Warped Passages - Lisa Randall [122]
Because the Higgs particle interacts with heavy particles whose mass is as high as the GUT scale mass, some of the paths that the Higgs particle takes involve the vacuum spitting out a virtual heavy particle and its virtual antiparticle, and the Higgs particle temporarily turning into those particles as it travels along (see Figure 61). The heavy particles that pop in and out of the vacuum influence the motion of the Higgs particle. They are the culprits responsible for large quantum contributions.
Figure 61. Virtual contribution to the Higgs particle’s mass from heavy particles in a GUT theory. The Higgs particle can convert into virtual heavy (GUT-mass) particles, which then turn back into a Higgs particle. This is illustrated schematically on the left, and with a Feynman diagram on the right.
Quantum mechanics tells us that if we are to determine the mass that the Higgs particle actually possesses, we have to add such paths with virtual heavy particles to the single path without them. The problem is that the paths containing virtual heavy particles generate contributions to the Higgs particle’s mass that are about the same size as the masses of the heavy particles in a GUT—thirteen orders of magnitude larger than the desired mass. All these enormous quantum mechanical contributions from virtual heavy particles must be added to the classical value for the Higgs particle’s mass to yield the physical value that would appear in a measurement, which should be about 250 GeV if we want to get the weak gauge boson masses right. That means that, even though any individual GUT mass contribution is thirteen orders of magnitude too large, when we add together all the enormous contributions to the mass, some of which are positive and some of which turn out to be negative, the answer should be approximately 250 GeV. If even a single virtual heavy particle interacts with the Higgs particle, there is inevitably a problem.
If, as in the previous chapter, we think of virtual particles as members of a bureaucracy, it’s as if the employees are U.S. Immigration and Naturalization Service (INS) officers whose job is to delay letters from certain suspect individuals, but they instead scrutinize all the letters that pass through. Instead of a two-tier system in which some letters quickly pass through and others are delayed, all the letters are treated the same way. Similarly, the Higgs mechanism requires that the “bureaucracy” of virtual particles should keep some particles heavy but let others, including the Higgs particle, be light. But instead, like the overzealous officers, quantum paths involving virtual particles give comparable contributions to all particle masses. So we would expect all particles, including the Higgs particle, to be as heavy as the GUT mass scale.
Without new physics, the only (and very unsatisfying) way around the problem of the overly large mass of the Higgs particle is to assume that its classical mass takes precisely the value (which could be negative) that would cancel the large quantum contribution to its mass. The parameters in the theory that determine the masses would have to be such that all contributions add up to a very small number, even though each individual contribution is very large. This is the fine-tuning I mentioned in the previous section.
This is conceivable, but extremely unlikely to happen in reality. It is not simply a question of fudging a parameter a little bit to get the mass correct. This fudge is enormous, and enormously precise: anything less than thirteen digits of precision would give dramatically incorrect results. Just to be clear, this bizarre fudge is not the same sort of thing as precisely measuring some quantity, say the speed of light. Ordinarily, qualitative predictions don’t depend on a parameter taking any particular value. Only one value will match the precise quantity that is measured, but the world wouldn’t be very different had that parameter taken a slightly different value. If Newton’s constant of gravitation