Sum rule calculations in a toy model

We consider a two-point correlator in a massless Φ3 model within the ladder approximation. The spectral density of the correlator is known explicitly and does not contain any resonances. Meanwhile making use of the standard sum rule technique with a simple “resonance + continuum” model of the spectrum allows one to predict the parameters of the “resonance” very accurately in the sense that all necessary criteria of stability are perfectly satisfied.