Imaginary scaling invariance of the one-loop effective potential

TL;DR

This paper explores the one-loop properties of models with r0 or 'GOOFy' symmetries, revealing conditions under which these symmetries are preserved and their implications for two-Higgs doublet models.

Contribution

It introduces and analyzes the one-loop behavior of the r0 symmetry in specific bosonic field theories, expanding understanding of renormalization group stable relations.

Findings

r0 symmetry is present at one-loop if the UV cutoff squared transforms non-trivially

The minimal model requires two real fields for symmetry preservation

Identifies conditions for symmetry stability at the quantum level

Abstract

Recently, a hitherto unknown class of renormalization group stable relations between parameters of bosonic field theories have been identified and dubbed as the r0 or 'GOOFy' symmetries. Here, one-loop properties of the r0 invariant two-Higgs Doublet Model and a minimal symmetric model are discussed. It is concluded that the symmetry is present at the one-loop provided the UV cutoff squared transforms non-trivially under r0. The minimal model requires the presence of two real fields.