Knocking on Heaven's Door - Lisa Randall [144]
Some models even suggest that a fundamental Higgs scalar does not exist but that the Higgs mechanism is implemented by a more complicated particle that is not fundamental but is rather a bound state of more elementary particles—akin to the paired electrons that give mass to the photon in a superconducting material. If this is the case, the bound state Higgs particle should be surprisingly heavy and have other interaction properties that distinguish it from a fundamental Higgs boson. These models are currently disfavored, since they are hard to match to all experimental observations. Nonetheless, LHC experimenters will search to make sure.
THE HIERARCHY PROBLEM OF PARTICLE PHYSICS
And the Higgs boson is only the tip of the iceberg for what the LHC might find. As interesting as a Higgs boson discovery will be, it is not the only target of LHC experimental searches. Perhaps the chief reason to study the weak scale is that no one thinks the Higgs boson is all that remains to be found. Physicists anticipate that the Higgs boson is but one element of a much richer model that could teach us more about the nature of matter and perhaps even space itself.
This is because the Higgs boson and nothing else leads to another enormous enigma known as the hierarchy problem. The hierarchy problem concerns the question of why particle masses—and the Higgs mass in particular—take the values that they do. The weak mass scale that determines elementary particle masses is ten thousand trillion times smaller than another mass scale—the Planck mass that determines the strength of gravitational interactions. (See Figure 54.)
The enormity of the Planck mass relative to the weak mass corresponds to the feebleness of gravity. Gravitational interactions depend on the inverse of the Planck mass. If it is as big as we know to be the case, gravity must be extremely weak.
[ FIGURE 54 ] The hierarchy problem of particle physics: The weak energy scale is 16 orders of magnitude smaller than the Planck scale associated with gravity. The Planck length scale is correspondingly shorter than the distances probed by the LHC.
The fact is that fundamentally, gravity is by far the weakest known force. Gravity might not seem feeble, but that’s because the entire mass of the Earth is pulling on you. If you were instead to consider the gravitational force between two electrons, you would find the force of electromagnetism is 43 orders of magnitude larger. That is, electromagnetism wins out by 10 million trillion trillion trillion. Gravity acting on elementary particles is completely negligible. The hierarchy problem in this way of thinking is: Why is gravity so much more feeble than the other elementary forces we know?
[ FIGURE 55 ] Quantum contribution to the Higgs boson mass from a heavy particle—for example with GUT-scale masses—and its antiparticle (left) and from a virtual top quark and its antiparticle (right).
Particle physicists don’t like unexplained large numbers, such as the size of the Planck mass relative to the weak mass. But the problem is even worse than an aesthetic objection to mysterious large numbers. According to quantum field theory, which incorporates quantum mechanics and special relativity, there should be barely any discrepancy at all. The urgency of the hierarchy problem, at least for theorists, is best understood in these terms. Quantum field theory indicates that the weak mass and the Planck mass constant should be about the same.
In quantum field theory, the Planck mass is significant not only because it is the scale at which gravity is strong. It