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RE: What does an experimental particle physicist do: Measure particles!
Now I see what you meant by reconstruction from decay products... I will still dig into the fermions and bosons... I only know a little bit about them.
If you want, you can have a look to my last posts where I started to write particle physics lecture notes for steemit. This is a kind of starter (see here for the lecture number 1 which may answer your fermionic/bosonic question).