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

Abstract

We study the Yukawa model with one scalar and one axial scalar fields, coupled to N copies of Dirac fermions, in curved spacetime background. The theory possesses a reach set of coupling constants, including the scalar terms with odd powers of scalar fields in the potential, and constants of non-minimal coupling of the scalar fields to gravity. Using the heat-kernel technique and dimensional regularization, we derive the one-loop divergences, describe the renormalization of the theory under consideration and calculate the full set of beta-and gammafunctions for all coupling constants and fields. As a next step, we construct the renormalized one-loop effective potential of the scalar fields up to the terms linear in scalar curvature. This calculation includes only the contributions from quantum scalar fields, and is performed using covariant cut-off regularization and local momentum representation. Some difficulties of the renormalization group approach to the effective potential in the case under consideration are discussed.

One-loop effective scalar-tensor gravity

“…This interaction also belongs to Horndeski gravity and was found before [24]. We also would like to highlight that this non-minimal interaction is generated by the interaction odd in scalar field which were found to be important for renormalizability of certain models [44,45]. Finally, the second term in (18) can be treated in full analogy with the previous case.…”

Renormalization group improvement of the effective potential: an EFT approach

“…The Coleman-Weinberg potential and RG improvement in curved spacetimes has been studied in refs. [13,14]. The methods in this paper also apply to curved spacetime calculations.…”

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

“…The result for all the beta functions are listed below in (31) and (32). Let us analyze the infrared and ultraviolet regimes of these runnings with more detail.…”

“…In this paper, we further extend this renormalization procedure to fermions and by including interactions, specifically, a Yukawa interaction between the quantized field and a classical and prescribed scalar field. This model has been recently studied by using dimensional regularization and minimal subtraction (MS) [30][31][32] (it has also been extended including gauge fields in [33,34]) 2 . However MS subtraction does not fulfill the Appelquist-Carazzone theorem since the beta functions do not decouple, even in flat spacetimes.…”