Positive commutators, Fermi golden rule and the spectrum of zero temperature Pauli-Fierz Hamiltonians

We perform the spectral analysis of a zero temperature Pauli-Fierz system for small coupling constants. Under the hypothesis of Fermi golden rule, we show that the embedded eigenvalues of the uncoupled system disappear and establish a limiting absorption principle above this level of energy. We rely on a positive commutator approach introduced by Skibsted and pursued by Georgescu-Gérard-Møller. We complete some results obtained so far by Dereziński-Jakši? on one side and by Bach-Fröhlich-Sigal-Soffer on the other side.