A partner for every particle?

A master student has started with me a thesis on a new topic, one on which I have not been working before. Therefore, before going into details about the thesis' topic itself, I would like to introduce the basic physics underlying it.

The topic is the rather famous concept of supersymmetry. What this means I will explain in a minute. Supersymmetry is related to two general topics we are working on. One is the quest for what comes after the standard model. It is with this respect that it has become famous. There are many quite excellent introductions to why it is relevant, and why it could be within the LHC's reach to discover it. I will not just point to any of these, but write nonetheless here a new text on it. Why? Because of the relation to the second research area involved in the master thesis, the ground work about theory. This gives our investigation a quite different perspective on the topic, and requires a different kind of introduction.

So what is supersymmetry all about? I have written about the fact that there are two very different types of particles we know of: Bosons and fermions. Both types have very distinct features. Any particle we know belong to either of these two types. E.g. the famous Higgs is a boson, while the electron is a fermion.

One question to pose is, whether these two categories are really distinct, or if there are just two sides of a single coin. Supersymmetry is what you get if you try to realize the latter option. Supersymmetry - or SUSY for short - introduces a relation between bosons and fermions. A consequence of SUSY is that for every boson there is a fermion partner, and for every fermion there is a boson partner.

A quick counting in the standard model shows that it cannot be supersymmetric. Moreover, SUSY also dictates that all other properties of a boson and a fermion partner must be the same. This includes the mass and the electric charge. Hence, if SUSY would be real, there should be a boson which acts otherwise like an electron. Experiments tell us that this is not the case. So is SUSY doomed? Well, not necessarily. There is a weaker version of SUSY where it only approximately true - a so-called broken symmetry. This allows to make the partners differently massive, and then they can escape detection. For now.

SUSY, even in its approximate form, has many neat features. It is therefore a possibility desired by many to be true. But only experiment (and nature) will tell eventually.

But the reason why we are interested in SUSY is quite different.

As you see, SUSY puts tight constraints on what kind of particles are in a theory. But it does even more. It also restricts the way how these particles can interact. The constraints on the interactions are a little bit more flexible than on the kind of particles. You can realize different amounts of SUSY by relaxing or enforcing relations between the interactions. What does 'more or less' SUSY mean? The details are somewhat subtle, but a hand-waving statement is that more SUSY not only relates bosons and fermions, but in addition also partner particles of different particles more and more. There is an ultimate limit to the amount of SUSY you can have, essentially when everything and everyone is related and every interaction is essentially of the same strength. That is what is called a maximal SUSY theory. A fancy name is N=4 SUSY for technical reason, if you should come across it somewhere on the web.

And it is this theory which is interesting to us. Having such very tight constraints enforces a very predetermined behavior. Many things are fixed. Thus, calculations are more simple. At the same time, many of there more subtle questions we are working on are nonetheless still there. Using the additional constraints, we hope to understand this stuff better. With these insights, we may have a better chance to understand the same stuff in a less rigid theory, like the standard model.