My understanding is that 'fundamental' pertains to there being a distinct quantum field corresponding to the particle. I ask the question above based on the fact that the heavier generations of particles decay. What reason do we have to believe that what was originally, say, a localised excitation of the tau field corresponding to a tau particle, was not a collective excitation of the particle fields it subsequently decays into? I would think of answering this question in two ways:
Experimentally, I suspect we try to do scattering experiments. I should think that the theorists would have a prediction of the differential scattering cross section if the 'tau' were to be a collective excitation of several other fields which subsequently disperse. But i'm not so sure about how convincing this kind of evidence is.
Another experimental factor may be acceleration experiments to 'observe' the particles with longer lifetimes in the lab frame, and we wouldn't expect a collective excitation of several fields to have the same behaviour.
Theoretically. I am vaguely familiar with the group structure of the standard model, but not enough about the details to see how this answers the question above and, again, how convincingly.
Essentially, I am just interested in how someone who has much more knowledge in particle physics would answer this question. I have read through this post but I can't see it containing an answer. I know classical and (some) quantum field theory, and am presently taking a course in particle physics. But this hasn't been addressed.