Knocking on Heaven's Door - Lisa Randall [145]
But the result when we apply similar principles to incorporate quantum mechanical contributions to the Higgs mass due to virtual particles is extraordinarily perplexing. The virtual contributions from just about any particle in the theory seem to give a Higgs particle a mass almost as big as the Planck mass. The intermediate particles could be heavy objects, such as particles with enormous GUT-scale masses (see left-hand-side of Figure 55) or the particles could be ordinary Standard Model particles, such as top quarks (see right-hand-side). Either way, the virtual corrections would make the Higgs mass much too large. The problem is that the allowed energies for the virtual particles being exchanged can be as big as the Planck energy. When this is true, the Higgs mass contribution too can be almost this large. In that case, the mass scale at which the symmetry associated with the weak interactions is spontaneously broken would also be the Planck energy, and that is 16 orders of magnitude—ten thousand trillion times—too high.
The hierarchy problem is a critically important issue for the Standard Model with only a Higgs boson. Technically, a loophole does exist. The Higgs mass, in the absence of virtual contributions, could be enormous and have exactly the value that would cancel the virtual contributions to just the level of precision we need. The problem is that—although possible in principle—this would mean 16 decimal places would have to be canceled. That would be quite a coincidence.
No physicist believes this fudge—or fine-tuning as we call it. We all think the hierarchy problem, as this discrepancy between masses is known, is an indication of something bigger and better in the underlying theory. No simple model seems to address the problem completely. The only promising answers we have involve extensions of the Standard Model with some remarkable features. Along with whatever implements the Higgs mechanism, the solution to the hierarchy problem is the chief search target for the LHC—and the subject of the following chapter.
CHAPTER SEVENTEEN
THE WORLD’S NEXT TOP MODEL
In January 2010, colleagues gathered at a conference in Southern California to discuss particle physics and dark matter searches in the LHC era. The organizer, Maria Spiropulu, a CMS experimenter and member of the Caltech physics department, asked me to give the first talk and outline the LHC’s major issues and physics goals for the near future.
Maria wanted a dynamic conference, so she suggested we start with a “duel” among the three opening speakers. As if the term “duel” applied to three people wasn’t confusing enough, the audience of invited guests posed an even greater challenge since it ranged from experts in the field to interested observers from the California technology world. Maria asked me to dig deep and look into subtle and overlooked features of current theories and experiments, while one of the attendees, Danny Hillis—a brilliant nonphysicist from the company Applied Minds—suggested I make everything as basic as possible so the nonexperts could follow.
I did what any rational person would do in the face of such contradictory and impossible-to-satisfy advice: procrastinate. The result of my web surfing was my first slide (see Figure 56), which ended up in Dennis Overbye’s New York Times article on the subject—typo and all.
The topics referred to the subject matter that the subsequent speakers and I were scheduled to cover. But the humor in the sound effects I inserted to accompany the entrance of each of the dueling cats (which I can’t reproduce here) was meant to reflect