Warped Passages - Lisa Randall [125]
Figure 62. A contribution to the Higgs particle’s mass from a virtual top quark and a virtual antitop quark. The Higgs particle can convert to a virtual top quark and virtual antitop quark, and this gives an enormous contribution to the Higgs particle’s mass.
Particle physics in its present state is like a too effective “trickle-down” theory. In economics, a hierarchy of wealth is not difficult to achieve. The application of trickle-down economics has never raised poor people’s financial well-being much at all, let alone to the level of the upper classes. In physics, though, the transfer of wealth is far too efficient. If one mass is large, then quantum contributions tell us that all masses of elementary particles are expected to be about as large. All particles end up rich in mass. But we know from measurements that high mass (the Planck scale mass) and low mass (particle masses) coexist in our world.
Without modifying or extending the Standard Model, particle physics theory can achieve a small mass for the Higgs particle only through a miraculous value for its classical mass. That value must be extremely large—and possibly negative—so that it can precisely cancel the large quantum contributions. All the mass contributions must add up to 250 GeV.
For this to happen, as in the Grand Unification Theory we considered earlier, the mass must be a fine-tuned parameter. And this fine-tuned parameter would have to be an enormous yet amazingly exact fudge specifically designed to give a small net mass to the Higgs particle. Either the quantum contributions from virtual particles or the classical contribution must be negative, and almost equal in magnitude to the other. The positive and negative terms, each of which is sixteen orders of magnitude too large, must add up to a much smaller value. The required fine-tuning, which must have sixteen-digit accuracy, is more extreme than the fine-tuning required to make your pencil stand on end. It’s about as likely as someone randomly winning the guessing game with Ike.
Particle physicists would prefer a model that didn’t involve the fine-tuning that is required in the Standard Model to ensure a light Higgs particle. Although we might fine-tune in an act of desperation, we hate it. Fine-tuning is almost certainly a badge of shame reflecting our ignorance. Unlikely things sometimes happen, but rarely when you want them to.
The hierarchy problem is the most urgent of the mysteries confronting the Standard Model. To put a positive spin on things, the hierarchy problem provides a clue to what plays the role of the Higgs particle and breaks the electroweak symmetry.
Any theory that replaces the two-field Higgs theory should naturally accommodate or predict a low electroweak mass scale—otherwise it is just not worth thinking about. Many underlying theories are compatible with the physical phenomena we see, but very few of them address the hierarchy problem and include a light Higgs particle in a compelling manner that avoids fine-tuning. While the task of unifying forces is a fascinating, if potentially tenuous, theoretical lure from high-energy physics, the task of solving the hierarchy is a concrete necessity urging progress at relatively low energies. What makes this challenge most exciting is that anything that addresses the hierarchy problem should have experimental consequences that will be measurable at the Large Hadron Collider, where experimenters expect to find particles with masses of about 250 to 1,000 GeV. Without such additional particles, there is no way to get around the problem. We’ll soon see that the experimental consequences of solving the hierarchy problem might be the supersymmetric