A Higgs and a Higgs make what?

Recently, I have mostly written about increasingly technical details of my work. Though these are absolutely necessary foundations for what I do, they are of limited use when taken out of context. I will try to be a bit more up-to-date and less technical, and will try to write more about what motivates me at a current time. What am I really working on?

So let me start with what I am doing right now, just before I started writing this entry. You will probably all have heard about the Higgs discovery. Or, more appropriately, of a particle of which we strongly suspect, but do not yet know, that it is the Higgs. But let me assume for now that it is. As exciting and important as this discovery is in itself, there is much more to this. One of the fascinating things about modern theories is that they do not only describe one or two phenomena, but have an enormous richness.

Concerning the standard model, and in particular the Higgs sector, there are quite some subtle phenomena going on. Why subtle? Well, the Higgs is actually quite a seclusive type. It does not play very much with the rest of the standard model, perhaps except for the top quark. In our language, we say that it is weakly coupled. The Higgs is not the only such particle in the standard model. Everything which has to do with electromagnetism is also not very strongly coupled.

Nonetheless, electrically charged particles play along very well. They like to group together in what we call atoms. These are so-called bound states of electrically charged particles, like the proton and the electron.

Now, for the Higgs actually something similar applies. It has been already suspected in the early 1980ies that Higgs particles could form bound states. In fact, there are very strong theoretical arguments for it, as soon as you include enough of the standard model. The crucial question was (and still is), how long do such Higgs atoms live? Of course, normal atoms live essentially forever, if no physicist comes by and smashes them or some chemist tries to let them react with each other. This is, because the things making up a normal atom are stable themselves. Electrons and protons are, to the best of our knowledge, very, very stable. Even the neutrons, once packed into a nucleus, remain stable. Well, at least if do not select too exotic a nucleus.

Anyway, this is different in the Higgs case. Here the constituents of these 'atoms', just two Higgses, really, are unstable themselves. Thus, it is at all not clear whether you can ever observe such a thing. But since rather deep theoretical arguments say that this could be, I want to know what the answer is. Even more, I am not satisfied with whether they could exist in principle, but if we can see them in an experiment, say the LHC.

To get an answer to this question, I have to invest everything I know. I first have to gather the basic foundation of the theory describing the Higgs. Then, I use simulations to determine the properties of such Higgs atoms. To be able to do this, I have to simplify quite a lot, because otherwise the simulations would be unbearable slow. Once I have these properties, I put them into a model. This step is necessary, because the simulations are not very efficient to give experimental predictions. Thus, I have to take a detour to get an answer. Such a model can be obtained using the appropriate equations to link both worlds.

Then, finally, I have a description of these atoms, and how they interact. With this, I have finally reached the point to use different types of simulations to make an experimental prediction.

That may sound like an afternoons work. But, unfortunately, it is not. Determining the properties of the atoms, even very roughly, has already required something like eighteen months. Constructing the model took another month in its simplest version. And right now, I just get acquainted with the basic simulations for an experiment. I just finished 'rediscovering' the well-known Z, as a first exercise. I hope that I will be able to present a first result at a small workshop in January, almost two years after I started thinking about this question. This result will be extremely simplified, and will be at best a motivation to go on. I have estimated that to get a real quantitative result, which is correct within about 20-30 percent, will require probably another ten-twenty man-years, and likely a couple of thousand core-years of computing time. But well, if we can find them, that would be really something. But even if not, then we have learned a lot about the theory we are working with. And that would be something in itself. So stay tuned, what will happen next.