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

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.

arXiv comment16 pages, 3 figures. New version with modifications in the canonical quantization and accepted in PRD

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