Lessons from Tμμ on inflation models: Two-loop renormalization of η in the scalar QED

Abstract

© 2021 authors. Published by the American Physical Society.A nonminimal coupling η has been attracting growing interest particularly in the context of inflation models, though its quantum nature is not clear yet. We study the renormalization of η in the scalar quantum electrodynamics (QED). There are one-loop diagrams, which could give the finite correction to η in the scalar QED. We find that they cancel with each other. We also find no inhomogeneous term of the renormalization group equation (RGE) at the two-loop level, while there could be the two-loop order finite correction. This is similar to other theories, where an inhomogeneous term of the RGE appears only at a higher-loop order: e.g., four-loop order in λφ4 theory.