Renormalization, running couplings and decoupling for the Yukawa model in curved spacetime

TL;DR

This paper investigates how heavy fields decouple in the renormalization process of the Yukawa model in curved spacetime, revealing that scalar field mass does not decouple, unlike other parameters.

Contribution

It provides a detailed calculation of beta functions in curved spacetime, demonstrating decoupling behavior for various fields and highlighting the non-decoupling of the scalar mass.

Findings

Beta functions show decoupling for scalar and Dirac fields.

Gravitational beta functions also exhibit decoupling.

Scalar field mass does not decouple, contrary to expectations.

Abstract

The decoupling of heavy fields as required by the Appelquist-Carazzone theorem plays a fundamental role in the construction of any effective field theory. However, it is not a trivial task to implement a renormalization prescription that produces the expected decoupling of massive fields, and it is even more difficult in curved spacetime. Focused on this idea, we consider the renormalization of the one-loop effective action for the Yukawa interaction with a background scalar field in curved space. We compute the beta functions within a generalized DeWitt-Schwinger subtraction procedure and discuss the decoupling in the running of the coupling constants. For the case of a quantized scalar field, all the beta function exhibit decoupling, including also the gravitational ones. For a quantized Dirac field, decoupling appears almost for all the beta functions. We obtain the anomalous result that the mass of the background scalar field does not decouple.