of the SME principles and consider the issues related to a high-energy electron handled within this framework. The Lagrangian of the SME is obtained as the most general one describing the possible Lorentz non-invariant interactions and consistent with the fundamental principles of the modern quantum field theory (such as gauge invariance and power-counting renormalizability) [@sme_theory]. It is believed that these interactions are due to the spontaneous Lorentz symmetry breaking in the underlying theory, and this imposes the requirement that the corresponding Lagrangian terms are Lorentz scalars. Consequently, in the low-energy limit, there emerges the extended quantum electrodynamics from the lepton-gauge sector of the SME. Its Lagrangian can be written in the following general form: $$\label{theory_L}
    {\cal L}^\text{QED Extension} =
        {\cal L}^\text{QED}
        + {\cal L}_\text{lepton}
        + {\cal L}_\text{photon},$$ where $ {\cal L}^\text{QED} $ is the well-known QED Lagrangian: $${\cal L}^\text{QED} =
        - \frac{1}{4} F_{\mu \nu} F^{\mu \nu}
        + \frac{1}{2} \overline{\psi} i \gamma^{\mu} \overset{\leftrightarrow}{D_{\mu}} \psi
        - \overline{\psi} m \psi,$$ $ {\cal L}_\text{lepton} $, $ {\cal L}_\text{photon} $ are the terms describing the Lorentz non-invariant interactions in the electron and the photon sector of the theory respectively. They can be decomposed into the sum of the CPT-even and odd parts:

$$\label{theory_L_even_lepton}
    {\cal L}^{\rm 