The r0 symmetry is preserved at one-loop in the r0-invariant two-Higgs Doublet Model if the UV cutoff squared transforms non-trivially under r0; the minimal model requires two real fields.
Grzadkowski, talk ”Semisymmetries of Two-Higgs- doublet models” presented at the workshop ”New Physics Directions in the LHC era and beyond”, 23rd April, 2024, Heidelberg, Germany,
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Imaginary scaling invariance of the one-loop effective potential
The r0 symmetry is preserved at one-loop in the r0-invariant two-Higgs Doublet Model if the UV cutoff squared transforms non-trivially under r0; the minimal model requires two real fields.