  The Lee-Wick models are higher-derivative theories that are claimed to be
unitary thanks to a peculiar cancelation mechanism. In this paper, we provide a
new formulation of the models, to clarify several aspects that have remained
quite mysterious, so far. Specifically, we define them as nonanalytically Wick
rotated Euclidean theories. The complex energy plane is divided into
disconnected regions, which can be related to one another by a well-defined,
albeit nonanalytic procedure. Working in a generic Lorentz frame, the models
are intrinsically equipped with the right recipe to treat the pinchings of the
Lee-Wick poles, with no need of external ad hoc prescriptions. We describe
these features in detail by calculating the one-loop bubble diagram and
explaining how the key properties generalize to more complicated diagrams. The
physical results of our formulation are different from those of the previous
ones. The unusual behaviors of the physical amplitudes lead to interesting
phenomenological predictions.
