Wednesday, May 30, 2012


Last time, I described our reasons and attempts to go beyond the standard model. Among the myriads of possibilities of extensions of the standard model there is one, on which I work. Let me describe it first. Then, I will tell you, why I find especially this one interesting.

This extension of the standard model is called technicolor. It is one of the bottom-up approaches. It was mainly conceived to cure problems we have with the Higgs particle. One particular annoying problem with the Higgs is that its mass is not constrained in the standard model. Well, this is not yet really a problem, since neither are the masses of any of the other particles. But the Higgs mass is in so far different as it is very sensitive to the rest of the standard model. If we change the properties of the standard model by a factor of, say, a hundred, the electron mass will only change by a factor of two, or so. But the Higgs mass will change by a factor ten thousand. Both statements are, of course, very rough, but you should get the idea: To get the Higgs mass to the value we will, hopefully soon, measure, we have to be very careful with the standard model. We have to tune it very finely. This is called the fine-tuning problem, or also the hierarchy problem. It is actually a perceived problem only. Nature may be "just so". But so far, whenever nature seemed to be "just so", there was actually a deeper reason behind it.

Thus, people have set out to find an explanation for this extreme sensitivity of the Higgs mass. Well, actually, people rather have searched for an alternative to the standard model, where this is not the case.

One of the possibilities, which has been conceived, was technicolor. The rather poetic name comes from the historical fact that QCD with its colors has been a role model for technicolor. However, in the decades after its original inception in the 1970ies, technicolor has changed a lot. Today, this theory has only remote similarities to QCD, but, of course, the name stuck once more.

So how does technicolor works? Actually, technicolor is not really a single theory. Since we do not yet have any experimental information about the Higgs, we are not yet able to restrict such extensions of the standard model very well. Thus, there are many theories, which could be called technicolor. It is more an idea than a strict mathematical concept, and it can come in many disguises. The basic idea is that the Higgs is not an elementary particle. Rather, it is made out of other particles, which are called techniquarks. These are held together by exchanging technigluons - once more you see how QCD has been inspirational to the naming.

You may ask what one wins by making the Higgs a more complicated object. The answer is that the Higgs mass, once made out of other (fermionic) particles, is no longer so sensitive, but behaves like the other masses in the standard model. Thus, this solves the problem one has set out to solve.

Of course, as long as we do not yet have found the Higgs, we cannot yet tell whether it is really made up out of other particles. And even when we find it, it will be very complicated to determine whether it is, and it will take a lot of time and a lot of experiments.

But it turns out that things do not come so freely. As you may remember, we needed the Higgs also to provide mass to the other particles in the standard model. And this becomes much more complicated once the Higgs is made out of techniquarks. The reason is that the standard model Higgs is rather flexible, and we can adjust its interactions with the other particles so that the right mass of, say, the electron comes out. This is no longer easily possible once the Higgs has a substructure. This has led in the 1980ies to the believe that technicolor cannot work.

In 1990ies, and now after 2000, however, clever people found a way to make it work. The original problem came about because in the beginning technicolor was made too much alike to QCD. Once one is satisfied with a theory being more different from QCD, and being willing to add a few more particles, the situation improves. Unfortunately, without guidance by experimental results it becomes somewhat ambiguous how to solve the problem, but it seems feasible after all.

So far, this is the status of technicolor. Why am I interested in it?

If you want to make the Higgs from two techniquarks and at the same time simulate the Higgs effect, it is necessary to introduce a new mechanism to the theory. When you look at QCD, its strength depends on the energy. Actually, it does so in a very violent way, and QCD changes from strongly interacting to weakly interacting very quickly. To make the technicolor idea work, this had to change. Technicolor needs to change from strongly interacting to weakly interacting very slowly. To make this distinction more vivid, QCD is called a running theory while technicolor is called a walking theory. This means that technicolor is strongly interacting for a large range of energies. As with any strongly interacting theory, its description is very complicated. Since we know such theories only since a couple of years, we are really at the beginning of understanding them, even the very basic mechanisms of them. But this is what we need to do, if we ever want to make a real quantitative comparison to experiment. And that interests me. I want to understand how such theories work at a very fundamental level. They are so strange compared to the rest of the standard model, and to many other proposal beyond the standard model, that they are a very fascinating topic. And that is, why I am studying them.

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