I am a bit confused about resonances in QFT. I am reading Schwarz's QFT book and as far as I understand, if in a reaction the mass of the particle acting as a propagator is bigger than the sum of the masses of the particles interacting, the propagator particle can be on shell, thus the propagator has an imaginary part and doing some math you get the Breit-Winger distribution (this is chapter 24.1.4). However, the particles that were discovered as resonances are not propagators, as far as I understand. For example, in muon-muon scattering to obtain the J/psi particle, the 2 muons interact by exchanging a photon, not a J/psi particle. So the propagator is that corresponding to a photon. Can someone explain to me how does this work? How do resonances from and how does this on-shell propagator comes into play? Thank you!
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