Unitarity and Lee-Wick prescription at one loop level in the effective Myers-Pospelov electrodynamics: the $e^++e^-$ annihilation

TL;DR

This paper examines unitarity in a Lorentz-violating QED model with higher derivatives, demonstrating stability and verifying the optical theorem at one loop using the Lee-Wick prescription to handle indefinite metrics.

Contribution

It extends Lee-Wick unitarity methods to the Myers-Pospelov model, analyzing stability and unitarity at the quantum level with a focus on the fermionic sector and one-loop processes.

Findings

Hamiltonian is stable with indefinite metric decomposition.

Optical theorem verified at one-loop level.

Lee-Wick prescription ensures unitarity in the model.

Abstract

We study perturbative unitarity in a Lorentz-symmetry-violating QED model with higher-order derivative operators in the light of the results of Lee and Wick to preserve unitarity in indefinite metric theories. Specifically, we consider the fermionic sector of the Myers-Pospelov model, which includes dimension-five operators, coupled to standard photons. We canonically quantize the model, paying attention to its effective character, and show that its Hamiltonian is stable, emphasizing the exact stage at which the indefinite metric appears and decomposes into a positive-metric sector and a negative-metric sector. Finally, we verify the optical theorem at the one-loop level in the annihilation channel of the forward-scattering process $e^+(p_2, r) + e^-(p_1,s)$ by applying the Lee-Wick prescription in which the states associated with the negative metric are left out from the asymptotic Hilbert space, but nevertheless are considered in the loop integration via the propagator.