What makes the Higgs boson such a rich target for a future collider? -------------------------------------------------------------------- It is the first example we’ve seen of the simplest possible type of elementary particle. It has no spin, no charge, only mass, and this extreme simplicity makes it theoretically perplexing. There is a striking difference between massive and massless particles that have spin. For instance, a photon is a massless particle of spin one; because it moves at the speed of light, we can’t “catch up” with it, and so we only see it have two “polarisations”, or ways it can spin. By contrast the Z boson, which also has spin one, is massive; since you can catch up with it, you can see it spinning in any of three directions. This “two not equal to three” business is quite profound. As we collide particles at ever increasing energies, we might think that their masses are irrelevant tiny perturbations to their energies, but this is wrong, since something must account for the extra degrees of freedom. The whole story of the Higgs is about accounting for this “two not equal to three” issue, to explain the extra spin states needed for massive W and Z particles mediating the weak interactions. And this also gives us a good understanding of why the masses of the elementary particles should be pegged to that of the Higgs. But the huge irony is that we don’t have any good understanding for what can explain the mass of the Higgs itself. That’s because there is no difference in the number of degrees of freedom between massive and massless spin-zero particles, and related to this, simple estimates for the Higgs mass from its interactions with virtual particles in the vacuum are wildly wrong. There are also good theoretical arguments, amply confirmed in analogous condensed-matter systems and elsewhere in particle physics, for why we shouldn’t have expected to see such a beast lonely, unaccompanied by other particles. And yet here we are. Nature clearly has other ideas for what the Higgs is about than theorists do. Is supersymmetry still a motivation for a new collider? ------------------------------------------------------- Nobody who is making the case for future colliders is invoking, as a driving motivation, supersymmetry, extra dimensions or any of the other ideas that have been developed over the past 40 years for physics beyond the Standard Model. Certainly many of the versions of these ideas, which were popular in the 1980's and 1990's, are either dead or on life support given the LHC data, but others proposed in the early 2000's are alive and well. The fact that the LHC has ruled out some of the most popular pictures is a fantastic gift to us as theorists. It shows that understanding the origin of the Higgs mass must involve an even larger paradigm change than many had previously imagined. Ironically, had the LHC discovered supersymmetric particles, the case for the next circular collider would be somewhat weaker than it is now, because that would (indirectly) support a picture of a desert between the electroweak and Planck scales. In this picture of the world, most people wanted a linear electron–positron collider to measure the superpartner couplings in detail. It’s a picture people very much loved in the 1990's, and a picture that appears to be wrong. Fine. But when theorists are more confused, it’s the time for more, not less experiments. What definitive answers will a future high-energy collider give us? ------------------------------------------------------------------- First and foremost, we go to high energies because it’s the frontier, and we look around for new things. While there is absolutely no guarantee we will produce new particles, we will definitely stress test our existing laws in the most extreme environments we have ever probed. Measuring the properties of the Higgs, however, is guaranteed to answer some burning questions. All the drama revolving around the existence of the Higgs would go away if we saw that it had substructure of any sort. But from the LHC, we have only a fuzzy picture of how point-like the Higgs is. A Higgs factory will decisively answer this question via precision measurements of the coupling of the Higgs to a slew of other particles in a very clean experimental environment. After that the ultimate question is whether or not the Higgs looks point-like even when interacting with itself. The simplest possible interaction between elementary particles is when three particles meet at a space–time point. But we have actually never seen any single elementary particle enjoy this simplest possible interaction. For good reasons going back to the basics of relativity and quantum mechanics, there is always some quantum number that must change in this interaction – either spin or charge quantum numbers change. The Higgs is the only known elementary particle allowed to have this most basic process as its dominant self-interaction. A 100 TeV collider producing billions of Higgs particles will not only detect the self-interaction, but will be able to measure it to an accuracy of a few %. Just thinking about the first-ever probe of this simplest possible interaction in nature gives me goosebumps. What are the prospects for future dark-matter searches? ------------------------------------------------------- Beyond the measurements of the Higgs properties, there are all sorts of exciting signals of new particles that can be looked for at both Higgs factories and 100 TeV colliders. One I find especially important is WIMP dark matter. There is a funny perception, somewhat paralleling the absence of supersymmetry at the LHC, that the simple paradigm of WIMP dark matter has been ruled out by direct-detection experiments. Nope! In fact, the very simplest models of WIMP dark matter are perfectly alive and well. Once the electroweak quantum numbers of the dark-matter particles are specified, you can unambiguously compute what mass an electroweak charged dark-matter particle should have so that its thermal relic abundance is correct. You get a number between 1–3 TeV, far too heavy to be produced in any sizeable numbers at the LHC. Furthermore, they happen to have miniscule interaction cross sections for direct detection. So these very simplest theories of WIMP dark matter are inaccessible to the LHC and direct-detection experiments. But a 100 TeV collider has just enough juice to either see these particles, or rule out this simplest WIMP picture.