Tuesday, September 25, 2012

What means 'radiative correction'?

A term, which comes up very often when one reads about the Higgs, are radiative corrections. The thing hiding behind this name is also very essential in both my own work, and in particle physics in general. So what is it?

Again, the name is historic. There are two parts in it, referring to radiation and to correction. It describes something one comes across when one wants to calculate very precisely something in quantum physics.

When we sit down to calculate something in theoretical quantum physics, we have many methods available. A prominent one is perturbation theory. The basic idea of perturbation theory is to first solve a simpler problem, and then add the real problem in small pieces, until one has the full answer.

Usually, when you starts to calculate something with perturbation theory in quantum physics, you assume that the quantum effects are, in a certain sense, small. A nice starting point is then to neglect quantum physics completely, and do just the ordinary non-quantum, often called classical, part. To represent such a calculation, we have developed a very nice way using pictures. I will talk about this soon. Here, it is only necessary to say that the picture of this level of calculation looks like a (very, very symbolic) tree. Therefore, this simplest approximation is also known as tree-level.

Of course, neglecting quantum effects is not a very good description of nature. Indeed, we would not be able to build the computer on which I write this blog entry, if we would not take quantum effects into account. Or have the Internet, which transports it to you. In perturbation theory we add these quantum contributions now piece by piece, in order of increasing 'quantumness'. This can be mathematically very well formulated what this means, but this is not so important here.

If the quantum contributions are small, these pieces are just small corrections to the tree-level result. So, here comes the first part of the topic, the correction.

When people did this in the early days of quantum mechanics, in the 1920ies, the major challenge was to describe atoms. In atoms, most quantum corrections involve that the electron of an atom radiates a photon or captures a photon radiated from somewhere else. Thus, the quantum corrections where due to radiation, and hence the name radiative corrections, even if quantum corrections would be more precise. But, as always, not the best name sticks, and hence we are stuck with radiative corrections for quantum corrections.

Today, our problems have become quite different from atoms. But still, if we calculate a quantum correction in perturbation theory, we call it a radiative correction. In fact, by now we have adapted the term even when what we calculate is no small correction at all, but may be the most important part. Even if we use other methods than perturbation theory. Then, the name radiative correction is just the difference between the classical result and the quantum result. You see, there is no limit to the abuse of notation by physicists.

Indeed, calculating radiative corrections for different particles is a central part of my research. More or less every day, I either compute such radiative corrections, or develop new techniques to do so. When I finally arrive at an expression for the radiative correction, I can do two things with them. Either I can try to understand from the mathematical structure of the radiative corrections what are the properties of the particles. For example, what is its mass. Or how strongly does it interact with other particles. Or I can combine the radiative corrections for several particles or interactions to determine a new quantity. These can be quite complicated. Recently, one of the things I have done was to use the radiative corrections of gluons to calculate the temperature of the phase transition of QCD. There, I have seen that at a certain temperature the radiative correction to the behavior of gluons change drastically. From this, I could infer that a phase transition happened.

So you see, this term, being used so imprecisely, is actually an everyday thing in my life as a theoretician.