Knocking on Heaven's Door - Lisa Randall [146]
[ FIGURE 56 ] Candidate models, as I presented on a slide at a conference.
The LHC presents us with a unique opportunity to create new understanding and new knowledge. Particle physicists hope to soon know the answers to the deep questions we have been thinking about: Why do particles have the masses they do? What is dark matter composed of? Do extra dimensions solve the hierarchy problem? Are extra symmetries of spacetime involved? Or is there something completely unforeseen at work?
Proposed answers include models with names like supersymmetry, technicolor, and extra dimensions. The answers could turn out to be different from anything anticipated, but models give us concrete targets of what to look for. This chapter presents a few of the candidate models that address the hierarchy problem and gives a flavor of the type of explorations that the LHC will perform. Searches for these and other models happen concurrently and will provide valuable insights no matter what turns out to be the true theory of nature.
SUPERSYMMETRY
We’ll begin with the bizarre symmetry called supersymmetry and the models that incorporate it. If you did a survey among theoretical particle physicists, a good fraction of them would likely say that supersymmetry solves the hierarchy problem. And if you asked experimenters what they wanted to look for, a large fraction of them would suggest supersymmetry as well.
Since the 1970s, many physicists have considered the existence of supersymmetric theories so beautiful and surprising that they believe it has to exist in nature. They have furthermore calculated that forces should have the same strength at high energy in a supersymmetric model—improving on the near-convergence that happens in the Standard Model, allowing the possibility of unification. Many theorists also find supersymmetry to be the most compelling solution to the hierarchy problem, despite the difficulty in making all the details agree with what we know.
Supersymmetric models posit that every fundamental particle of the Standard Model—electrons, quarks, and so on—has a partner in the form of a particle with similar interactions but different quantum mechanical properties. If the world is supersymmetric, then there exist many unknown particles that could soon be found—a supersymmetric partner for every known particle. (See Figure 57.)
Supersymmetric models could help solve the hierarchy problem and, if so, would do it in a remarkable fashion. In an exactly supersymmetric model, the virtual contributions from particles and their superpartners cancel exactly. That is, if you add together all the quantum mechanical contributions from every particle in the supersymmetric model and tally their effect on the Higgs boson mass, you would find they all add up to zero. In a supersymmetric model, the Higgs boson would be massless or light, even in the presence of quantum mechanical virtual corrections. In a true supersymmetric theory, the sum of the contributions of both types of particles exactly cancel. (See Figure 58.)
[ FIGURE 57 ] In a supersymmetric theory, every Standard Model particle would have a supersymmetric partner. The Higgs sector is also enhanced beyond that of the Standard Model.
This sounds miraculous perhaps but is guaranteed because supersymmetry is a very special type of symmetry. It’s a symmetry of space and time—like the symmetries you are familiar with such as rotations and translations—but it extends them into the quantum regime.
[ FIGURE 58 ] In a supersymmetric model, contributions from virtual supersymmetric particles exactly cancel the Standard Model particles’ contributions to the Higgs boson mass. For example, the sum of the contributions from the two diagrams above is zero.
Quantum mechanics divides matter into two very