# Where, in the standard model, do resonance widths come from?

For example, the Z boson decays and hence the propagator is: $$\frac{1}{p^2-m^2-i \Gamma}$$ Where does this arise in QFT, is it that the lagrangian mass is complex or is it that when we compute the self-energy and get the renormalised mass we find that the propagator takes this form.

The bubbles in the expansion of the$$Z$$ propagator become imaginary when the internal particles can go on-shell. The imaginary part is just the inverse lifetime of the $$Z$$.