Leading Singularities in Higher-Derivative Yang–Mills Theory and Quadratic Gravity

Abstract

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.