[frob]

Truly, you never really know which pair of particles came from a specific decay, and which come from some other processes and just happen to line up with the mass/energy you're looking at. Fortunately, for most particles, the combinatorial background signal follows a smooth curve around the energies you're looking at, so you can fit a curve to that background signal and then attribute the rest of the signal to the particle production. For an example, see the main plot on the Upsilon page in Wikipedia (https://en.wikipedia.org/wiki/Upsilon_meson). You can see there is a linear decline (in log space) of the background signal but then there's another peak around 9.5 GeV which is the additional signal from the Upsilon decay.

The point is, we cannot tell which pair of electrons/muons come from the decay of a specific particle, but we can tell how many extra occurred beyond what we would expect from all other known processes.

[NovaS1X]

Thanks so much for the explanation and the example. I at least know a little more about these complicated endeavours now.

[frob]

Happy to do it! Thanks for asking insightful questions. :)