# A new formulation of Lee-Wick quantum field theory

## TL;DR

This paper introduces a new formulation of Lee-Wick quantum field theories as nonanalytically Wick rotated Euclidean theories, clarifying their properties and leading to different physical predictions from previous models.

## Contribution

It provides a novel nonanalytic Euclidean formulation of Lee-Wick models, clarifying their mathematical structure and pole treatment without external prescriptions.

## Key findings

- Distinct physical results compared to previous formulations
- Detailed treatment of Lee-Wick pole pinchings in loop diagrams
- Potential for new phenomenological predictions

## Abstract

The Lee-Wick models are higher-derivative theories that are claimed to be unitary thanks to a peculiar cancelation mechanism. In this paper, we provide a new formulation of the models, to clarify several aspects that have remained quite mysterious, so far. Specifically, we define them as nonanalytically Wick rotated Euclidean theories. The complex energy plane is divided into disconnected regions, which can be related to one another by a well-defined, albeit nonanalytic procedure. Working in a generic Lorentz frame, the models are intrinsically equipped with the right recipe to treat the pinchings of the Lee-Wick poles, with no need of external ad hoc prescriptions. We describe these features in detail by calculating the one-loop bubble diagram and explaining how the key properties generalize to more complicated diagrams. The physical results of our formulation are different from those of the previous ones. The unusual behaviors of the physical amplitudes lead to interesting phenomenological predictions.