Two-loop renormalization of the CPT-even Lorentz-violating Scalar QED

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.