  Investigating quantum effects arising from high loops in perturbation theory
is crucial for the physical applications of any quantum field theory. This
paper presents a comprehensive analysis of the two-loop renormalization of
CPT-even Lorentz-violating scalar electrodynamics at the first order in the
background vectors. We provide results for the self-energies of the photon and
scalar field, as well as for the three-point function associated with the
scalar-scalar-photon vertex, ensuring a thorough examination of the quantum
effects. The calculations satisfy the ward identities, demonstrating their
consistency. Computational tools were employed to carry out the calculations,
and we provide additional details in the Supplemental Material for interested
readers. Our contribution presents, for the first time, a two-loop calculation
within the framework of the Lorentz-violating Standard Model Extension.

High Energy Physics - Theory