  We study a toy model for an interacting scalar field theory in which the
fundamental excitations are confined in the sense of having unphysical,
positivity-violating propagators, a fact tracing back to a decomposition of
these in propagators with complex conjugate mass poles (the so-called
$i$-particles). Similar two-point functions show up in certain approaches to
gluon or quark propagators in Yang-Mills gauge theories. We investigate the
spectrum of our model and show that suitable composite operators may be
constructed having a well-defined K\"all\'{e}n-Lehmann spectral representation,
thus allowing for a particle interpretation. These physical excitations would
correspond to the "mesons" of the model, the latter being bound states of two
unphysical $i$-particles. The meson mass is explicitly estimated from the pole
emerging in a resummed class of diagrams. The main purpose of this paper is
thus to explicitly verify how a real mass pole can and does emerge out of
constituent $i$-particles that have complex masses.
