Analytic properties of thermal corrected boson propagators

We investigate the analytic properties of finite-temperature self-energies of bosons interacting with fermions at one-loop order. A simple boson-fermion model was chosen due to its interesting features of having two distinct couplings of bosons with fermions. This leads to a quite different analytic behavior of the bosons self-energies as the external momentum K-mu=(k(0),k) approaches zero in the two possible limits. It is shown that the plasmon and Debye masses are consistently obtained at the pole of the corrected propagator even when the self-energy is analytic at the origin in the frequency-momentum space.