Renormalization and decoupling for the Yukawa model in curved spacetime

TL;DR

This paper investigates the renormalization of the Yukawa interaction in curved spacetime, demonstrating decoupling of heavy fields in the beta functions, with an unusual result regarding the scalar field mass parameter.

Contribution

It provides the first detailed calculation of beta functions for Yukawa interactions in curved spacetime using the DeWitt-Schwinger scheme, highlighting decoupling phenomena.

Findings

Heavy fields decouple in beta functions for scalar and Dirac fields.

Gravitational couplings also exhibit decoupling.

The scalar field mass parameter does not decouple.

Abstract

We consider the renormalization of the one-loop effective action for the Yukawa interaction. We compute the beta functions in the generalized DeWitt-Schwinger subtraction scheme. For the quantized scalar field we obtain that all the beta functions exhibit decoupling for heavy fields as stated by the Appelquist-Carazzone theorem including also the gravitational couplings. For the quantized Dirac field, decoupling appears for almost all of them. We obtain the atypical result that the mass parameter of the background scalar field does not decouple.