  In this work we explore general leading singularities of one-loop amplitudes
in higher-derivative Yang-Mills and quadratic gravity. These theories are known
to possess propagators which contain quadratic and quartic momentum dependence,
which leads to the presence of an unstable ghostlike resonance. However,
unitarity cuts are not to be taken through unstable particles and therefore
unitarity is still satisfied. On the other hand, this could engender issues
when calculating leading singularities which are generalizations of unitarity
cuts. Nevertheless, we will show with explicit examples how leading
singularities are still well defined and accordingly they are able to capture
relevant information on the analytic structure of amplitudes in such
higher-derivative theories. We discuss some simple one-loop amplitudes which
clarify these features.
