The Higgs beyond the obvious

It is very likely that you have heard in the media of my next research topic: It is the Higgs particle. Well, actually it is not just the Higgs particle alone. In isolation, without its connection to the weak interactions and all the rest of the standard model, the Higgs is actually a very boring particle. In fact, the Higgs particle in isolation is almost every particle theorists first encounter with particle physics. Because it is so boring and simple. Just that it is then not called the Higgs particle, but usually phi, and the theory is called the phi-to-the-fourth theory. Much less fancy.

I guess from all the attention the Higgs has received you may be assuming that many people are working on it. That is true. So, what is particular about my research? What is the specific twist of this thing that I am interested in?

Most people nowadays are interested in either of two aspects of the Higgs: What are its properties? More precisely, what is its mass? And how does it play along with the rest of the bunch? Or: Where does it come from? Is there some theory where the standard model is just a special case of? And if yes, what role does the Higgs plays there?

Me, I am more interested in some more subtle questions. Actually, in three.

The first question concerns the validity of our theoretical description of Higgs physics. As you may remember, the standard model is only valid up to a certain amount of energy. We assume that there will be another theory including it and resolving all (or at least a fair amount of) our questions. Until we figure out this theory, we try to hide our ignorance. For a theory like QCD, this works very well. There we can hide our ignorance just in a few numbers, which we can determine unambiguously in an experiment. After that, we are fine, and we can make predictions. With the Higgs, this is different. And the difference is here in the word 'unambiguous'.

The theory with only Higgs particles I mentioned before is actually a sad story. It turns out that it has the same problems as the standard model, but we cannot hide them unambiguously. And thus our predictions for it are flawed. We can only prevent this by switching off all the interactions. But then the theory is boring, because nothing happens. That is what we call a trivial theory.

The question I am interested in is, what happens when we put the Higgs in the standard model. Does it remain ambiguous? Or do the interaction with the other particles cure this problem in some fancy way? Right now, the judge is still out. If it cannot be cured, the search for the new theory becomes even more important. Because then the standard model would be much more flawed. Deciding what is the case is one of the questions I am looking into.

To even ponder the other two questions, I assume that the combination of the Higgs and the weak interactions do not have such a problem. Or that the resolution of the problem is not altering the answer to the two questions substantially. This may seem a bit like cheating or evading the problem. But we quite often come across problems not immediately solvable. These maybe so hard that we will take a long time to solve them. To get not totally stuck, we do often assume such solutions do exist, and carry on. Of course, we do not forget these questions, but work on them further, to have eventually an answer. This has the risk that some of what we may do then becomes invalid once we solved the problem. In fact, this has happened often. But as often it has also resolved the original problem, or gave us fundamental new insights. That is one thing we have to do in science: Always explore all the possibilities. Since we do not know what lies ahead, this is the only way to eventually find the right answer.

But after this detour, back to the two questions.

One is again rather fundamental. The theory with the Higgs is very peculiar. If you would switch off the Higgs effect, you would end up with a theory like QCD. Especially, the weak interactions would confine the Higgs particles, just like the strong interaction confines quarks. In fact, both phenomena could even be linked in a very abstract fashion. Merely two sides of the same coin. This is something which has been noticed already back in the 1970s. We do not yet understand what this is really about. One of the reasons was that back then confinement was not well understood. We understood much more about confinement since then, especially in the last ten years. Armed with this knowledge, I reinvestigate this connection. And try to clarify what is going on.

The last question concerns bound states. That is right! We have not yet discovered the Higgs alone, but I am already try to understand how two Higgs particles could come together and form something like a Higgs meson. That is a rather new problem I came across recently. There are some fascinating consequences of it. Some people speculate that we can observe such objects at the LHC. I am currently trying to understand, whether we have a realistic chance of seeing them. And if yes, how they are build up.