# Unitarity, stability and loops of unstable ghosts

**Authors:** John F. Donoghue, Gabriel Menezes  
**arXiv:** [1908.02416](https://arxiv.org/abs/1908.02416)  
**Date:** 2019-08-07  
**Summary page:** https://www.summarizepaper.com/en/paper/1908.02416v2/

## Key points

- Authors John F. Donoghue and Gabriel Menezes present a novel understanding of the unstable ghost-like resonance in theories like quadratic gravity and Lee-Wick type theories.
- Quantum corrections render the resonance unstable, leading to its absence in the asymptotic spectrum.
- The authors maintain unitarity across all orders by incorporating only cuts from stable states in the unitarity sum, eliminating the need to treat the resonance as a ghost state within the sum.
- They discuss the use of a narrow-width approximation and emphasize the importance of utilizing a contour defined by Lee and Wick for accurate results at one loop.
- Quantum effects introduce damping in both Feynman and retarded propagators, ensuring stability under perturbations.
- Donoghue and Menezes provide valuable insights into addressing challenges associated with unstable resonances in quantum field theories, advancing understanding of unitarity and stability within these systems.

## Summary

In their paper titled "Unitarity, stability and loops of unstable ghosts," authors John F. Donoghue and Gabriel Menezes present a novel understanding of the unstable ghost-like resonance that arises in theories such as quadratic gravity and Lee-Wick type theories. They delve into how quantum corrections render this resonance unstable, leading to its absence in the asymptotic spectrum. The authors demonstrate that these theories maintain unitarity across all orders by incorporating only cuts from stable states in the unitarity sum. This approach eliminates the necessity to treat the resonance as a ghost state within the unitarity sum. Additionally, they discuss the common practice of employing a narrow-width approximation and highlight how obtaining accurate results requires utilizing a contour originally defined by Lee and Wick for the unstable ghost resonance at one loop. Furthermore, Donoghue and Menezes explore how quantum effects introduce damping in both Feynman and retarded propagators, ensuring stability under perturbations. Through their comprehensive analysis, they shed light on intricate aspects of these theoretical frameworks and provide valuable insights into addressing challenges associated with unstable resonances in quantum field theories. Their findings contribute significantly to advancing our understanding of unitarity and stability within these complex systems.