correctly taking into account warped spacetime, the KK particles turn out to have masses of about a TeV. Both the lightest KK particle, and the difference between the masses of the successively heavier KK particles, turn out to be about a TeV when the fifth dimension ends at the Weakbrane, as we have been assuming. KK particles pile up on the Weakbrane (because their probability function peaks there) and they have all the properties of Weakbrane particles.
This means that there are heavy KK partners of the graviton that are about 1 TeV, 2 TeV, 3 TeV,…in mass. And, depending on the ultimate energy reach of the LHC, there is a good chance of finding one or more of them. Unlike the KK partners in the large extra dimensions scenario, these KK partners interact much more strongly than gravity.
These KK particles are not nearly as feebly interacting as the graviton of four dimensions—they have an interaction strength sixteen orders of magnitude bigger. The graviton KK partners interact so strongly in our theory that any KK partner produced at the collider will not simply disappear out of sight, carrying away energy but leaving no visible signal. Instead, they will decay inside the detector into detectable particles, perhaps muons or electrons, which can be used to reconstruct the KK particle from which they originated (see Figure 84).
This is the conventional recipe for discovering new particles: study all the decay products and deduce the properties of what they came from. If what you find isn’t something you already know about, it must be something new. If the KK particles decay in the detector, the signal of extra dimensions should be very clean. In our model, rather than simply a missing energy signature, which has no significant labels that would definitively identify the missing energy’s origin and let us distinguish the model from other possibilities, the reconstructed masses and spins of the KK particles should be enormously helpful clues that will tell us quite a lot about the new particles’ identities. The spin value of the KK particles—spin-2—will be a virtual ID tag that will tell us that the new particles have something to do with gravity. A spin-2 particle with a mass of about a TeV would be extremely strong evidence for an extra warped dimension. Few other models give rise to such heavy spin-2 particles, and the ones that do would have other distinguishing features.
Figure 84. Two protons collide, and a quark and an antiquark annihilate and produce a KK partner of the graviton. The KK particle can then decay into visible particles, such as an electron and a positron. The gray lines are sprays of particles from the protons.
If we’re lucky, in addition to the KK partners of the graviton, experiments might also produce an even richer set of KK particles.