  We explicitly show that general local higher-derivative theories with only
complex conjugate ghosts and normal real particles are unitary at any
perturbative order in the loop expansion. The proof presented here relies on
integrating the loop energies on complex paths resulting from the deformation
of the purely imaginary paths, when the external energies are continued from
imaginary to real values. Contrary to the case of nonlocal theories, where the
same integration path was first proposed, for the classes of theories studied
here the same procedure is not analytic, but the resulting theory is unitary
and unique when the complex ghosts are present in pairs. As an explicit
application, a special class of higher-derivative super-renormalizable or
finite gravitational and gauge theories turns out to be unitary at any
perturbative order if we exclude the complex ghosts from the spectrum of the
theory, as it is normally accepted for Becchi-Rouet-Stora-Tyutin (BRST) ghosts.
Finally, we propose an analogy between confined gluons in quantum Yang-Mills
theory and classical complex pairs in local higher-derivative theories.
According to such interpretation, complex ghosts will not appear on shell as
asymptotic states because confined in what is natural to name "ghostballs."

High Energy Physics - Theory