[frutiger]

The scattering matrix predicts the distribution of output particle momenta given input particle moments and output particles.

The scattering matrix is calculated by including all the possible interactions you expect. So a matrix including some intermediate C will be different from one that does not.

Then you can line up what you actually observe and select the matrix that most accurately describes it.

[im3w1l]

So if I understand it correctly, it's a statistical phenomenon. Looking at one particular (heh) collision, you cannot be sure. But if you run it a lot of times, the frequency of the occurence will be the tell-tale signal. And what the existence of the particle does is provide an additional path. It allows the pair to be formed in two different ways, which raises the overall probability. That right?

[frutiger]

Yes it’s statistical. In fact all physical measurements are statistical. When you measure the length of a table, there is some error term due to imperfections in your measuring stick as well as possible errors when you aligned/looked at the stick and table.

The extra path does not necessarily raise the probability. The interactions are more complex than that. The simplest thing to say is that it affects the distribution.