Tuesday, February 10, 2015

Take your theory seriously

I have published a new paper. This paper has a somewhat simple message, even if it is technical. This message is just: Take your theory seriously. This may seem obvious, but it is not necessarily so. The reason is that if a theory works spectacularly well, if you do not take it serious, why should you care? And if I mean spectacular, I mean an agreement with experimenter where any deviations are smaller than any background noise we could not yet eliminate. The theory which works so well is, of course, the standard model.

The paper is a follow-up of the proceeding I have discussed last year. The upshot of this proceeding is that we use perturbation theory to describe the physics we measure, e.g., at the LHC at CERN. However, perturbation theory is not taking the theory too seriously, but it works so very well. The reason for this can be understood: It is an almost miraculous coincidence that taking the theory seriously gives almost the same results. We have checked this in very great detail.

But understanding what is going on in the standard model is one thing. One of the big aims in modern particle physics is to understand what else there could be.

Now, comfortable with the success within the standard model, we have for a very long time assumed that taking the candidate theories for new physics also not seriously should work out. Of course, there have been some exceptions, where we knew it should not work. But by and large, the success with the standard model made us comfortable with using the same techniques.

In the proceeding, I already raised some doubt whether this would be justified when there should be a second Higgs. Under certain conditions, this may not be correct. In the full paper I now extend these doubts also to other theories, and even conclude it may be necessary to rethink even the cases where we thought we were careful.

What is the reason behind this departure? Why should it not work? Well, I do not state that it will not work, just that it might not work. In the standard model, we were in the comfortable situation that experiments told us that it does work. Now, in the absence of experimental results, we are left to theory to tell us where to look. So we do not know whether taking the theory not seriously works out, and may be misguided if it does not.

But why should it fail this time, when it works so well for the standard model? A legitimate question. It requires to understand why it does work for the standard model. Looking at it in detail shows that it requires two conditions to work. One is that the relative masses of the particles lie within a certain range. That is satisfied by the standard model. The second is that the relative number of particles is just right. Both conditions are or may not be met by the theories we have for new physics. In the paper, I give particular examples for several theories, and formulate requirements which have to be met for things to work out.

So is the paper now killing of models? No. At least not yet. I only formulate conditions and requirements. Whether a particular theory meets these is a question to the theory. I give some examples where the situation is very much on the borderline to have a starting point where to check. But what actually happens requires a calculation. A calculation in which we do take the theory very seriously. This will be very complicated, and in the end we may just figure out that it was unnecessary. But then we can be sure to be right, and the theory gives us the leeway to not take it too seriously. And being sure is a basic requirement when one ones to explain the unknown.