Knocking on Heaven's Door - Lisa Randall [150]
Down the road, even if supersymmetry is discovered, experimenters won’t stop there. They will try their best to determine the entire supersymmetric spectrum, and theorists will work to interpret what the results could mean. A lot of interesting theory underlies supersymmetry and the particles that could spontaneously break it. We know which supersymmetric particles should exist if supersymmetry is relevant to the hierarchy problem, but we don’t yet know the precise masses they should have or how those masses arise.
Different mass spectra will make an enormous difference to what the LHC should see. Particles can only decay into other particles that are lighter. The decay chain, the sequence of possible decays of supersymmetric particles, depends on the masses—what is heavier and what is lighter. The rates of various processes also depend on particle masses. Heavier particles in general decay more quickly. And they are usually more difficult to produce since only collisions with a good deal of energy can create them. Combining all the results together could give us important insights into what underlies the Standard Model and what awaits at the next energy scales. This will be true of any analysis of new physical theories that we might find.
Nonetheless, one should keep in mind that despite supersymmetry’s popularity among physicists, there are several reasons for concern about whether it truly applies to the hierarchy problem and the real world.
The first, and perhaps the most worrisome, is that we have not yet seen any experimental evidence. If supersymmetry exists, the only explanation for why we haven’t yet seen evidence is that the superpartners are heavy. But a natural solution to the hierarchy problem would require that superpartners be reasonably light. The heavier the superpartners are, the more inadequate supersymmetry appears as a solution to the hierarchy problem. The fudge required is determined by the ratio of the mass of the Higgs boson to the supersymmetry breaking scale. The bigger this is, the more “fine-tuned” the theory.
Not yet having seen the Higgs boson either compounds the problem. It turns out that in a supersymmetric model, the only way to make the Higgs heavy enough to have eluded detection is to have big quantum mechanical contributions that can come only from heavy superpartners. But again, those masses need to be so heavy that the hierarchy becomes a little unnatural, even with supersymmetry.
The other problem with supersymmetry is the challenge of finding a fully consistent model that includes supersymmetry breaking and agrees with all experimental data to date. Supersymmetry is a very specific symmetry that relates many interactions and prohibits interactions that quantum mechanics would otherwise permit. Once supersymmetry is broken, the “anarchic principle” takes over. Anything that can happen will. Most models would predict decays that have either never been seen in nature or are seen only much too infrequently to agree with predictions. Because of quantum mechanics, a whole can of worms is opened once supersymmetry is broken.
Physicists might simply be missing the right answers. We certainly cannot say definitively that no good models exist or that a little fine tuning doesn’t happen. Certainly, if supersymmetry is the correct resolution of the hierarchy problem, we should find evidence for it soon at the LHC. So it is certainly worth pursuing. A discovery of supersymmetry would mean that this exotic new spacetime symmetry applies not just in a theoretical formulation on a piece of paper, but also in the real world. However, in the absence of discovery, it is also worth considering alternatives. The first we’ll consider is known as technicolor.
TECHNICOLOR
Back in the 1970s, physicists also first considered an alternative potential solution to the hierarchy problem known as technicolor. Models under this rubric involve particles that interact strongly via a new force, playfully