  In this study, we systematically calculate one-loop corrections to the
Lorentz-violating vertices within the framework of CPT-odd Quantum
Electrodynamics, encompassing scalar and photon fields in arbitrary gauge.
Additionally, we ascertain the finite two-loop corrections to the
Carroll-Field-Jackiw term. Furthermore, we analyze the UV divergent component
of the two-loop Lorentz-violating correction in the self-energy of the scalar
field.
