Tree-level unitarity, causality and higher-order Lorentz and CPT violation

TL;DR

This paper investigates the effects of higher-order CPT and Lorentz violation in the SME framework, demonstrating that microcausality is maintained and tree-level unitarity can be achieved using the Lee-Wick prescription.

Contribution

It provides a detailed analysis of unitarity and causality in Lorentz and CPT violating models, especially addressing ghost states and the application of the Lee-Wick prescription.

Findings

Microcausality is preserved through residue cancellations.

Tree-level unitarity is established using the Lee-Wick prescription.

Ghost states can be managed to maintain physical consistency.

Abstract

Higher-order effects of CPT and Lorentz violation within the SME effective framework including Myers-Pospelov dimension-five operator terms are studied. The model is canonically quantized by giving special attention to the arising of indefinite-metric states or ghosts in an indefinite Fock space. As is well-known, without a perturbative treatment that avoids the propagation of ghost modes or any other approximation, one has to face the question of whether unitarity and microcausality are preserved. In this work, we study both possible issues. We found that microcausality is preserved due to the cancellation of residues occurring in pairs or conjugate pairs when they become complex. Also, by using the Lee-Wick prescription, we prove that the $S$ matrix can be defined as perturbatively unitary for tree-level $2\to 2$ processes with an internal fermion line.