The size of the W

As discussed in an earlier entry we set out to measure the size of a particle: The W boson. We have now finished this, and published a paper about our results. I would like to discuss these results a bit in detail.

This project was motivated because we think that the W (and its sibling, the Z boson) are actually more complicated than usually assured. We think that they may have a self-similar structure. The bits and pieces of this is quite technical. But the outline is the following: What we see and measure as a W at, say, the LHC or earlier, is actually not a point-like particle. Although this is the currently most common view. But science has always been about changing the common ideas and replacing them with something new and better. So, our idea is that the W has a substructure. This substructure is a bit weird, because it is not made from additional elementary particles. It rather looks like a bubbling mess of quantum effects. Thus, we do not expect that we can isolate anything which resembles a physical particle within the W. And if we try to isolate something, we should not expect it to behave as a particle.

Thus, this scenario gives two predictions. One: Substructure needs to have space somewhere. Thus, the W should have a size. Two: Anything isolated from it should not behave like a particle. To test both ideas in the same way, we decided to look at the same quantity: The radius. Hence, we simulated a part of the standard model. Then we measured the size of the W in this simulation. Also, we tried to isolate the most particle-like object from the substructure, and also measured its size. Both of these measurements are very expensive in terms of computing time. Thus, our results are rather exploratory. Hence, we cannot yet regard what we found as final. But at least it gives us some idea of what is going on.

The first thing is the size of the W. Indeed, we find that it has a size, and one which is not too small either. The number itself, however, is far less accurate. The reason for this is twofold. On the one hand, we have only a part of the standard model in our simulations. On the other hand, we see artifacts. They come from the fact that our simulations can only describe some finite part of the world. The larger this part is, the more expensive the calculation. With what we had available, the part seems to be still so small that the W is big enough to 'bounce of the walls' fairly often. Thus, our results still show a dependence on the size of this part of the world. Though we try to accommodate for this, this still leaves a sizable uncertainty for the final result. Nonetheless, the qualitative feature that it has a significant size remains.

The other thing are the would-be constituents. We indeed can identify some kind of lumps of quantum fluctuations inside. But indeed, they do not behave like a particle, not even remotely. Especially, when trying to measure their size, we find that the square of their radius is negative! Even though the final value is still uncertain, this is nothing a real particle should have. Because when trying to take the square root of such a negative quantity to get the actual number yields an imaginary number. That is an abstract quantity, which, while not identifiable with anything in every day, has a well-defined mathematical meaning. In the present case, this means this lump is nonphysical, as if you would try to upend a hole. Thus, this mess is really not a particle at all, in any conventional sense of the word. Still, what we could get from this is that such lumps - even though they are not really lumps, 'live' only in areas of our W much smaller than the W size. So, at least they are contained. And let the W be the well-behaved particle it is.

So, the bottom line is, our simulations agreed with our ideas. That is good. But it is not enough. After all, who can tell if what we simulate is actually the thing happening in nature? So, we will need an experimental test of this result. This is surprisingly complicated. After all, you cannot really get a measure stick to get the size of a particle. Rather, what you do is, you throw other particles at them, and then see how much they are deflected. At least in principle.

Can this be done for the W? Yes, it can be done, but is very indirect. Essentially, it could work as follows: Take the LHC, at which two protons are smashed in each other. In this smashing, it is possible that a Z boson is produced, which smashes of a W. So, you 'just' need to look at the W before and after. In practice, this is more complicated. Since we cannot send the W in there to hit the Z, we use that mathematically this process is related to another one. If we get one, we get the other for free. This process is that the produced Z, together with a lot of kinetic energy, decays into two W particles. These are then detected, and their directions measured.

As nice as this sounds, this is still horrendously complicated. The problem is that the Ws themselves decay into some leptons and neutrinos before they reach the actual detector. And because neutrinos escape essentially always undetected, one can only indirectly infer what has been going on. Especially the directions of the Ws cannot easily be reconstructed. Still, in principle it should be possible, and we discuss this in our paper. So we can actually measure this size in principle. It will be now up to the experimental experts if it can - and will - be done in practice.