I have written some time ago that most of the particles we know decay, i.e. after some time they fall apart into other particles. Probably that is not to surprising. After all, essentially everything we know tends to fall apart after a while. Hence, we can think of these particles being made out of the particles into which they decay. Such particles made up out of other particles are called bound states or composite particles. The particles into which it decays are called decay products, but here I will just use particles. Actually, even the particles into which the composite particle decays may in turn decay further. But for the things I want to write about in this entry, this will not matter. Thus, I will just talk about a composite particle and the particles it decays into.
But there is an important difference between usual things falling apart and particles falling apart.
Think about a tower made from wood logs, like a child's toy. You build it from the logs, and after some time it will break down again into the logs. Especially, when a child is around to kick it. But the logs themselves remain intact. So far, this is the same with composite particles. You start with a composite particle, it then decays into other particles. You can rebuild your tower from the logs. This is also possible with the particles. The decay products can be refused into the original composite particle.
But now there is a difference. When you build the tower, the logs keep there identity. If you look close enough at the tower, you can still see the individual logs you used to build the tower. That is not so simple with particles. This is best seen by a specific example. Start with two particles, and fuse them to a new composite particle. So far, nothing new. But then it may happen that this composite particle decays into entirely different other particles then the original ones, or it may decay into the original ones. The expression we use is that the composite particle has different decay channels. It is not that all the possible particles are stored in the original particle, it really changes its identity. It would be like the wood logs turn into plastic ones while being in the tower.
Describing such a spontaneous change is not simple. We have become quite expert in modeling the starting composite particle, and then perform at some point an explicit change into the different particles. But that is a little bit like taking the tower and, very nifty, exchanging each log while it is inside the tower from wood to plastic. What we would like to be able is to have this as a dynamical process. Without our interference, the structure of the composite particle changes, and thus decays differently as it has been formed.
We actually know how to simulate this. But there we can just observe that this happens. We also would like to know how this proceeds inside the structure of the composite particle itself, what governs this process in detail.
Learning this is another project which I now supervise as a PhD project. We will use the so-called equations of motion to dissect the process. For this, we will be looking at a very simple particle, the so-called (charged) pion. It is a composition of two quarks, but can also decay into an electron and a neutrino. Choosing this particular composite particle has a number of reasons. One is that it is very well studied both experimentally and theoretically. We can therefore concentrate on the new aspects, the change of identity of the constituents. The decay is also rather slow, ad therefore technically easier to control. And finally, quarks, electrons and neutrinos are very different particles. As theoreticians, we can use this fact by modifying their properties, and therefore switch on and off various features of the process. And finally, though the pion is made up (sometimes) of quarks, it can actually not really decay into them, due to confinement. Therefore, we need only to consider the change inside the pion, but not outside. This also reduces the technical challenges.
Solving this question, we will continue on to more interesting composite particles, like bound states of the Higgs. But this project is an enormously important first step on this road.