Renormalização em modelos de Yukawa sem e com campo escalar axial

Abstract

We explore the classical and quantum properties of a sterile scalar field coupled to N copies of Dirac fermions in an external gravitational field in two different models. We find that the self-interaction scalar potential of a model that is consistent at the quantum level, includes odd (first and third) powers of a scalar. In particular, one has to consider, besides the standard non-minimal coupling of the form ξϕ2R, the new type of non-minimal coupling of the form fϕR with new non-minimal parameter f. We study the one-loop renormalization of such a theory including renormalization of the new non-minimal coupling. Also, we calculate the one-loop effective potential for the sterile scalar model using the renormalization group method and show how the renormalization group analysis should be extended, compared to the standard expression which was derived in 1980-ies. This conclusion is supported by the direct calculation of effective potential using normal coordinates and covariant cut-off regularization. The important features of the classical theory with a sterile scalar are related to the presence of the qualitatively new terms in the induced action of gravity, coming from the odd terms. Keywords: Renormalization; Yukawa model; curved space.