Publication Date
2019
Journal or Book Title
Physical Review D
Abstract
We present a new understanding of the unstable ghostlike resonance which appears in theories such as quadratic gravity and Lee-Wick type theories. Quantum corrections make this resonance unstable, such that it does not appear in the asymptotic spectrum. We prove that these theories are unitary to all orders. Unitarity is satisfied by the inclusion of only cuts from stable states in the unitarity sum. This removes the need to consider this as a ghost state in the unitarity sum. However, we often use a narrow-width approximation where we do include cuts through unstable states and ignore cuts through the stable decay products. If we do this with the unstable ghost resonance at one loop, we get the correct answer only by using a contour which was originally defined by Lee and Wick. The quantum effects also provide damping in both the Feynman and the retarded propagators, leading to stability under perturbations.
ORCID
https://orcid.org/0000-0001-7282-5894, https://orcid.org/0000-0001-7838-3759
DOI
https://doi.org/10.1103/PhysRevD.100.105006
Volume
100
Issue
10
License
UMass Amherst Open Access Policy
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Recommended Citation
Donoghue, John F. and Menezes, Gabriel, "Unitarity, stability, and loops of unstable ghosts" (2019). Physical Review D. 1256.
https://doi.org/10.1103/PhysRevD.100.105006