Pairing and polarization in systems with retarded interactions

In a system where a boson (e.g, a phonon) of finite frequency ω 0 is coupled to electrons, two phenomena occur as the coupling is increased: electron pairing and polarization of the boson field. Within a path integral formalism and a Dynamical Mean-Field approach, we introduce ad hoc distribution function which allow us to pinpoint the two effects. When ω 0 is smaller than the bandwidth D , pairing and polarization occur for fairly similar couplings for all considered temperatures. When ω 0 > D , the two phenomena tend to coincide only for T ≫ ω 0 , but are no longer tied for low temperatures so that a state of paired particles without finite polarization is stabilized.