Leading singularities in higher-derivative Yang-Mills theory and quadratic gravity

TL;DR

This paper investigates the leading singularities of one-loop amplitudes in higher-derivative Yang-Mills and quadratic gravity, demonstrating their well-defined nature despite the presence of ghost-like resonances, and clarifying their analytic structure.

Contribution

It provides explicit examples showing that leading singularities remain well-defined in higher-derivative theories with unstable resonances, extending the understanding of amplitude analytic structure.

Findings

Leading singularities are well-defined despite ghost-like resonances.

Unitarity cuts exclude unstable particles, preserving unitarity.

Explicit examples clarify the analytic structure of one-loop amplitudes.

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.