Resonances Formed by Massless Bosons Coupled to a Harmonic Oscillator

For a harmonic oscillator coupled to a massless boson field, with a coupling function fulfilling certain conditions, we prove the existence of resonances, or possibly stable states, which are not in one-to-one correspondence with the energies of the isolated oscillator. The result suggests the existence of such states in other systems coupled to massless bosons. It indicates that complex scaling is a way to look for these states.