Imaginary scaling invariance of the one-loop effective potential

Recently, a hitherto unknown class of renormalization group stable relations between parameters of bosonic field theories has been identified and dubbed as the r 0 or “GOOFy” symmetries. Here, one-loop properties of the r 0 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 nontrivially under r 0 . The minimal model requires the presence of two real fields.