  In scattering experiments, physicists observe so-called resonances as peaks
at certain energy values in the measured scattering cross sections per solid
angle. These peaks are usually associate with certain scattering processes,
e.g., emission, absorption, or excitation of certain particles and systems. On
the other hand, mathematicians define resonances as poles of an analytic
continuation of the resolvent operator through complex dilations. A major
challenge is to relate these scattering and resonance theoretical notions,
e.g., to prove that the poles of the resolvent operator induce the above
mentioned peaks in the scattering matrix. In the case of quantum mechanics,
this problem was addressed in numerous works that culminated in Simon's seminal
paper [33] in which a general solution was presented for a large class of pair
potentials. However, in quantum field theory the analogous problem has been
open for several decades despite the fact that scattering and resonance
theories have been well-developed for many models. In certain regimes these
models describe very fundamental phenomena, such as emission and absorption of
photons by atoms, from which quantum mechanics originated. In this work we
present a first non-perturbative formula that relates the scattering matrix to
the resolvent operator in the massless Spin-Boson model. This result can be
seen as a major progress compared to our previous works [13] and [12] in which
we only managed to derive a perturbative formula.
