Renormalization of Yukawa model with sterile scalar in curved spacetime

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. 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 ξϕ 2 R, the new type of non-minimal coupling of the form f ϕ R 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 using the renormalization group and show how the renormalization group analysis should be extended compared to the standard expression which was derived in 1980ies. This conclusion is supported by the direct calculation of effective potential using normal coordinates and covariant cutoff 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. We show that this new feature of the theory may have phenomenologically relevant consequences, both in the low-energy gravitational physics and at the high energies, corresponding to inflation.

Quantum aspects of Yukawa model with scalar and axial scalar fields in curved spacetime

“…In this respect one can mention recent analysis that includes both scalar and a pseudoscalar couplings [1] and more recently with the inclusion of a gauge field [2,3]. In the present work we continue the previous treatment of Yukawa model with sterile scalar discussed in [4] and extend it to the case of the two (ordinary and axial) scalars with a Yukawa coupling to fermions and general renormalizable form of self-interaction. Our immediate purpose will be the calculation of divergences in the most economic way, as it was done in the original publication on the renormalization of the Abelian model with Yukawa coupling in curved spacetime with torsion from long ago [5] (see also the book [6]) .…”

“…[6] for detailed introduction and further references. The generalization to the model with a single sterile scalar proceeds is done in a close analogy to the standard approach, but with some modification due to the presence of the odd interaction terms [4].…”

“…The symbolic expressions ln with k = 1, 2, ..., 6, in the formula (28) depend on the theory under consideration. For instance, in the model with a single sterile scalar [4], these quantities appear as linear combinations of the logarithms…”

“…The form of the self-interaction potential of a scalar field ensuring the renormalizability of such a theory is an interesting aspect, that was not explored completely in the original work [5]. It was shown and discussed in details in the recent work [4] that the renormalizable scalar with Yukawa interaction includes self-interactions with odd powers of the scalar fields. These qualitatively new interactions include linear term, the term with a cubic coupling, and also a linear term describing the interaction between scalar field and scalar curvature.…”

“…In all examples of renormalizable quantum field theories with scalar fields, which were known until now, it was possible to construct solutions to the renormalization group equation for the effective action which enable to derive the effective potential in the most economic way [7], including in curved spacetime [8] (see also the generalization to other sectors of effective action in [9,6]). In the model with a single sterile scalar one has to extend this nicely working scheme to include odd powers of the scalar field, with this generalization it still works pretty well [4].…”